40 Years and Still Growing | Lifetime Assistance Inc.
Four decades ago, Donna and Donald Lowry and a small group of devoted parents banded together with tremendous courage and a vision to challenge the status quo. At that time, each found their children with developmental disabilities without specialized care options as they themselves approached adulthood.
These seven parents risked much to invent, create, design and build a full spectrum of services that were almost non-existent at the time, but necessary to support the needs of their children and others with developmental disabilities throughout their adult lives.
With the establishment in 1978 of a day treatment program serving 32 people in Brockport, Lifetime Assistance, Inc. was born. In 1979, 21 Holley Street in Brockport became Lifetime's first community residence as well as the first community residence for adults in western Monroe County. Two years later LAICO Industries was founded, offering employment services to 70 people.
Lifetime Assistance has reached many milestones; each one has created a monumental step towards the extraordinary agency it has become 40 years later.
Today, Lifetime Assistance serves over 1,800 people at over 70 residential, day service and community sites throughout western New York. With 1,500 staff members and hundreds of volunteers, some of whom are the original trailblazers of this pioneering enterprise, Lifetime continues to assure that each person supported is given every opportunity to succeed and reach their greatest potential.


Whether your team are all in one place, in multiple offices and locations, remote workers or on the road – being able to rely upon the most efficient communications and IT systems and maintenance for your business is not only good business sense, it can give you a major advantage over your competitors, and that's essential.
Here at Green City Solutions we are committed to the continual improvement of our environmental performance, click here to find out more.
GreenCity Solutions ensure you keep in touch in the most effective ways possible with the people who are most important to your business – your clients and customers, your colleagues and your suppliers.
GreenCity Solutions always providing great tariffs for mobiles services with up to date handsets at all times. Also ensuring that our costs are kept as low as possible and providing great customer service at all times with a smile.
From fixed line telephones and mobiles to webinars, video conferencing and e-commerce portals, an IT infrastructure to suit your business now and in the future to protection of your business data with a full backup solution – having a highly efficient, uninterrupted, flexible, secure and fast service means you can maximise your productivity, reduce your downtime and increase your sales and productivity – and that means higher profits.
GreenCity Solutions provide communication systems to businesses across the UK supported by our team of expert and experienced Technicians and Engineers.


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Aga Muhlach, Enrique Gil, Cristine Reyes, Dingdong Dantes to topbill an upcoming Star Cinema movie
by Lion's Den June 27, 2017, 4:55 pm
Star Cinema has just announced its new movie offering soon.
The film, titled "Seven Sundays", will be top-billed by biggestt stars in showbiz industry.
Based on Star Cinema's Instagram post, the main cast for this film are Aga Muhlach, Enrique Gil, Cristine Reyes, Ronaldo Valdez and Dingdong Dantes.
It will be directed by former "La Luna Sangre" director Cathy Garcia-Molina.
Star Cinema has a new treat for their avid viewers soon!
The movie outlet has just announced an upcoming film to be top-billed by "Pinoy Boy Band Supertar" judge Aga Muhlach, "My Ex and Whys" actor Enrique Gil, "I Can Do That" first runner-up Cristine Reyes, KFC's newest ambassador Ronaldo Valdez, and Kapuso actor Dingdong Dantes.
On their Instagram account, the film production posted series of photos from the cast's story conference held at the ELJ Building on June 27.
According to Star Cinema, the title of the flick is "Seven Sundays" and it will be directed by the award-winning director Cathy Garcia-Molina.
The film will mark Aga's return on the big screen after a 5-year hiatus. If the film will be released this year, then it will be Enrique's second biggest project after "My Ex and Whys" with his onscreen partner Liza Soberano.
On the other hand, "Seven Sundays" will also be Cristine's first film under Star Cinema after four years. Her last film under the movie outlet was the highest-grossing film of 2013, "Girl, Boy, Bakla, Tomboy", starring Vice Ganda and Maricel Soriano.
Meanwhile, the film will be Dingdong's sixth non-consecutive film under Star Cinema. His movies, under the production company, when combined, will gross more than P867 million.
Are you excited to see this big stars on the big screen?
Written by Lion's Den
LionhearTV has always believed in what the everyday reader can contribute, and has always been open to receiving input, help, or leads on stories. Readers are always encouraged to drop us their thoughts either by either by leaving a comment on a post, or contact us directly – email us at [email protected]
Aga MuhlachCathy Garcia-MolinaCristine ReyesDingdong DantesEnrique GilGirl Boy Bakla TomboyLa Luna SangreLiza SoberanoMaricel SorianoMy Ex and Why'sRonaldo ValdezSeven SundaysStar CinemaStar Cinema Seven SundaysStar Cinema's Seven SundaysVice Ganda
Manunuri ng Pelikulang Pilipino reveals the nominees for the 40th Gawad Urian
Lea Salonga was Aga Muhlach's "the one that got away," according to actor's 4-year-old love letter

redpajama_set_name: RedPajamaCommonCrawl


Francis Parker School seeks a qualified Associate Director for Lower School Admissions. Working under the direction of the Director of Enrollment, the Associate Director for Lower School Admissions acts as the primary resource for outreach and admissions for prospective students and families in the Lower School. This is an 11 month position that will start August 1, 2019.


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The 2002 Chrono des Herbiers was the 21st edition of the Chrono des Nations cycle race and was held on 22 October 2002. The race started and finished in Les Herbiers. The race was won by Michael Rich.

General classification

References

2002
2002 in road cycling
2002 in French sport
October 2002 sports events in France

redpajama_set_name: RedPajamaWikipedia


physical health. They promote a sedentary lifestyle, and many believe that the sensory overload that comes from playing many types of games actually contributes to learning disabilities such as attention deficit hyperactivity disorder, or ADHD. However, apparently it does take a psychology degree to see past those hypotheses. Some studies have shown that playing video games may actually be beneficial to children with ADHD, rather than harmful to them.
It's not too difficult to understand how playing video games can help treat ADHD. While some believe that the addictive quality and sensory overload that video games provide could make ADHD symptoms worse, many video games require players to concentrate and focus on tasks for long periods of time in order to achieve goals. As a child plays through a video game, he or she learns to develop strategies, recognize patterns, and focus intently on the task at hand. In other words, players can learn the same skills that ADHD patients often struggle with by playing video games. One example of a game that may prove helpful in treating ADHD is the classic puzzle game Tetris. Tetris is a simple game in which players organize blocks of different shapes as they fall to the bottom of the screen. The object is to organize the blocks into solid lines to get them to disappear. When the pile of blocks reaches the top of the screen, the game ends. The game speeds up at regular intervals, requiring faster and faster reaction times. It also doesn't end until the player loses, so the only goal is to achieve the highest possible score. It's a simple game, but the ever-increasing challenge and simple goal of getting a high score can challenge ADHD-affected players and raise their attention span.
Modern video games such as those available for the X-Box 360 or Playstation 3 can help some players overcome ADHD symptoms as well. Many of these games have achievements and hidden items to find, and they can keep gamers busy for months. They may not be as effective in helping children with ADHD as games such as Tetris simply because they are not forced to work towards these goals, but the fact that they require children to concentrate and pay close attention means that it can be at least somewhat beneficial to children who have difficulty doing so.
The idea that video games can be effective in treating ADHD is centered around a relatively new treatment called neurofeedback. In neurofeedback, a patient is asked to focus on a monitor or television screen while electrodes are placed on his or her scalp. As the patient focuses on the images on the screen, special software monitors the electrical activity in their brain. This software is able to tell how focused the patient is on the images that he or she sees. In a typical neurofeedback session, the patient is rewarded with pleasant imagery, such as blooming flowers in a field. If his or her attention begins to wane, the flowers might wilt or the lush green field may turn grey. It's a way to tell patients to work harder to pay attention and provide a reward when they do. There is evidence that suggests that neurofeedback is helpful in treating ADHD, although it is still a controversial method of treatment. Neurofeedback treatment currently requires at least 40 sessions and can cost thousands of dollars. It is also scientifically unproven, so much of the evidence that suggests that it works is anecdotal.
The idea of video games being used as treatment for ADHD has been around for a while now. Children who are heavily affected with ADHD will still lose interest in a game after a while, but a game combined with neurofeedback could help children do the exact opposite. Neurofeedback software can be used with a video game system such as a Playstation or X-Box to keep an ADHD-affected child focusing on the task at hand. For example, a neurofeedback system could involve a typical racing game. As long as the player remains engaged and focused on the game itself, the car controls as normal. As the child begins to lose focus, the car slows down until it no longer moves. The child has to remain engaged in the game to keep playing. While many people can point out the drawbacks of playing too many video games, there can be little doubt that they can be effective in helping to treat children with ADHD. The treatments that attempt to follow this theory are new, but there haven't been many generations who have grown up playing video games. Perhaps if old prejudices about video games can be put aside we could have a novel way to treat ADHD and similar learning disabilities.
In the beginning of this article she says there are studies that show video games can actually help children with ADHD. Really?! What studies? As a teacher, I am constantly trying to keep my ADHD kids, who had their meds adjusted or didn't get them that day, pay attention to their schoolwork. Then when I call parents, they say things like, " he can pay attention just fine. He can play video games for hours with no problem. He is just acting up," or "don't let him use his medication as an excuse, he knows how to behave." Video games offer instant and continuous gratification, changing environments, sound effects, and exciting fantasy worlds. I have a classroom, books, and a whiteboard. So please don't dupe the public with your made up studies of how "playing video games can actually help ADHD students pay attention."
Not everything works for everyone. Personally I think that video games are a wonderful idea for treating mental disorders like ADHD.
Parents unwittingly make the mistake of letting their kids play video games and it makes it worse. I've seen first hand as a mom to 2 children. My son is very sensitive has an LD and my daughter is very even keeled and socially aware. Behaviour and attitude in BOTH my kids improved drastically when electronics where taken away.
There have been some controlled small studies done.
I don't find your article as trying to dupe the public at all. I can see how kids get diagnosed. Boring teachers, boring material, that is not their fault, it's how some kids are wired. Education needs to be kicked up a notch for these kids who can't sit for hours passively. They need active stimulation.
This is just one of many articles I have seen about using video games to help treat ADHD and I'm all for it! If I don't have to drug my child and can get the same results by letting him play a few video games that's awesome! Continue the research!!
That's a joke. All video games do is turn kids into little addicts.
I completely disagree with this hypothesis. My son had screen time - 1 hour per night during the week and 2 hours per day on weekends (as rewards for finishing homework, etc.). He was 7 and I only let him play educational games.
He became increasingly defiant, socially inept, aggressive, angry, unable to focus, sleeping horribly, etc. I began to get calls from his school teacher.
We took away ALL electronics at home including morning TV and within a week, my seemingly oppositional defiant disordered child became, calm happy and cooperative.
My son, who was once not interested in making friends or cooperating at school has since joined the chess club, Lego club and is getting along with the other kids much better.
There are numerous studies confirmed by psychologists that have no affiliation with gaming companies that concur of the damage screen time does to kids with pre-existing conditions like ADHD.
I have ADHD myself, It's sometimes hard to control it.
ADHD Female Leaders: Patricia Quinn, M.D.


