extfieldsofstudy:
Computer Science
Medicine

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Construction of 5G all-wireless network and information system for cabin hospitals

Abstract The epidemic of coronavirus disease 2019 (COVID-19) broke out in Wuhan, China, in early 2020. In an effort to curb the spread of the epidemic, the government has requisitioned a variety of venues and plant buildings and built more than 20 cabin hospitals to receive patients with mild symptoms within 48 hours. Under this circumstance, we worked out a 5G all-wireless solution to divide the overall network system of the cabin hospital into multiple network units by function. While ensuring good signal coverage of the local unit, each network unit was independently connected to the host hospital’s data center over a virtual private network (VPN) tunnel built on the 5G wireless network. Our successful experience with the application of this 5G + VPN all-wireless network system well points to the bright prospect of 5G wireless network. In addition, the 5G + VPN solution can also be used for multihospital network interconnection and rapid network recovery during the failure of wired network.

INTRODUCTION
The epidemic of coronavirus disease 2019 (COVID-19) broke out in Wuhan, China, in early 2020. In the early stages of outbreak, the epidemic spread quickly and sparked social panic because of insufficient knowledge of the virus, lack of protective measures, strong infectivity, long incubation period, lack of effective treatment options, and slow-improving treatment methods. Given the sudden outbreak, the local medical resources in Wuhan were insufficient to cope with the epidemic. In the face of the daunting challenge to outbreak control, General Secretary Xi Jinping held a video conference with key medical institutions in the affected areas and gave important instructions. 1 The National Health Commission of China also mobilized healthcare workers and medical supplies from all parts of China to help Wuhan contain the epidemic. The Wuhan Municipal Government decisively closed off Wuhan and announced the principle of leaving no one unattended. Given the severe fact that the number of daily confirmed cases increased by 3000 in the peak period and that the number of infected people might reach up to 100 000, the government requisitioned a variety of venues and plant buildings and quickly built more than 20 cabin hospitals 2 to receive patients with mild symptoms. In the meantime, the government also transferred critically ill patients to designated medical institutions for treatment and quarantined suspected patients at hotels. Through all these efforts, the epidemic was gradually brought under control.
The construction of cabin hospitals could not be done without the support of information technology (IT). IT engineers faced a daunting challenge, as they were given 1 to 2 days to take account of the setup of network systems, the renovation of information systems, the deployment of video conference and group consultation systems, the maintenance of various types of information, and the operational management of the hospital.

DEMAND ANALYSIS AND SOLUTION DESIGN
The cabin hospital is a fast-deploying mobile medical and surgical platform combined medical resources and medical facilities. 3 The cabin hospital, which emerged in Wuhan in its most difficult time, was a new type of hospital and an important tool to prevent and control the spread of COVID-19, playing a critical role in containing the epidemic. Receiving only patients confirmed with mild and basically consistent symptoms, 4 the cabin hospitals mainly treated patients with oral medicine and only engaged in blood testing, nucleic acid testing, mobile computed tomography (CT) scanning, and other testing functions. Inpatients were registered using their real names, and all medical expenses were borne by the government. The cabin hospitals were built by the government, which was also responsible for logistical support and supply allocation. The units were operated and managed by the local hospitals under the support of various medical teams from all parts of China. The functional units in cabin hospitals were the doctors' unit, a nurses' unit, a testing unit, an examination unit, a pharmacy, an infection control unit, a management unit, and a logistic support unit. The medical team was composed of both native and non-native medical staff from all parts of China. Not all healthcare workers came from infectious diseases departments or severe respiratory departments; thus, their working habits and approaches to treatment and diagnosis differed. Owing to the lack of experience with the operation of cabin hospitals, the entire workflow and the operational rules were determined on a temporary basis and adjusted gradually. Once the cabin hospital was put into use, the healthcare area would be immediately quarantined, and all work could only be done by individuals wearing protective clothing. Owing to the heavy workload, it was impossible to carry out large-scale construction.
The construction of IT systems for cabin hospitals typically follows a certain pattern. In order to complete the IT system construction for such a hospital within 24 to 48 hours, we usually need to include the cabin hospital within an existing hospital's information network. Specifically, we need to lease a line from an Internet service provider, connect it to the network system of the host hospital, and then route the fiber cables from the convergence switch all the way to each work unit to interconnect the computer terminals at the access layer, while wireless access points can also be deployed to provide wireless coverage. After the network is set up, the client applications of the host hospital's information system will then be installed and put into use.
However, because Wuhan was closed off, there were not many engineers and technicians available. Moreover, construction workers also had to quarantine themselves from each other. Many young people were fearful and did not want to work in or around the hospital. Vendors often provided technical support remotely, with very few being able to get to the site. The movement of people and vehicles was prohibited, equipment and supplies were snapped up, and related equipment could not be mobilized.
In the face of all these challenges, and giving consideration to such aspects as technology, management, operation and maintenance, and sustainable development, 5 and taking account of the fact that the wireless medical healthcare management system was targeted at the frontline medical staff, 6 we worked out a 5G allwireless solution to divide the overall network system of the cabin hospital into multiple network units by function. While ensuring good signal coverage of the local unit, each network unit was independently connected to the host hospital's data center over a virtual private network (VPN) built on the 5G wireless network. In order to comply with relevant medical regulations, we developed this system based on the host hospital's original information system. This move reduced the difficulty and complexity in the use of traditional information systems, thereby building a cabin hospital information sys-tem with streamlined processes, uniform access rules, and easy-touse tools. The terminals were mainly all-in-one or laptop computers equipped with a laser printer. In this way, we could narrow the types of equipment needed and so reduce the maintenance workload.