"FDA Bashes Green Tea – Is It Correct?"
A large Japanese tea company recently asked our FDA to allow them to say that green tea lowers your risk of heart disease. The FDA refused. The FDA said there's no credible scientific evidence to support such a claim. In the past, the FDA concluded that green tea doesn't reduce the risk for any cancer, either. Is this true?
* A Japanese study published in the British Medical Journal found green tea lowers cholesterol and triglycerides and increases good (HDL) cholesterol in over 1,300 men. The more tea they drank, the greater the protection.
* Researchers conducted a seven-year study on women who had either stage-1 or stage-2 breast cancer. They found that women who drank green tea before diagnosis had a lower rate of recurrence.
* A Chinese study of over 1,400 participants concluded that people who drank green tea had a lower risk of stomach cancer no matter how old they were when they began drinking it. The researchers suggest that green tea may interrupt carcinogenesis in the stomach.
No credible scientific evidence? Come on! People throughout Japan know green tea as a cancer preventive because of its extensive scientific research. And this much is clear: Green tea is high in antioxidants, and we know that increasing antioxidants in our diet is protective against both heart disease and various cancers.
I've written about the beneficial effects of green tea over the past six years in Women's Health Letter. As you may know, I base the information in my articles on science, not theory. I've talked about green tea's ability to help reduce weight, control inflammation, and even help you sleep better. I've written about its role in cancer prevention and treatment, and its ability to reduce anxiety.
I stand by these comments with a cup of green tea in my hand. No matter what the FDA says, it's clear that green tea is not only a healthier beverage than soft drinks and coffee. It has a role in disease prevention and treatment.
Imai, K. and K. Nakachi. "Cross sectional study of effects of drinking green tea on cardiovascular an liver diseases," British Medical Journal, March 18, 1995.
Nakachi, K., et al. "Influence of drinking green tea on breast cancer malignancy among Japanese patients," Cancer Science, March 1998.
Guo-pei, Yu, et al. "Green tea consumption and risk of stomach cancer: A population-based case-control study in Shanghai, China," Cancer Causes and Control, November 1995.
Serafini, M., et al. "In vivo antioxidant effect of green and black tea in man," Eur J Clin Nutr, January 1996.


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Chiara Tommencioni Pisapia uses moths to transform unwanted clothing into "precious" bio-waste material
Alyn Griffiths | 30 October 2019 Leave a comment
Central Saint Martins graduate Chiara Tommencioni Pisapia has proposed a method for improving the textile recycling process by using moths to break down the natural fibres in discarded clothing.
Pisapia, who says she is "interested in sustainability related to fashion, textile recycling, bio-design and the circular economy", wanted to find a more efficient way to deal with mixed-fibre textiles, which are currently complicated to recycle.
These textiles, containing a combination of manmade and natural fibres such as wool and polyester, typically end up in landfill or incinerators as it is difficult to separate the fibres for recycling.
"Textile recycling is currently done mainly using chemicals or mechanical methods," the designer told Dezeen.
"As we are in a time where biology and design are interweaving, I thought it would be interesting to explore how nature is recycling and breaking down fibres and this brought me to look at clothes moths," she added.
Pisapia initially proposed using common clothes moths to remove animal fibres from clothes, leaving behind the synthetic fibres so these can be recycled separately.
The moths feed exclusively on natural materials such as wool, fur, silk, felt and leather, as these contain a fibrous protein called keratin that their larvae can digest.
"I just thought that if clothes moths eat the beloved woollen clothes in our closet, why shouldn't they eat those we don't use anymore that have keratin inside," the designer added.
Pisapia developed the Made by Moths project during her final-year studies on the MA Material Futures course at Central Saint Martins art school in London.
The London-based Italian designer worked with experts from the Center for Novel Agricultural Products (CNAP) at the University of York to explore the potential for farming the moths' larvae and using them to digest the keratin-based fibres.
The dust-like waste produced by the larvae is entirely natural and will biodegrade over time. It can therefore be composted and will give something back to the environment rather than polluting it.
Pisapia said she views the bio-waste as "a precious material" due to the number of larvae and the time required to produce even a tiny amount of material. For this reason, she chose to celebrate its properties by transforming it into jewellery.
"I liked the idea that a brooch is something that goes on garments where the material comes from," she pointed out, "and also because a brooch can be used to hide or to highlight a hole that moths might have made in a garment."
The length of time it takes for the larvae to break down even small quantities of fibres prompted the team to explore alternatives, including the potential for extracting the digestive enzymes of the larvae and reproducing them as a bacteria that could perform the same task.
The result of this process would likely be an amino acid that could have alternative applications to the bio-waste produced by the larvae.
According to the designer, the process would take place initially in a laboratory, with the potential to upscale it to an industrial level.
"To manage this successfully would require a strong collaboration between designers, biologists, chemists and investors," she claimed.
Pisapia is continuing to speak with her collaborators at CNAP about the potential to develop the project and hopes to obtain funding to expand her research into the use of the moths' enzymes to improve the textile recycling process.
Vollebak's plant and algae T-shirt becomes "worm food" in 12 weeks
Tech-based clothing startup Vollebak also developed fashion that becomes insect food. The company used wood pulp and algae to make a t-shirt that breaks down in soil or in a composter within three months.
More sustainable fashion


Three stone engagement rings are a piece of jewellery that everyone is familiar with but the symbolism still rings through today. The past, present and the future. Is there a better way to encompass a love story than with a piece which represents a relationship entirely?
This vintage three stone ring is a prime piece to advocate any love story. Set in 18kt gold it houses three Old European Cut diamonds which give off such fire it will instantly spark anyone?s attention. The 1ct centre stone is balanced either side, giving the wearer balance and proportion across the hand. Once adorned, one simply cannot help but to watch it sparkle and move in the light.
Here at Courtville we recognise the individuality and the beauty in vintage and antique pieces and celebrate them fully. We strive on having an eclectic collection to show our clients. If you wish to try any of our pieces on we are located in Powerscourt Townhouse Dublin, or our pieces are available to purchase online through our website.


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3.9 We may process information relating to transactions, including purchases of goods and services, that you enter into with us and/or through our website and online stores ("transaction data"). The transaction data may include your contact details, your card details and the transaction details. The transaction data may be processed for the purpose of supplying the purchased goods and services and keeping proper records of those transactions. The legal basis for this processing is the performance of a contract between you and us and/or taking steps, at your request, to enter into such a contract and our legitimate interests, namely the proper administration of our website, store fronts and business.
4.2 We may disclose name, address, email address and/or telephone number to our suppliers or subcontractors insofar as reasonably necessary for completing our contractual agreement with you.
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Personal date will be retained for a minimum period of 1 year, and for a maximum period of 7 years following consent and/or contractual start date.
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A former English teacher and newspaper and magazine journalist, most recently for 22 years at People, Ron Arias has published the following books: The Road To Tamazunchale, a novel nominated for a National Book Award; Five Against the Sea, a true survival saga; Healing from the Heart, with Dr. Mehmet Oz; Moving Target: A Memoir of Pursuit, and White's Rules:Saving Our Youth, One Kid At A Time, with Paul D. White. An amateur potter, he lives with his wife Joan in Hermosa Beach, CA, while their filmmaker son Michael resides in Japan, which increasingly has become a second home for them.
My Life as a Pencil
"Pencils to the left, shooters to the right."
In this collections of short essays Ron Arias relates the ups and downs, ins and outs, and memorable people he met in his years as a magazine journalist. While traveling with a notebook and pen, a photographer, and not much else, Arias managed to capture the people as well as the places with honesty and understanding. Following the advice of his mentor Toby, Arias tells it personal, and makes it real.
The first review of My Life as a Pencil
Posted by John Coyne on Saturday, March 14, 2015
By Ron Arias (Peru 1963-64)
Red Bird Chapbooks, $12
I once asked Ron Arias (Peru 1963-64) what he did at People Magazine and he said, and I quote, "I cover the Third World." I laughed, thinking he was being sarcastic, and he was, but Ron was also being serious. Thanks to his fluency in Spanish, his experience in the Peace Corps, his traveling and working in Latin America, plus his ability, his need perhaps, to go everywhere and do anything to get a story, made him a minor celebrity in the complex and competitive conglomerate of Time/Life.
A few of Ron's brushes with danger around the world are implied and hinted at in this collection of funny, insightful, touching and true stories entitled My Life as a Pencil, a chapbook recently published by Red Bird Chapbooks.
The book title comes from orders given by a Marine officer in Saudi Arabia in 1991 to Ron and a group of other journalists and photographers when he shouted out, "Pencils to the left, shooters to the right."
Click on the link to read the complete review. http://peacecorpsworldwide.org/pc-writers/2015/03/14/review-of-ron-arias/
Southbay Magazine feature written by Kelly Dawson, Summer 2015
Hermosa Beach's Ron Arias turns to ceramics after a career in storytelling.
Non Fiction, Essays and Memoir
8.5" x 5.5" single signature with hand sewn binding
Read more about My Life as a Pencil


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October 11th in the FDNY
In the Line of Duty FF Patrick J Quail, Ladder 18. October 11th, 1902 While running to an alarm for a window curtain fire, Ladder 18 ran upon the curb along Attorney Street turning onto Delancey. FF Patrick Quail, the tillerman, was thrown from his seat. He died at Bellevue Hospital 8 hours later from…
In the Line of Duty FF Carl Herer, Ladder 19. October 10th, 1967 FF Herer died at home from a heart attack. He was injured June 9th 1967 at box 2767. He was appointed June 1st, 1938. FF Dennis J Heedles, Engine 151. October 10th, 2015. FF Heedles succumbed to 9/11 related illness.
October 8th in FDNY history
In the Line of Duty FF Thomas Casey, Ladder 52. October 8th, 1958 FF Casey was injured & died almost instantly during drill. He was tillering the ladder truck back & forth at the drill site. First aid was given immediately & he was pronounced by a department doctor. FF Peter F McLaughlin, Rescue 4.…
February 10th in the FDNY
Lt John R Eastburn, Engine 54. February 10th, 1970 Retired FF Kevin T Murphy, Engine 166. February 10th, 2015 9/11 illness
February 9th in the FDNY
Assistant Engineer George A Erlacher, Battalion 2. February 9th, 1873. Injured January 17th, 1873, died February 9th, 1873 Box 38- 183 Water Street, Manhattan Asst Engineer Erlacher was thrown from a hose tender while responding. At Peck Slip & Water St, the tender of Engine 12 was upset when it ran over a pile of…
February 7-8th in the FDNY
Retired EMS Lt Paige Humphries, Station 16. February 7th, 2021 EMS Lt Humphries died from 9/11 illness. FF David Muldrew & FF David Clute & Asst Foreman John H Bush Engine 30. February 8th, 1876 Box 0167 – 442-452 Broadway Manhattan. While operating a handline, the 3 firemen were buried beneath a collapse of the…
FF James P Smith, Engine 17. February 4th, 1885 Box 64, 58 Park Place Manhattan. FF Smith was operating on a ladder helping with a charged hose line. The nozzle was operating into a 5th floor window when it slipped from the grasp of the men above him. Fireman Smith, being in the center of…
February 3rd in the FDNY
FF John Slowey, Lafayette Engine & FF George W Badger, Americus Engine 6. February 3rd, 1863 209 Cherry Street, Manhattan The 3rd floor of the Goodwin Bakery caught fire around 8pm. Within a very short time, the 3rd floor had spread throughout the 5 story bldg. The building & it's contents were a total loss…
February 2nd in the FDNY
FF James W Kojac, Ladder 128. February 2nd, 1956 FF Kojac suffered a heart attack while operating at a 2 story row of taxpayers. The fire started in the delicatessen & spread to a meat market, real estate agency & children's clothing shop. FF Kojac was taken to St Johns Hospital where he died several…
January 31st in the FDNY
FF Arthur J Renk & FF Christopher Dressel, Engine 138(238). January 31st, 1904 FF Peter J Gaffeney Injured January 31st, died February 1st, 1904 Box 493 2-50 Noble Street Brooklyn. 3 members of Engine 138 ( Now 238) were killed at a fire in the American Manufacturing Company plant at the foot of Noble Street.…
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Mariah Carey was born in Long Island on March 27, 1970. Carey is a renowned singer, songwriter, actress, record producer and philanthropist. Carey began her singing career at the age of three, after imitating her mother who practiced Italian Opera. Carey is among the world's best singers and biggest divas. She was also the best-selling performer of the nineties. She owes her stardom to her astonishing five-octave voice. In a career spanning two decades, she sold over 200 million records, all over the world, which made her one of the top-selling music artist of all time. In fact, at the World Music Awards in 2000, she was named the best-selling pop artist (female) of the Millennium. Since 1990, she has won around 245 awards. She married Tommy Mottola in 1993 and they separated in 1998. On April 30, 2008, she married Nick Cannon. They have two children named Monroe Cannon and Moroccan Scott Cannon. Mariah Carey loves wearing perfumes and has her own collection of perfumes.
M by Mariah Carey


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Newcastle nuclear submarine base shortlisting dismissed as 'pork-barrelling'
ABC Newcastle
/ By Liz Farquhar and Madeline Lewis
Posted Tue 8 Mar 2022 at 2:31am Tuesday 8 Mar 2022 at 2:31am Tue 8 Mar 2022 at 2:31am
The Port of Newcastle has made a shortlist of three cities being considered for a new submarine base. (ABC News: John Gunn)
abc.net.au/news/newcastle-submarine-base-shortlist/100890846
Is being shortlisted for a new nuclear-powered submarine base pork-barrelling or an amazing jobs and investment opportunity? Well, it depends on who you ask.
Newcastle is one of three locations shortlisted for a new east coast submarine base
Senator Rex Patrick says all three scored poorly in a recent Defence study recommending Sydney and Jervis Bay
Lord Mayor Nuatali Nelmes says the city is determined to remain nuclear-free
The announcement that Newcastle is among three cities shortlisted has sparked some mixed reactions.
Independent Senator Rex Patrick has dismissed the shortlisting of Newcastle, Port Kembla, and Brisbane for the submarines' base as pure pork-barrelling in the lead up to the federal election.
Independent Senator Rex Patrick says Newcastle scored poorly in a defence review of potential submarine bases. (AAP: Lukas Coch)
Speaking on RN Breakfast, Senator Patrick said in 2018 he obtained a defence study under Freedom of Information which revealed all three cities had scored very poorly in relation to accommodating a submarine base.
"When [the Prime Minister] made that announcement yesterday he said it was off the back of a study that had 19 different options and they were down to three options," Senator Patrick said.
"The three options that he picked scored very low in the analysis.
"The best city for a future sub base was Sydney, followed by Jervis Bay."
Senator Patrick said the Port of Newcastle in particular had several problems including a difficult entry and hectic shipping schedule.
"I think it's been picked for pork-barrelling reasons. It's a pre-election announcement that offers the prospect of jobs and economic activity," he said.
"But obviously that's a nice carrot for anyone considering voting for the Coalition, and the Prime Minister knows that."
The proposal is to procure nuclear-powered submarines in partnership with the US and the UK. (AP: US Navy, file photo)
Australia's nuclear subs deal explained
Are you wondering why there's so much fuss about Australia's decision to acquire nuclear submarines? We've broken it down for you.
Senator Patrick said the two other cities shortlisted, Port Kembla and Brisbane, were also listed as unsuitable in the defence report.
"You've got to wonder why the government departed from the strong recommendations that came from the Department of Defence," he said.
"It's riddled with politics and we know that when politics gets in the way, defence capability generally suffers."
The Hunter Defence Taskforce has thrown its support behind Newcastle being chosen for the new base.
Tim Owen believes the city is an ideal spot for the new submarine base. (ABC News: Dan Cox)
Taskforce spokesman Tim Owen believes the Port of Newcastle is an ideal location, citing the region's connections to an international airport, inland rail, and a strong defence industries workforce.
Mr Owen said a new base would include maintenance and repair operations, space for the naval fleet, and accommodation for sailors.
"We've heard that we don't necessarily have to have a substantial nuclear industry to support it because we're looking at a self-sustaining capability within the submarine," he said.
Nuclear opposition from Lord Mayor
Newcastle Lord Mayor Nuatali Nelmes said the city had been nuclear-free since 1982 and hoped Newcastle was not high on the list of options.
"I really think it's galling to consider the AUKUS arrangement and the purchase of these nuclear submarines has somehow meant that we've shifted our international defence strategy from not being nuclear to nuclear," she said.
Lord Mayor Nuatali Nelmes says her city is proudly nuclear-free and would not welcome a base for nuclear powered submarines. (Supplied: Nuatali Nelmes)
"There are so many issues with the way Scott Morrison and this coalition government are behaving, but just to assume that somehow the city of Newcastle is going to be a target if ever there is a war.
"I know the people of Newcastle and I know how they would feel if they were over-ridden, particularly when it comes to nuclear disarmament and weaponising our port.
"They [the government] wouldn't just have an issue with the City of Newcastle, they'll have an issue with the people of Newcastle."
Newcastle newsletter: Local news in your inbox
ABC Newcastle will deliver a wrap of the week's news, stories and photos every Wednesday. Sign up here.
Posted 8 Mar 2022 8 Mar 2022 Tue 8 Mar 2022 at 2:31am
Is this key industrial hub the 'obvious choice' for a nuclear submarine base?
Prime Minister denies nuclear submarine announcement timed for election
There are still 10 Australians in France working on the government's scrapped submarine project
'Remember what you did to Macron?': Turnbull says submarine deal has torpedoed trust for years
Defence Industry
Port Kembla


A powerful group of financial services veterans including banker Mark Johnson and Shadforth Financial Group founder Kevin Bailey have invested $5 million into a digital advice platform set up by former Vanguard Australia chair Jeremy Duffield.
SuperEd was founded in 2012 by Mr Duffield and former Westpac executive and technology entrepreneur Hugh Morrow, with a mission to help the 80 per cent of Australians who go into retirement without help access cheaper financial advice online.
The Sydney-based venture raised over $2.5 million last year from its team and angel investors, and completed the latest $5 million capital raising at the end of 2017, with staff and existing investors making up 10 per cent of the raise.
Mr Morrow told The Australian Financial Review, the fintech venture had canvassed a wide range of investors and got support from $8.6 billion annuities specialist Challenger Limited and Campbell McComb-founded High Line Alternative Investments, which is in the midst of being purchased by ASX-listed Yonder and Beyond Group.
High profile investors such as Mr Bailey and Mr Johnson, who co-founded Macquarie Bank and was the author of the government's report on making Australia a regional financial hub, were joined in the raise by chairman of UniSuper and former head of Colonial First State Chris Cuffe and Paul Rogan, the founder of Retirement Essentials, an online advice platform for those already in retirement.
Former long-serving Challenger executive Mr Rogan said the rising cost of healthcare, electricity and council rates meant many retirees were still finding it difficult to achieve a comfortable standard of living in retirement.


text:
INTERVIEW: Coley looks ahead to Lincoln cup tie
Reds boss will reshuffle his pack for knockout tie
John Coleman shifts his focus from the League One promotion race to the Papa John's Trophy as Stanley travel to Lincoln tomorrow night in the last 16 of the now knock-out competition.
The Imps, managed by Michael Appleton, currently top the League One table and the two sides played out a goalless draw at the Wham Stadium in their league encounter in November.
The Reds had a good win at Charlton live on Sky on Friday night which moved them into the Play-Off positions, with games in hand on those above them, but Coleman says they are keeping their feet on the ground as he looks back to the Addicks clash and forwards to tomorrow night.
"You don't get carried away with things like that, it's only one win, you only get three points for it and it doesn't matter who you play.
"It was pleasing it was on the television, maybe teams will take a little bit more notice of us now, but we have just got to try and focus on winning as many games as we can.
"That's always been our remit every season and nothing has changed. It's a good win but the moment you step back and start smelling yourself and think you have arrived, you will very quickly plummet down to earth and we will guard against that.
"We have got players in there who will guard against it themselves and keep everyone else in check and they are a great set of lads, they will work hard and try and get as many points as they can.
"Lincoln is a big game, I have made no secret of the fact I want to get to Wembley, I want to get rid of that jinx of us being one of only two clubs in the EFL who haven't been to Wembley so we would like to get that off our backs.
"It will be a tough game and we have got to gear ourselves up for a lot of tough games in a short space of time."
Coleman says he will re-shuffle his pack for the 7pm kick off with Michael Nottingham and Jon Russell cup-tied and Cameron Burgess suspended.
"I have got to give others a chance due to players being cup-tied, injuries and suspensions, I have got no choice but to change my starting XI but we focus a lot on shape in training and patterns of play and players know what is expected of them and whoever goes in to do their jobs will be aware of what their roles are."
If it's all-square after 90 minutes at LNER Stadium then it will go straight to penalties.
"I always like cup games, this competition has been maligned but not for me. I like the cup, it's a realistic chance to get to Wembley we can earn a few bob along the way which is always good for a club of our stature.
"Football is always exciting for me but it's a pale imitation without the fans but we can only do what we can do and give it our best shot and we will do."
The full pre-match interview video with John Coleman is available to watch on the club's official YouTube channel, CLICK HERE to find out more!
Lincoln City vs Accrington Stanley on 12 Jan 21