5G ALL-WIRELESS NETWORK SYSTEM
Based on the physical location of respective functional units in the cabin hospital and the signal coverage of the wireless devices, we divided all work areas into several network units. In the cabin, we set up a registration and filing network unit at the entrance of the ward. We also set up 3 medical network units in the cabin within which patients were attended by the medical staff. Outside the cabin, we also set up a mobile CT network unit, a laboratory network unit, a pharmacy network unit, and a management network unit (8 network units in total), according to the location of each functional unit. All network units have access to the intranet and Internet. The detailed architecture and performance of the 5G all-wireless network is shown in Figures 1 and 2.

5G-based wireless link
We deployed a network security gateway at the host hospital's data center to set up a VPN tunnel for accepting authenticated connections to the host hospital's information system over the Internet. Each network unit was provided with a 5G data card, and a wireless router was deployed to allow each network unit to access the Internet wirelessly. In the meantime, we connected a small branch router with VPN support to the wireless router and configured the VPN settings on this router to set up a secure, stable, and reliable authenticated link to the host hospital's data center over the Internet, thereby ensuring secure and encrypted data transmission between the cabin hospital's network units and the host hospital's data center.

Wireless network connection in the cabin hospital
The wireless router covering the local network unit was configured to access the Internet, so as to address the need for Internet access, report various types of data, and enable file sharing between the cabin hospital and the outside. The small branch router covering the local network unit was configured to access the intranet, so that the terminal computers could access the internal network and the information system of the host hospital. After testing, we found that 5G signals were stable without packet drops, that the network bandwidth was nearly 10 times faster than 4G, and that the intranet bandwidth exceeded 50M, thus meeting the demand placed on the network. Patients' need for Internet access was left to the signal coverage of telecom operators.

Cloud-based network management platform
The network administrator could use a mobile phone or desktop computer to log into the Web-based cloud network management platform to perform important tasks. They were able to set up virtual LANs. They could also configure the stateful firewalls, switches, and mobile terminals. They were able to monitor network operation status, event logs, and operation summary reports. Finally, they could optimize network parameters and configure various access control policies and network security policies such as DHCP, NAT, and QoS. This accessibility ensured the uninterrupted and secure operation of the cabin hospital's information system. 7

LIGHTWEIGHT INFORMATION SYSTEM FOR THE CABIN HOSPITAL
According to the characteristics of the cabin hospital, we developed a new information system based on the original hospital information system. By integrating the transformed electronic outpatient medical records and the picture archiving and communication system (PACS), the laboratory information system, the maintenance system, other management information systems, and the Internet-assisted medical system of the host hospital, we managed to integrate all data through the information integration platform and built a lightweight information system for the cabin hospital. The main functions of the system are shown in Table 1:

Patient record filing
The record filing was done by a nurse, who would assign a bed to each patient. All patients needed to register using their real name, as well as provide such information as hospital admission number, name, ID number, and mobile phone number. The hospital admission number consisted of 10 digits, with the first 2 digits being the cabin hospital number, the next 4 digits being the unified bed number, and the last 4 digits being the admission date (excluding the year). The hospital admission number was the unique identification number for the patient, who only needed to remember the bed number and to report the bed number to the medical staff at the time of admission. No other medium was used. Relevant information would also be sent to the patient's mobile phone.