Splitting up is a course of action this is certainly never imagined of in the beginning of a married relationship nonetheless data demonstrate one half of all marital relationships result in divorce, things could possibly get really ugly rapidly when each of you actually feel you are entitled to a lot more than your once companion would most likely like to surrender. It's normal to find partners fight vigorously for each and every resource, as reactions get very hot.
The answer to this is often deciding on a prenuptial contract just before engaged to be married. The agreement has to be agreed upon by both sides before the official day of the wedding. The contract will deal with the financial concerns for the husband and wife involved in a contract is going to address financial circumstances, debts, real estate involved. The prenuptial agreement will consider how all properties and assets is going to be managed if a divorce develops. One of the more common solutions to this is often to enable each partner to keep their own properties and assets ahead of getting into the relationship.
Regardless what you may have discovered, marriage agreements aren't just for celebrities or even the wealthy. Anything you determine on the prenuptial agreement is up to you, and the prenuptial could be under legal standing and enforced, the agreement can vary from couple to couple in accordance with their circumstance. As soon as you both recognize the contract you both really should seek private attorneys to ensure that you completely grasp and go along with the prenuptial agreement.
If ever the contract has not been seen by a separate family law attorney which represents the other party, there does exist a possibility the legal system might void the contract, declaring unfair benefits. It's best you don't attempt to have your future significant other authorize it without requiring their own personal Divorce lawyer in Toronto reviewing it with them. In the event your predicament changes, the contract can always be amended to better serve the both of you.
Marriage agreements are vulnerable themes that married couples wouldn't like to focus on before getting married. Everyone is expecting their marital life to become an entire life devotion, but this is often a specific thing you never know. Talking about and finding a solution on a policy to accommodate many of the assets in the eventuality of a divorce proceeding shouldn't be pessimistic, it is the sensible decision to make. A relationship is an union of properties and assets, in fact it is smart to take care of your investments in the eventuality of unpredicted happenings.
These are merely several factors why you must think of a prenuptial agreement just before getting a wife or husband, this isn't viewing things negatively, it really is being practical when you recognize that a large number of relationships result in breakup. Discover more with regards to divorce process, Visit this Website, and see how you can protect yourself and also your possessions from a divorce and read more about the variety of types of separation and divorce that exist in society currently.


text:
Q: What is the equivalence of MS SQL Server's getutcdate() in postgresql? I migrate from SQL Server to PostgreSQL. How to translate the getutcdate function like:
Insert into mytable (mypk, toucheddate) values (99, getutcdate() )

(I'm not asking for an equivalent to MySQL, this is a different platform)

A: There are at least two ways to get the current time in UTC:
select now() at time zone 'utc';

select current_timestamp at time zone 'utc';

A: Postgres has current_timestamp for the current date and time, current_date for the current date and current_time for the current time.
Additional details can be found in the documentation.

A: I believe you are looking for now():
postgres=# select now();
            now
---------------------------
 2015-05-05 13:52:45.81-04
(1 row)

redpajama_set_name: RedPajamaStackExchange


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Here at R3 Data Recovery Hospital, wiping drives is part of our day to day process. When we set out to do a recovery every device gets assigned an image drive where a sector by sector clone is made, however once the recovery is done we have to wipe the image. So wiping drives happens all the time here.
Some people may think that formatting the drive is enough to get rid of the data, however any one with data recovery experience will know that even though the drive has been formatted it is still possible to recover the data that was on the device.
So fully wiping the drive will prove that the drive is in a good state and can be used for imaging purposes if we need it, it also shows that it can be used as a storage device without possible imminent failure.


Step Stake, lightweight – Signs in the Making, Inc.
A 10" w x 30" h lightweight step stake made from galvanized metal.
Use for temporary signage to direct potential buyers to an open house or house for sale.
For hard soil conditions or longer term use, choose Step Stake, heavy duty.


Target betting hits a bull's eye BOWL 'EM OVER!
Those punters who believe that level stakes betting is dull, conservative and a copout are probably interested in any other form of staking. Anything which can bring with it a touch of excitement, or just something out of the ordinary.
Many years ago, when my colleague Brian Blackwell and I were kids in England, we were greyhound devotees, and one of our pals was Don Rice, a zealous greyhounds bettor who always operated with target betting.
Don still uses his target betting plan today (well, the last time I saw him in England some eight or nine years ago, he was). He swears by it. I have dubbed the approach The Rice Bowl Plan, for obvious reasons(!).
You start off your first race and your aim is to win 1 unit. Example: If your first selection is a 5/1 chance, you will not need to bet 1 unit on it to achieve your initial 1 unit target. You can, if you wish, bet a half unit and if the horse wins you will still win 2.5 units, thus easily achieving your target.
My recommendation is that you always kick off with a 1 unit bet, but after that you can cut back to smaller bets if you like. Okay, we will assume the first bet loses. You then proceed to bet No. 2 and your target is now a new 1 unit figure, PLUS the I unit you have just lost, PLUS the I unit you were seeking to get from your first bet. You now have a target of three.
However, with the rules of this plan you will not be able to stake more than 2 units to achieve that target of three. After that, your bet is determined by the length of the losing run. For example, your stake rises by one each time you strike a loser. So on your fifth bet the maximum bet will be 5 units.
Your sixth bet, maximum six. And so on. You will find that with good selections (sensible ones!) you will rarely need to bet to the maximum to achieve your target.
If, for example, your second bet is at 4/1 and the target is three, you still need to bet only I unit to achieve the target. If your horse won, you would win 4 units and you would then rule off that betting series and start again.
If we assume your second bet lost ' you then go to bet No. 3 with a target this time of the old three, plus 1 for the third bet and one for the bet you had on the second horse, giving you a target of 5 units with a maximum bet allowed of 3 units. If your next selection was at, say, 5/2, you would need to invest 2 units to achieve your target of five. If the horse won, you would have got your 5 units target, giving you a profit of two.
My approach, and that of Don Rice, is to stop betting on a series as soon as you show a profit. Rule off, and start again. Odds-on chances are not backed.
Below is a recent example, using the selections of Stephen Moran of Best Bets, September 27.
When the day's racing ends this series would currently be minus 2 units.
You can see from this example that the day's betting at Moonee Valley saw two winning series and a third ended after two losing bets. This series can be closed off completely, or else continued at the next meeting.
The day's betting ended up with 4.5 units profit on two series and a 2 unit loss on the third. The total outlay was 7 units, for a 64 per cent profit. The total return was 11.5 units on the two winners. Don't forget that this third series can still be turned into a winner with further betting.
At level stakes, you would have bet 6 units for a return of 8.5 units, a profit of 2.5 units, or 41.5 per cent profit.
Series ends: Profit 3 units.
Series ends: Profit 3.5 units.


Freedom for Dinah and Sipho, Justice for Papi!
Shortly before his disappearance Papi's dog was killed and a member of the Boiketlong Concern Group said they had heard rumors that Papi's life was in danger prior to his disappearance.
• Make the South African government know that this case is in the international spotlight by phoning, emailing and faxing the Presidency and the Department of Justice and Constitutional Development to demand the conviction be overturned, the charges dropped and a full scale investigation into the fate of Paps Tobias be launched.


text:
\section*{Acknowledgment}
This work was partially supported by the Wallenberg Autonomous Systems and Software Program (WASP).

\section{Problem formulation and algorithm overview}
\label{sec:ProblemFormulationAlgorithmOverview}

\begin{figure}[t]
    \centering

    \input{images/system.tikz}
    \caption{Algorithm overview. The \gls{mot} algorithm has two modules, detection (left, red) and tracking (right, blue/green). The tracking modules consists of a recursive tracking filter (prediction+update) and an object extraction.}
    \label{fig:system}
\end{figure}

The KITTI object tracking dataset~\cite{Geiger2012CVPR} contains data from multiple sensors, e.g., four cameras and a lidar sensor. The data from such sensors can be used for environment perception, i.e., tracking of moving objects and mapping of the stationary environment. In this work we focus on data from a forward looking camera, with the objective to track the other vehicles that are in the environment.

Each vehicle is represented by a state vector $\vv{x}$ that contains the relevant information about the object. For 3D object tracking, the following state vector is used,
\begin{align}
	\vv{x} = \begin{bmatrix} x & y & z & v_x & v_y & v_z & w & h \end{bmatrix}^{T},
\end{align}
where $(x,y,z)$ is the 3D position in world coordinates, $(v_x , v_y , v_z)$ is the corresponding velocity, and $(w,h)$ is the width and height of the object's bounding box in the camera image. The position and velocity describes the tracked object's properties of interest; the width and height of the bounding box are used for evaluation analogue to the KITTI object tracking benchmark~\cite{Geiger2012CVPR}.

The number of vehicles in the environment is not known, and changes with time, so the task is to estimate both the number of vehicles, as well as each vehicle's state. The vehicles at time step $k$ are represented by a set $\set{X}_{k}$ that contains the state vectors of all vehicles that are present in the vicinity of the ego-vehicle. The set of vehicles $\set{X}_{k}$ is modeled as a Random Finite Set (\gls{rfs}) \cite{Mahler2007}.  That is, the number of objects, or the cardinality of the set, is modeled as a time varying discrete random variable and each object's state is a multivariate random variable.

The problem addressed in this paper is the processing of the sequence of images $\mm{I}_k$ into a sequence of estimates $\hat{\set{X}}_{\given{k}{k}}$ of the set of vehicles,
\begin{align}
	I_{0},I_{1},\ldots,I_{k} \qquad \Rightarrow \qquad \hat{\set{X}}_{0|0},\hat{\set{X}}_{1|1},\ldots,\hat{\set{X}}_{k|k},
\end{align}
where the sub-indices denote time. In other words, we wish to process the image sequence to gain information at each time step about the number of vehicles (the cardinality of the set $\set{X}$), and the state of each vehicle.
The proposed \gls{mot} algorithm has two main parts: object detection, and object tracking; an illustration of the algorithm is given in~\cref{fig:system}.

In the detection module, each image is processed to output a set of object detections $\set{Z}_{k}$,
\begin{align}
	I_{k} \quad \xRightarrow{\text{Detection}} \quad \set{Z}_{k}.
\end{align}
The set of detections $\set{Z}_{k}$, where each  $\vv{z}_k^i\in\set{Z}_{k}$ is an estimated object, is also modeled as a \gls{rfs}. The detection is based on a \gls{cnn}, which is presented in detail in Section~\ref{sec:Detections}.

The tracking module takes the image detections as input and outputs an object set estimate; it has three parts: prediction, update, and extraction. Together, the prediction and the update constitute a tracking filter that recursively estimates a multi-object set density,
\begin{align}
	\set{Z}_{k} \quad \xRightarrow{\text{PMBM filter}} \quad f_{k|k}(\set{X}_{k} | \set{Z}^k),
\end{align}
where $\set{Z}^k$ denotes all measurement sets up to time step $k$, $\{\set{Z}_t\}_{t\in(0,k)}$. Specifically, in this work we estimate a \gls{pmbm} density \cite{Williams2015}. The Chapman-Kolmogorov prediction
\begin{subequations}
    \begin{multline}
      f_{\given{k}{k-1}}(\given{\set{X}_k}{\set{Z}^{k-1}}) \\
      =\int g(\given{\set{X}_k}{\set{X}_{k-1}})f_{\given{k-1}{k-1}}(\given{\set{X}_{k-1}}{\set{Z}^{k-1}})\delta\set{X}_{k-1},
    \end{multline}
predicts the \gls{pmbm} density to the next time step using the multi-object motion model $g(\given{\set{X}_{k+1}}{\set{X}_k})$. We use the standard multi-object motion model~\cite{Mahler2007}, meaning that $g(\given{\cdot}{\cdot})$ models a Markovian process for objects that remain in the field of view, combined a \gls{ppp} birth process.

Using the set of detections $\set{Z}_{k}$ and the multi-object measurement model $h(\given{\set{Z}_k}{\set{X}_k})$, the updated \gls{pmbm} density is computed using the Bayes update
  \begin{equation}
    f_{\given{k}{k}}(\given{\set{X}_k}{\set{Z}^k})=
    \frac{h(\given{\set{Z}_k}{\set{X}_k})f_{\given{k}{k-1}}(\given{\set{X}_k}{\set{Z}^{k-1}})}
    {\int h(\given{\set{Z}_k}{\set{X}_k})f_{\given{k}{k-1}}(\given{\set{X}_k}{\set{Z}^{k-1})\delta\set{X}_k}},
  \end{equation}%
  \label{eq:MultiObjectBayesFilter}%
\end{subequations}%
We use the standard multi-object measurement model~\cite{Mahler2007}, in which $h(\given{\set{Z}_k}{\set{X}_k})$ models noisy measurement with detection uncertainty, combined with \gls{ppp} clutter.

The final part of the tracking is the object extraction, where object estimates are extracted from the \gls{pmbm} density,
\begin{align}
	f_{k|k}(\set{X}_{k} | \set{Z}^k) \quad \xRightarrow{\text{Extraction}} \quad \hat{\set{X}}_{k|k}
\end{align}
The tracking is described further in Section~\ref{sec:Tracking}. The integrals in \eqref{eq:MultiObjectBayesFilter} are set-integrals, defined in~\cite{Mahler2007}.

\section{Conclusion}
\label{sec:Conclusion}
This paper presented an image based \gls{mot} algorithm using deep learning detections and \gls{pmbm} filtering.
It was shown that a \gls{cnn} and a subsequent \gls{pmbm} filter can be used to detect and track objects.
The algorithm successfully can track multiple objects in 3D from a single camera image, which can provide valuable information for decision making and control.

\section{Object Detection}
\label{sec:Detections}

In this section, we describe how deep learning, see, e.g., \cite{Lecun2015}, is used to process the images $\{I_{t}\}_{t=0}^{k}$ to output sets of detections $\{\set{Z}_{t}\}_{t=0}^{k}$. For an image $I_{t}$ with a corresponding set of detections $\set{Z}_{t}$, each detection $\vv{z} \in \set{Z}_{t}$ consists of a 2D bounding box and a distance from the camera center to the center of the detected object,
\begin{align}

  \vv{z} = \begin{bmatrix} x_{min} & y_{min} & x_{max} & y_{max} & d \end{bmatrix}^{T},
\end{align}
where $(x_{min},y_{min})$ and $(x_{max},y_{max})$ are the pixel positions of the top left and bottom right corner of the bounding box,
respectively, and $d$ is the distance from the camera to the object. The bounding box encloses the object in the image. Using this information, the angle from the camera center to the center of the detected object can be inferred. This, together with the camera-to-object-distance $d$, allows the camera to be transformed into a range/bearing sensor, which is suitable for object tracking in 3D world coordinates.

The object detection is implemented using a improved version of the network developed in~\cite{Krishnan2016}.
The network can be divided into two parts; the first part can be viewed as a feature extractor, and the second part consists of three parallel output headers.
The feature extractor is identical to the DRN-C-26~\cite{Yu2017} network, with the exception that the last two classification layers have been removed.
The last two layers are structured for the original classification task of DRN-C-26, which is not suitable in this work.

To represent objects using a bounding box and its distance, the network has three different types of output: classification score, bounding box and distance.
Each header in the network has two $1\times 1$ convolutional layers and finally a sub-pixel convolutional layer~\cite{Shi2016}, upscaling the output to 1/4th of the input image resolution.
The bounding box header has 4 output channels, representing the top left and bottom right corner of the bounding box, the distance header has one output channel, representing the distance to the object, and the classification header has an additional softmax function and represents the different class scores using one-hot encoding, i.e., one output channel for each class, where each channel represents the score for each class, respectively.
For each pixel in the output layer there will be an estimated bounding box, i.e., there can be more than one bounding box per object.
To address this, Soft-NMS~\cite{Bodla2017} is applied.
In this step, the box with the highest classification score is selected and the score of boxes intersecting the selected box are decayed according to a function of the \gls{iou}.
This process is repeated until the classification score of all remaining boxes are below a manually chosen threshold.

The feature extractor is pre-trained on ImageNet~\cite{JiaDeng2009} and the full network is fine-tuned using annotated object labels from the KITTI object data set~\cite{Geiger2012CVPR}.
The network is tuned using stochastic gradient descent with momentum. The task of classification used a cross entropy loss function while bounding box regression and distance estimation used a smooth L1 loss function~\cite{Girshick2015}.

\subsubsection{Extraction}
\label{sec:ObjectExtraction}
Let the set of updated \gls{pmbm} parameters be
\begin{align}
	D_{}^{u} , \{ (w_{}^{j}, \{(r_{}^{j,i},f_{}^{j,i})\}_{i\in\mathbb{I}_{}^{j}})\}_{j\in\mathbb{J}_{}}.
\end{align}
To extract a set of object estimates, the hypothesis with highest probability is chosen,
\begin{equation}
    j^{\star}=\argmax_{j\in\idxs{J}}w^j.
 \end{equation}
 From the corresponding \gls{mb}, with parameters
 \begin{align}
	 \{(r_{}^{j^{\star},i},f_{}^{j^{\star},i})\}_{i\in\mathbb{I}_{}^{j^{\star}}},
 \end{align}
 all Bernoulli components with probability of existence $r^{j^{\star},i}$ larger than a threshold $\tau$ are selected, and the expected value of the object state is included in the set of object estimates,
 \begin{subequations}
 \begin{align}
 	\hat{\set{X}} & = \left\{ \hat{\vv{x}}^{j^{\star},i} \right\}_{i \in \mathbb{I}^{j^{\star}} : r^{j^{\star},i} > \tau} , \\
	\hat{\vv{x}}^{j^{\star},i} & = E_{f^{j^{\star},i}}\left[ \vv{x}^{j^{\star},i} \right] = \int \vv{x} f^{j^{\star},i}(\vv{x}) d\vv{x}.
 \end{align}
\end{subequations}

\section{Introduction}

To enable a high level of automation in driving, it is necessary to accurately model the surrounding environment, a problem called environment perception.
Data from onboard sensors, such as cameras, radars and lidars, has to be processed to extract information about the environment needed to automatically and safely navigate the vehicle.
For example, information about both the static environment, such as road boundaries and lane information, and the dynamic objects, like pedestrians and other vehicles, is of importance. The focus of this paper is the detection and tracking of multiple dynamic objects, specifically vehicles.

Dynamic objects are often modeled by state vectors, and are estimated over time using a \gls{mot} framework.
\Gls{mot} denotes the problem of, given a set of noisy measurements, estimating both the number of dynamic objects, and the state of each dynamic object.
Compared to the single object tracking problem, in addition to handling measurement noise and detection uncertainty, the \gls{mot} problem also has to resolve problems like object birth and object death\footnote{Object birth and object death is when an object first appears within, and departs from, the ego-vehicle's surveillance area, respectively.}; clutter detections\footnote{Clutter detections are false detections, i.e., detections not corresponding to an actual object.}; and unknown measurement origin.

A recent family of \gls{mot} algorithms are based on \glspl{rfs}~\cite{Mahler2007}.
The \gls{phd}~\cite{Mahler2003} filter, and the \gls{cphd}~\cite{Mahler2007b} filter, are two examples of moment approximations of the multi-object density.
The \gls{glmb}~\cite{Vo2013,Reuter2014} and the \gls{pmbm}~\cite{Williams2015,Garcia-Fernandez2017} filters are examples of \gls{mot} filters based on multi-object conjugate priors; these filters have been shown to outperform filters based on moment approximation. A recent comparison study published in~\cite{XiaGSGF:2017} has shown that the filters based on the \gls{pmbm} conjugate prior both achieves greater tracking performance, and has favourable computational cost compared to \gls{glmb}, hence we use the \gls{pmbm} filter in this work.

All of the aforementioned \gls{mot} algorithms takes sets of object estimates, or \textit{detections}, as their input.
This implies that the raw sensor data, e.g., the images, should be pre-processed into detections.
The recent development of deep neural networks has lead to big improvement in fields of image processing.
Indeed, considerable improvements have be achieved for the object detection problem, see, e.g.,~\cite{Ren2015,Redmon2016}, which is is crucial to the tracking performance.

\Glspl{cnn} \cite{LeCun1998} have shown to vastly outperform previous methods in image processing for tasks such as classification, object detection and semantic segmentation.
\Glspl{cnn} make use of the spatial relation between neighbouring pixels in images, by processing data in a convolutional manner. Each layer in a \gls{cnn} consists of a filter bank with a number of convolutional kernels, where each element is a learnable parameter.

The most common approach for object detection using deep neural networks is \glspl{rcnn}. \Glspl{rcnn} are divided into two parts; a \gls{rpn}, followed by a box regression and classification network. The \gls{rpn} takes an image as input, and outputs a set of general object proposals, which are fed into the following classification and box regression network. The box regression and classification network will refine the size of the object and classify it into one of the object classes. This type of deep neural network structure is used in, e.g., Fast \gls{rcnn}~\cite{Girshick2015}, and later in the improved Faster \gls{rcnn}~\cite{Ren2015}. Another approach to the object detection problem is \gls{yolo}~\cite{Redmon2016}. Here, the region proposal step is omitted, and the box regression and classification are applied directly on the entire image.

In the automotive industry, monocular camera is a well studied and commonly used type of sensors for developing autonomous driving systems.
A monocular camera is a mapping between 3D world coordinates and 2D image coordinates~\cite{RichardHartley2004} where, in contrary to, e.g., radars and lidars, distance information is lost.
However, to achieve a high level of automation, tracking in the image plane is not adequate.
Instead, we need to track objects in world coordinates in order to obtain the relative pose between the ego vehicle the detected objects, information that is crucial for automatic decision making and control.
We refer to this as 3D tracking.

Previous work on object tracking using monocular camera data is restricted to tracking in the image-plane, see, e.g.,~\cite{Choi2016,He2016,Xiang2015}, for some recent work. The main contribution of this paper is a multi-vehicle 3D tracking algorithm, that takes as input mono camera data, and outputs vehicle estimates in world coordinates. The proposed \gls{mot} algorithm is evaluated using the image sequences from the publicly available KITTI tracking dataset~\cite{Geiger2012CVPR}, and the results show that accurate 3D tracking is achieved.

The presented 3D tracking filter has two main components: a detector and an object tracking filter.
The detector is a deep neural network trained to from an input image not only extract a 2D bounding box for each detected object, but also to estimate the distance from the camera to the object.
This is achieved by using object annotations in lidar data during the learning of the network parameters.
The object tracking filter is a state-of-the-art \gls{pmbm} object tracking filter~\cite{Williams2015,Garcia-Fernandez2017} that processes the detections and outputs estimates.
The tracking filter is computationally efficient, and handles both false detections and missed detections.
For each object, a position, as well as kinematical properties such as velocity, are estimated.

The paper is structured as follows. In Section~\ref{sec:ProblemFormulationAlgorithmOverview}, we give a problem formulation and present an overview of the algorithm. In Section~\ref{sec:Detections} we present the object detection, and in Section~\ref{sec:Tracking} we present object tracking.
The results of an experimental evaluation using data sequences from the KITTI dataset are presented in Section~\ref{sec:results}%
, and the paper is concluded in Section~\ref{sec:Conclusion}.

\section{Experimental results}
\label{sec:results}

\subsection{Setup}
For evaluation, the KITTI object tracking dataset~\cite{Geiger2012CVPR} is used.
The datasets consists of 21 training sequences and 29 testing sequences that were collected using sensors mounted on a moving car.
Each sequence has been manually annotated with ground truth information, e.g., in the images, objects from the classes \textit{Car}, \textit{Pedestrian} and \textit{Cyclist} have been marked by bounding boxes.
In this work, the training dataset was split into two parts; one for training the \gls{cnn}, and one for validation.
The sequences used for training are 0, 2, 3, 4, 5, 7, 9, 11, 17 and 20, and the remaining ones are used for validation.

\subsection{Evaluation}
In this work we are primarily interested in the 3D tracking results. However, the KITTI testing sequences evaluate the tracking in 2D, hence we present results in both 2D and 3D. Performance is evaluated using \gls{iou} of the image plane bounding boxes and Euclidean distance as distance measurements, respectively.
For a valid correspondence between a \gls{gt} object and an estimated object, the 2D \gls{iou} has to be at least \SI{50}{\percent}, and the 3D Euclidean distance has to be within \SI{3}{\meter}, for the 2D and 3D evaluation, respectively.
The performance is evaluated using the CLEAR MOT performance measures~\cite{Bernardin2008}, including \gls{mota}, \gls{motp}, with addition of \gls{mt}, \gls{ml}, \gls{ids} and \gls{frag} from~\cite{YuanLi2009}, and \gls{f1}, \gls{pre}, \gls{rec} and \gls{far}.
The \glsentrylong{f1} is the weighted harmonic mean of the \glsentrylong{pre} and \glsentrylong{rec}.
Note that, for the 2D \gls{iou} measure, a larger value is better, whereas for the 3D Euclidean distance, lower is better.

\subsection{Results}

Examples of the 3D tracking results are shown in~\cref{fig:qualitative_results}.
The three examples show that the tracking algorithm successfully estimates the states of vehicles moving in the same direction as the ego-vehicle, vehicles moving in the opposite direction, as well as vehicles making sharp turns in intersections. In dense scenarios, such as in~\cref{fig:qualitative_results_b}, there are big overlaps between the bounding boxes; this is handled without problem by the data association. Noteworthy is that the distance estimates are quite noisy. Sometimes this leads to incorrect initial estimates of the velocity vector, as can be seen at the beginning of the track of the oncoming vehicle labelled purple in~\cref{fig:qualitative_results_c}. However, the tracking filter quickly converges to a correct estimate.
Videos of these, and of additional sequences, can be seen at \mbox{\url{https://goo.gl/AoydgW}}.

\begin{figure*}[!ht]
  \centering
  \subfloat[][]{
    \begin{tabular}[b]{c}
      \includegraphics[width=2.1in]{images/img_0015_000335}\\
      \includegraphics[width=2.1in]{images/top_0015_000335}
    \end{tabular}
    \label{fig:qualitative_results_a}
  }
  \subfloat[][]{
    \begin{tabular}[b]{c}
      \includegraphics[width=2.1in]{images/img_0018_000099}\\
      \includegraphics[width=2.1in]{images/top_0018_000099}
    \end{tabular}
    \label{fig:qualitative_results_b}
  }
  \subfloat[][]{
    \begin{tabular}[b]{c}
      \includegraphics[width=2.1in]{images/img_0010_000082}\\
      \includegraphics[width=2.1in]{images/top_0010_000082}
    \end{tabular}
    \label{fig:qualitative_results_c}
  }
  \caption{Object estimates shown both projected to the image plane (top) and in top-view (bottom). The dotted tracks illustrate the \glsshort{gt} and tracked object estimates at previous time steps. The color of the tracks corresponds to the identity of the tracked object.}
  \label{fig:qualitative_results}
\end{figure*}

Quantitative results from the evaluation on the validation sequences are shown in~\cref{table:performance}. Noteworthy is the low amount of \glsentrylong{ids}, in both 2D and in 3D. Comparing the raw \gls{cnn} detections and the \gls{mot} algorithm, the \gls{mot} \glsentrylong{pre} is lower, and the \gls{mot} \glsentrylong{rec} is higher, leading to an \glsentrylong{f1} that is higher for the \gls{mot} than for the \gls{cnn}; in other words, the overall object detection performance is slightly improved.

\begin{table*}[ht]
  \centering
  \caption{Results of the evaluation of tracking performance in 2D and 3D on the \textit{Car} class. $\uparrow$ and $\downarrow$ represents that high values and low values are better, respectively. The best values are marked with bold font.}
  \label{table:performance}

  \begin{tabular}{ll|rrrrrrrrrrr}
     & Method & \glsshort{mota}$\uparrow$ & \glsshort{motp}$\uparrow$ & \glsshort{mt}$\uparrow$ & \glsshort{ml}$\downarrow$ & \glsshort{ids}$\downarrow$ & \glsshort{frag}$\downarrow$ & \glsshort{f1}$\uparrow$ & \glsshort{pre}$\uparrow$ & \glsshort{rec}$\uparrow$ & \glsshort{far}$\downarrow$ \\ \hline
    \multirow{2}{*}{2D}
     & \glsshort{cnn} &
                        -- & {\bf \SI{82.04}{\percent}} & \SI{74.59}{\percent} & \SI{3.78}{\percent} & -- & -- & \SI{91.16}{\percent} & {\bf \SI{95.72}{\percent}} & \SI{87.02}{\percent} & {\bf \SI{9.08}{\percent}}
    \\
     & \glsshort{mot}  &
                         {\bf \SI{81.23}{\percent}} & \SI{81.63}{\percent} & {\bf \SI{76.22}{\percent}} & \SI{3.78}{\percent} & 19 & 107 & {\bf \SI{91.26}{\percent}} & \SI{94.76}{\percent} & {\bf \SI{88.02}{\percent}} & \SI{11.46}{\percent}
    \\ \hline
    & Method & \glsshort{mota}$\uparrow$ & \glsshort{motp}$\downarrow$ & \glsshort{mt}$\uparrow$ & \glsshort{ml}$\downarrow$ & \glsshort{ids}$\downarrow$ & \glsshort{frag}$\downarrow$ & \glsshort{f1}$\uparrow$ & \glsshort{pre}$\uparrow$ & \glsshort{rec}$\uparrow$ & \glsshort{far}$\downarrow$ \\ \hline
    \multirow{2}{*}{3D}
     & \glsshort{cnn} &
                        -- & \SI{111.39}{\centi\meter} & \SI{45.95}{\percent} & {\bf \SI{10.27}{\percent}} & -- & -- & \SI{73.53}{\percent} & {\bf \SI{78.74}{\percent}} & \SI{68.97}{\percent} & {\bf \SI{41.90}{\percent}}

    \\
     & \glsshort{mot}  &
                         {\bf \SI{47.20}{\percent}} & {\bf \SI{110.73}{\centi\meter}} & {\bf \SI{48.65}{\percent}} & \SI{11.35}{\percent} & 20 & 166 & {\bf \SI{73.86}{\percent}} & \SI{78.18}{\percent} & {\bf \SI{70.00}{\percent}} & \SI{44.32}{\percent}

  \end{tabular}
\end{table*}

The runtime of the algorithm is on average in total \SI{52}{\milli\second}, \SI{38}{\milli\second} for the detection network and \SI{14}{\milli\second} for the tracking algorithm, on a Nvidia Tesla V100 SXM2 and a single thread on a \SI{2.7}{\giga\hertz} Intel Core i7.

\subsection{KITTI \textsc{\glsentryshort{mot}} benchmark}
The \gls{mot} algorithm was also evaluated in 2D using the test sequences on the KITTI evaluation server.
For these results, the full training set was used for training the detection \gls{cnn}. The results are presented in~\cref{table:kitti_mot_performance}; at the time of submission our algorithm was ranked \nth{3} in terms of \gls{mota} among the published algorithms.
Note that, even if not reaching the same \gls{mota} performance, the runtime of our algorithm (\gls{fps}) is one magnitude faster and has a significantly lower number of \glsentrylong{ids} than the two algorithms with higher \gls{mota}.

\begin{table}[ht]
  \begin{threeparttable}
  \centering
  \caption{KITTI \glsentryshort{mot} benchmark~\cite{Geiger2012CVPR} results for \textit{Car} class. $\uparrow$ and $\downarrow$ represents that high values and low values are better, respectively. The best values are marked with bold font. \cite{Choi2016} is TuSimple, \cite{Xiang2015} is IMMDP and \cite{Lee2016} is MCMOT-CPD. Only results of published methods are reported.}
  \label{table:kitti_mot_performance}
  \begin{tabular}{l | r | r | r | r | r | r | r}
    & \glsshort{mota}$\uparrow$ & \glsshort{motp}$\uparrow$ & \glsshort{mt}$\uparrow$ & \glsshort{ml}$\downarrow$ & \glsshort{ids}$\downarrow$ & \glsshort{frag}$\downarrow$ & \glsshort{fps}$\uparrow$\tnote{a}
    \\ \hline
    \cite{Choi2016} & {\bf\SI{86.6}{\percent}} & {\bf\SI{84.0}{\percent}} & {\bf\SI{72.5}{\percent}} & \SI{6.8}{\percent} & 293 & 501 & 1.7 \\
    \cite{Xiang2015} & \SI{83.0}{\percent} & \SI{82.7}{\percent} & \SI{60.6}{\percent} & \SI{11.4}{\percent} & 172 & {\bf 365} & 5.3 \\
    Our & \SI{80.4}{\percent} & \SI{81.3}{\percent} & \SI{62.8}{\percent} & {\bf\SI{6.2}{\percent}} & {\bf 121} & 613 & 73 \\
    \cite{Lee2016} & \SI{78.9}{\percent} & \SI{82.1}{\percent} & \SI{52.3}{\percent} & \SI{11.7}{\percent} & 228 & 536 & {\bf 100} \\
  \end{tabular}
  \begin{tablenotes}
      \footnotesize
      \item[a] The time for object detection is not included in the specified runtime.
    \end{tablenotes}
\end{threeparttable}
\end{table}

\section{Object tracking}
\label{sec:Tracking}
To associate objects between consecutive frames and filter the object detections from the neural network, a \gls{pmbm} tracking filter is applied.
Both the set of objects $\set{X}_{k}$ and the set of image detections $\set{Z}_{k}$ are modeled as \glspl{rfs}. The purpose of the tracking module is to process the sequence of detection sets, and output a sequence of estimates $\hat{\set{X}}_{\given{k}{k}}$ of the true set of objects. We achieve this by using a \gls{pmbm} filter to estimate the multi-object density $f_{\given{k}{k}}(\given{\set{X}_{k}}{\set{Z}_{k}})$, and to extract estimates from this density.

In this section, we first present some necessary \gls{rfs} background, and the standard point object models that are used to model both the object motion, as well as the detection process. Then, we present the \gls{pmbm} filter.

\subsection{\gls{rfs} background}
In this work, two types of \glspl{rfs} are important: the \gls{ppp} and the Bernoulli process. A general introduction to \gls{rfs} is given in, e.g.,~\cite{Mahler2007}.

\subsubsection{\Glsentrylong{ppp}}
A \gls{ppp} is a type of \gls{rfs} where the cardinality is Poisson
distributed and all elements are \gls{iid}.
A \gls{ppp} can be parametrized by an intensity function, $D(\vv{x})$, defined as
\begin{equation}
  D(\vv{x})=\mu f(\vv{x}).
\end{equation}
The intensity function has two parameters, the Poisson rate $\mu>0$ and the spatial distribution $f(\vv{x})$.
The expected number of set members in a \gls{ppp} S is $\int_{\vv{x}\in S}D(\vv{x})\text{d}\vv{x}$.

The \gls{ppp} density is
\begin{equation}
  f(\set{X})=e^{-\ip {D(\vv{x})}{1}}\prod_{\vv{x}\in\set{X}}D(\vv{x})=e^{-\mu}\prod_{\vv{x}\in\set{X}}\mu f(\vv{x}).
  \label{eq:poisson}
\end{equation}
The \glspl{ppp} are used to model object birth, undetected
objects and clutter measurements.

\subsubsection{Bernoulli process}
A Bernoulli \gls{rfs} is a \gls{rfs} that with the probability $r$ contains a single element with the \gls{pdf} $f(\vv{x})$, and with the probability $1-r$ is empty:
\begin{equation}
  f(\set{X})=
  \begin{cases}
    1-r, & \set{X}=\emptyset \\
    rf(\vv{x}), & \set{X}=\{\vv{x}\} \\
    0, & \card{X} > 1
  \end{cases}.
  \label{eq:bernoulli_set_densities}
\end{equation}
It is suitable to use a Bernoulli \gls{rfs} to model objects in a \gls{mot} problem, since it both models the object's probability of existence $r$, and uncertainty in its state $\vv{x}$.

In \gls{mot}, the objects are typically assumed to be
independent~\cite{Williams2015}.
The disjoint union of a fixed number of independent Bernoulli \glspl{rfs},
$\set{X}=\uplus_{i\in\idxs{I}}\set{X}^i$, where $\idxs{I}$
is an index set, is a \gls{mb} \gls{rfs}.
The parameters $\{r^i,f^i(\cdot)\}_{i\in\idxs{I}}$
defines the \gls{mb} distribution.

A \gls{mbm} density is a normalized, weighted sum of \gls{mb} densities.
The \gls{mbm} density is entirely defined by $\{w^j,\{r^{j,i},f^{j,i}(\cdot)\}_{i\in\idxs{I}^j}\}_{j\in\idxs{J}}$, where $\idxs{J}$ is an index set for the \glspl{mb} in the \gls{mbm}, $w^j$ is the probability of the $j$th \gls{mb}, and $\idxs{I}^j$ is the index set for the Bernoulli distributions.
In a \gls{mot} problem, the different \glspl{mb} typically corresponds
to different data association sequences.

\subsection{Standard models}
Here we present the details of the standard measurement and motion models, under Gaussian assumptions.
\subsubsection{Measurement model}
\label{sec:standardMeasModel}
Let $\vv{x}_{k}^{i}$ be the state of the $i$th vehicle at the $k$th time step.
At time step $k$, given a set of objects
$\set{X}_k=\{\vv{x}_k^i\}_{i\in\idxs{I}}$, the set of measurements is
$\set{Z}_k=(\uplus_{i\in\idxs{I}}\set{W}_k^i)\uplus\set{K}_k$, where
$\set{W}_k^i$ denotes the set of object generated measurements from
the $i$th object, $\idxs{I}$ is an index set and $\set{K}_k$ denotes
the set of clutter measurements.
The set $\set{K}_k$ is modeled as a \gls{ppp}
with the intensity $\kappa(\vv{z})=\lambda c(\vv{z})$, where $\lambda$ is the Poisson rate and the spatial distribution $c(\vv{z})$ is assumed to be uniform.

Assuming an object is correctly detected with probability of detection $p_{\rm D}$. If the object is detected, the measurement
$\vv{z}\in\set{W}_k^i$ has \gls{pdf}
$\phi_{\vv{z}}(\vv{x}_k^i) = \mathcal{N}(\vv{z} ; a(\vv{x}_k^i), R)$, where $a(\vv{x}_k^i)$ is a camera measurement model.
The resulting measurement likelihood is%
\begin{equation}
  \ell_{\set{Z}}(\vv{x}) = p(\given{\set{Z}}{\vv{x}})=\begin{cases}
    1-p_{\rm D}, & \set{Z}=\emptyset \\
    p_{\rm D} \phi_{\vv{z}}(\vv{x}), & \set{Z}=\{\vv{z}\} \\
    0, & \card{\set{Z}}>1
  \end{cases}.
  \label{eq:mptdb}
\end{equation}
\label{eq:mptd}%
As can be seen in \cref{eq:mptdb}, if multiple measurements are associated to one object this will have zero likelihood. This is a standard point object assumption, see, e.g., \cite{Mahler2007}.

Because of the unknown measurement origin\footnote{An inherent property of \gls{mot} is that it is unknown which measurements are from object and which are clutter, and among the object generated measurements, it is unknown which object generated which measurement. Hence, the update must handle this uncertainty.}, it is necessary to discuss data association. Let the measurements in the set $\set{Z}$ be indexed by $m\in\mathbb{M}$
\begin{align}
	\set{Z} = \left\{\vv{z}^m\right\}_{m\in\mathbb{M}},
\end{align}
and let $\mathcal{A}^{j}$ be the space of all data associations $A$ for the $j$th predicted global hypothesis, i.e., the $j$th predicted \gls{mb}. A data association $A\in\mathcal{A}^{j}$ is an assignment of each measurement in $\set{Z}$ to a source, either to the \emph{background} (clutter or new object) or to one of the existing objects indexed by $i\in\mathbb{I}^{j}$. Note that $\mathbb{M} \cap \mathbb{I}^{j} = \emptyset$ for all $j$. The space of all data associations for the $j$th hypothesis is $\mathcal{A}^{j} = \mathcal{P}(\mathbb{M} \cup \mathbb{I}^{j})$, i.e., a data association $A\in\mathcal{A}^{j}$ is a partition of $\mathbb{M} \cup \mathbb{I}^{j}$ into non-empty disjoint subsets $C\inA$, called index cells\footnote{For example, let $\mathbb{M}=\left(m_1,m_2,m_3\right)$ and $\mathbb{I}=\left( i_{1} , i_{2} \right)$, i.e., three measurements and two objects. One valid partition of $\mathbb{M}\cap\mathbb{I}$, i.e., one of the possible associations, has the following four cells $\{m_1\},\{m_2,i_{1}\},\{m_3\},\{i_{2}\}$. The meaning of this is that measurement $m_2$ is associated to object $i_{1}$, object $i_{2}$ is not detected, and measurements $m_1$ and $m_3$ are not associated to any previously detected object, i.e., measurements $m_1$ and $m_3$ are either clutter or from new objects.}.

Due to the standard \gls{mot} assumption that the objects generate measurements independent of each other, an index cell contains at most one object index and at most one measurement index, i.e., $| C\cap\mathbb{I}^{j} | \leq 1$ and $| C\cap\mathbb{M} | \leq 1$ for all $C\inA$. Any association in which there is at least one cell, with at least two object indices and/or at least two measurement indices, will have zero likelihood because this violates the independence assumption and the point object assumption, respectively. If  the index cell $C$ contains an object index, then let $i_C$ denote the corresponding object index, and if the index cell $C$ contains a measurement index, then let $m_C$ denote the corresponding measurement index.

\subsubsection{Standard dynamic model}
\label{sec:StandardDynamicModel}
The existing objects---both the detected and the undetected---survive from time step $k$ to time step $k+1$ with probability of survival $p_{\rm S}$. The objects evolve independently according to a Markov process with Gaussian transition density $g(\vv{x}_{k+1} | \vv{x}_{k}) = \mathcal{N}(\vv{x}_{k+1} ; b(\vv{x}_{k}), Q)$, where $b(\vv{\cdot})$ is a \gls{cv} motion model. New objects appear independently of the objects that already exist. The object birth is assumed to be a \gls{ppp} with intensity $D_{k+1}^{b}(\vv{x})$, defined in~\cref{eq:poisson}.

\subsection{\gls{pmbm} filter}
In this section, the time indexing has been omitted for notational
simplicity.
The \gls{pmbm} filter is a combination of two \glspl{rfs}, a \gls{ppp}
to model the objects that exist at the current time step, but have
not yet been detected and a \gls{mbm} to model the objects that have
been detected previously at least once.
The set of objects can be divided into two disjoint subsets,
$\set{X}=\set{X}^d\uplus\set{X}^u$, where $\set{X}^d$ is the set of
detected objects and $\set{X}^u$ is the set of undetected objects.
The \gls{pmbm} density can be expressed as
\begin{subequations}
  \begin{align}
    f(\set{X}) & = \sum_{\set{X}^u\uplus\set{X}^d=\set{X}}f^u(\set{X}^u)\sum_{j\in\idxs{J}}w^jf^j(\set{X}^d), \\
    f^u(\set{X}^u) & = e^{-\ip{D^u(\vv{x})}{1}} \men{D^u}{\set{X}^u}, \label{eq:undetected_objects} \\
    f^j(\set{X}^d) & = \sum_{\uplus_{i\in\idxs{I}^i}\set{X}^i=\set{X}^d}\prod_{i\in\idxs{I}^j}f^{j,i}(\set{X}^i), \label{eq:object_mb}
  \end{align}%
  \label{eq:PMBMdensity}%
\end{subequations}%
where
\begin{itemize}
\item $f^u(\cdot)$ is the \gls{ppp} density for the set of undetected
  objects $\set{X}^u$, where $D^u(\cdot)$ is its intensity.
\item $\idxs{J}$ is an index set of \gls{mbm} components. There are $\card{\idxs{J}}$ \glspl{mb}, where each \gls{mb} corresponds to a unique global data association hypothesis. The probability of each component in the \gls{mbm} is denoted as $w^j$.
\item For every component $j$ in the \gls{mbm}, there is an index set $\idxs{I}^j$, where each index $i$ corresponds to a potentially detected object $\set{X}^i$.
\item $f^{j,i}(\cdot)$ are Bernoulli set densities, defined in \cref{eq:bernoulli_set_densities}. Each \gls{mb} corresponds to a potentially detected object with a probability of existence and a state \gls{pdf}.
\end{itemize}
The \gls{pmbm} density in~\cref{eq:PMBMdensity} is defined by the involved parameters,
\begin{align}
	D_{}^{u} , \{ (w_{}^{j}, \{(r_{}^{j,i},f_{}^{j,i})\}_{i\in\mathbb{I}_{}^{j}})\}_{j\in\mathbb{J}_{}}.
\end{align}
Further, the \gls{pmbm} density is an \gls{mot} conjugate prior \cite{Williams2015}, meaning that for the standard point object models (Sections~\ref{sec:standardMeasModel} and \ref{sec:StandardDynamicModel}), the prediction and update in~\cref{eq:MultiObjectBayesFilter} both result in \gls{pmbm} densities. It follows that the \gls{pmbm} filter propagates the multi-object density by propagating the set of parameters.

In this work, we assume that the birth intensity $D^b$ is a non-normalized Gaussian mixture. It follows from this assumption that the undetected intensity $D^u$ is also a non-normalized Gaussian mixture, and all Bernoulli densities $f^{j,i}$ are Gaussian densities. Below, we present the parameters that result from the prediction and the update, and we present a simple method for extracting target estimates from the set of parameters. To compute the predicted and updated Gaussian parameters, we use the UKF prediction and update, respectively, see, e.g., \cite[Ch. 5]{Sarkka2013}.

\subsubsection{Prediction}
Given a posterior \gls{pmbm} density with parameters
\begin{align}
	D_{}^{u} , \{ (w_{}^{j}, \{(r_{}^{j,i},f_{}^{j,i})\}_{i\in\mathbb{I}_{}^{j}})\}_{j\in\mathbb{J}_{}} ,
\end{align}
and the standard dynamic model (Section \ref{sec:StandardDynamicModel}), the predicted density is a \gls{pmbm} density with parameters
\begin{subequations}
\begin{align}
	D_{+}^{u} , \{ (w_{+}^{j}, \{(r_{+}^{j,i},f_{+}^{j,i})\}_{i\in\mathbb{I}^{j}})\}_{j\in\mathbb{J}},
\end{align}
where

\begin{align}%
	D_{+}^{u} (\vv{x}) & = D^{b}(\vv{x}) + p_{\rm S} \ip{D_{}^{u}}{ g} , \label{eq:PredictionUndetected} \\
	 r_{+}^{j,i} & = p_{\rm S} r^{j,i} , \label{eq:PredictedBernoulliProbEx} \\
	 f_{+}^{j,i}(\vv{x}) & = \ip{ f_{}^{j,i}}{g} , \label{eq:PredictedBernoulliSpatialDistribution}
\end{align}%
\label{eq:PredictedParameters}%
\end{subequations}%
and $w_{+}^{j} = w_{}^{j} $. For Gaussian mixture intensity $D^u$, and Gaussian densities $f^{j,i}$, the predictions $\ip{\cdot}{g}$ in~\cref{eq:PredictedParameters} are easily computed using the UKF prediction, see, e.g.,~\cite[Ch. 5]{Sarkka2013}.

\subsubsection{Update}
Given a prior \gls{pmbm} density with parameters
\begin{align}
	D_{+}^{u} , \{ (w_{+}^{j}, \{(r_{+}^{j,i},f_{+}^{j,i})\}_{i\in\mathbb{I}_{+}^{j}})\}_{j\in\mathbb{J}_{+}},
\end{align}
a set of measurements $\set{Z}$, and the standard measurement model (Section~\ref{sec:standardMeasModel}), the updated density is a \gls{pmbm} density
\begin{subequations}
\begin{align}
	f(\set{X}|\set{Z}) & = \sum_{\set{X}^{u} \uplus \set{X}^{d} = \set{X}} f^{u}(\set{X}^{u}) \sum_{j\in\mathbb{J}_{+}} \sum_{A\in\mathcal{A}^{j}} w_{A}^{j} 	f_{A}^{j}(\set{X}^{d}) , \\
	f^{u}(\set{X}^{u}) & = e^{-\ip{D^{u}}{1}} \prod_{\vv{x}\in\set{X}^{u}} D^{u}(\vv{x}) , \\
	f_{A}^{j}(\set{X}^{d}) & = \sum_{ \uplus_{C\inA}\set{X}^{C} = \set{X} } \prod_{C\inA} f_{C}^{j}(\set{X}^{C}) ,
\end{align}%
\label{eq:UpdatedPMBMdensity}%
where the weights are
\begin{align}
	& w_{A}^{j} = \frac{w_{+}^{j} \prod_{C\inA} \mathcal{L}_C }{ \sum_{j'\in\mathbb{J}} \sum_{A'\in\mathcal{A}^{j'}} w_{+}^{j'} \prod_{C'\inA'} \mathcal{L}_{C'} } , \\
	& \mathcal{L}_{C} = \left\{ \begin{array}{cl}
			\text{\footnotesize $\kappa + p_{\rm D} \ip{ D_{+}^{u} }{ \phi_{\vv{z}^{m_{C}}} }$}  & \text{\footnotesize if $C\cap\mathbb{I}^{j} = \emptyset, C\cap\mathbb{M} \neq \emptyset,$} \\
			\text{\footnotesize $1- r_{+}^{j,i_{C}} p_{\rm D} $}     & \text{\footnotesize if $C\cap\mathbb{I}^{j}\neq\emptyset, C\cap\mathbb{M}=\emptyset,$} \\
			\text{\footnotesize $r_{+}^{j,i_{C}} p_{\rm D} \ip{f_{+}^{j,i_{C}}}{ \phi_{\vv{z}^{m_{C}}}}$}                  & \text{\footnotesize if $C\cap\mathbb{I}^{j}\neq\emptyset, C\cap\mathbb{M}\neq\emptyset ,$}
		\end{array} \right.
\end{align}
the densities $f_{C}^{j}(\set{X})$ are Bernoulli densities with parameters
\begin{align}
	& r_{C}^{j} = \left\{ \begin{array}{cl}
			\frac{ p_{\rm D} \ip{ D_{+}^{u} }{ \phi_{\vv{z}^{m_{C}}} } }{\kappa+ p_{\rm D}\ip{ D_{+}^{u} }{ \phi_{\vv{z}^{m_{C}}} }} & \text{\footnotesize if $C\cap\mathbb{I}^{j} = \emptyset, C\cap\mathbb{M} \neq \emptyset$,} \\
			\frac{r_{+}^{j,i_{C}} (1 - p_{\rm D}) }{1-r_{+}^{j,i_{C}} p_{\rm D} } & \text{\footnotesize if $C\cap\mathbb{I}^{j}\neq\emptyset, C\cap\mathbb{M}=\emptyset$,} \\
			1 & \text{\footnotesize if $C\cap\mathbb{I}^{j}\neq\emptyset, C\cap\mathbb{M}\neq\emptyset $,}
		\end{array} \right. \label{eq:NewBernoulliProbEx}\\
	& f_{C}^{j}(\vv{x}) = \left\{ \begin{array}{cl}
			\frac{ \phi_{\vv{z}^{m_{C}}}(\vv{x}) D_{+}^{u}(\vv{x}) }{ \ip{ D_{+}^{u} }{ \phi_{\vv{z}^{m_{C}}} } } & \text{\footnotesize if $C\cap\mathbb{I}^{j} = \emptyset, C\cap\mathbb{M}\neq\emptyset$,} \\
			\text{\footnotesize $f_{+}^{j,i_{C}}(\vv{x})$} & \text{\footnotesize if $C\cap\mathbb{I}^{j}\neq\emptyset, C\cap\mathbb{M}=\emptyset$,} \\
			\frac{ \phi_{\vv{z}^{m_{C}}}(\vv{x}) f_{+}^{j,i_{C}} (\vv{x})}{\ip{ f_{+}^{j,i_{C}} }{ \phi_{\vv{z}^{m_{C}}} }} & \text{\footnotesize if $C\cap\mathbb{I}^{j}\neq\emptyset, C\cap\mathbb{M}\neq\emptyset $,}
		\end{array} \right.  \label{eq:NewBernoulliProbEx}
\end{align}
\label{eq:UpdatedPGFLprevdet}%
\end{subequations}%
and the updated \gls{ppp} intensity is $D^{u}(\vv{x}) = (1 - p_{\rm D}) D_{+}^{u}(\vv{x})$. For Gaussian mixture intensity $D_{+}^u$, and Gaussian densities $f_{+}^{j,i}$, the updates $\ip{\cdot}{\phi}$ in \eqref{eq:UpdatedPGFLprevdet} are easily computed using the UKF update, see, e.g., \cite[Ch. 5]{Sarkka2013}.

\input{extraction}

redpajama_set_name: RedPajamaArXiv


"Wow!" Rowena stared in amazement at the rocks. It was beautiful, and even more so due to the bushes around.
Em said nothing and bent down. Parting a large patch of grass aside, she revealed a hole. Row, now intrigued, got closer. With a wide grin and unnecessary dramatism, Em slinked down the hole.
"EM!" Row cried in alarm before following her friend down the hole. She landed on a soft ground and walked on, intent on finding her slippery friend. She found her, sometime later, sitting on a mat smiling.
"What is this place?" She asked amazed.
They sat there for a while, chatting away idly. They left some time later, their stomachs growling, their hearts full and with the promise to return.
Written as a response to Thursday Photo Prompt hosted by Sue Vincent.
Rowena is based on my awesome friend Aakankshya. You can check her blog here.
Lovely nostalgia-evoking tale of childhood friendship.
Thank you. It was based on some of my own childhood experiences.