Doctors' workstation
According to the outpatient observation model, a doctor would first arrange the patient's admission, make a diagnosis, and then write the first course record. The doctor's daily routine included: filling out the electronic medical records, disease course records, and several brief evaluation forms; making a prescription for the pharmacy according to the patient's conditions and the examination and test results shown on the computer; prescribing nucleic acid tests and CT scans for the patients; and discharging or transferring the patients if their condition either improved or deteriorated. Doctors were also able to check the patient's past medical history and treatment history in real time through the quick search tool. 8

Nurses' workstation
Nurses did not use computers much. Nurses were primarily responsible for filling out the first-time nursing evaluation form and the nursing observation record, printing the test and CT scan application summary sheets, and implementing the summary sheets. Nurses needed to print the test barcode outside the cabin, affix it to the test tube, collect the sample inside the cabin, and send it to the test unit outside the cabin. The nurses also needed to check the list in the medicine package prepared by the pharmacist for the patients and distribute the medicine. In addition, nurses also needed to perform the required checkups using the query tool and to fill out the corresponding forms based on the doctor's discharge conclusion when the patient was discharged or transferred.

Pharmacists' workstation
Patients with mild symptoms needed few medications. Because all medicines were fully supplied by the government, there was no need to set up a medicine warehouse. The main job of the pharmacist was to receive electronic prescriptions from the doctors, pack medicines separately or in batches, print the corresponding lists to be included in the medicine package, and then ask the nurses to take the medicines into the cabin. The pharmacist could stay informed of the patients' use of drugs via the summary and query tools. Pharmacists also needed to complete the in-out-stock operations independently.

Medical technology workstation
The mobile CT scanner was wired to the branch router. Upon completion of CT scanning, the patient's CT image would be transmitted to the host hospital's PACS through the wireless link of the network unit. The radiologist at the host hospital would then use the PACS workstation to read the CT image in order to make a diagnosis and then forward the report to the doctors' station in the cabin. The test workstation would use the host hospital's laboratory information system to receive the samples, and then issue a report upon completion of the test. The mobile CT scanner could quickly and efficiently adapt to the operational pattern of the cabin hospital and could significantly enhance the capacity and outcomes of on-the-spot treatment. 9

Online doctor assistance system
We quickly developed a doctor assistance system to support the WeChat official account and mobile application of the host hospital so that doctors could communicate with patients online in their spare time, provide consultation service for patients, answer the questions raised by patients, and if necessary, go to the bed of the patient to handle the situation. In addition, whether the doctor was in the cabin or outside the cabin, they could always view the patient information anytime via mobile phone.

Rapid and convenient system construction
With remote technical support from various vendors, engineers of the host hospital completed application development, software integration, and system integration within 48 hours. In the meantime, a brief training session was organized immediately upon arrival of the medical staff. At the time of implementation, engineers completed the installation of 50 client applications within 3 hours. After arriving at the cabin hospital, 3 engineers completed the installation of network devices and computer terminals and the power-on and printer connection tests within 6 hours. Soon, each network unit was successfully put into use.

Zero maintenance of network and terminal devices
There were only wireless routers, all-in-one computers, and several printers in the cabin. Except for the printers, there were no other cable connections. These devices were configured to support plug and play. Should any device fail or a new computer be added, the medical staff or management personnel would bring the device in and replace it by themselves. Laser printers were simple to connect and drivers could be installed remotely. Should any laser printer Radiologists' workstation Scan review, inspection report, audit report, report issuance, etc. Doctor Intranet 6 Lab technicians' workstation Sample reception and testing, report auditing, report issuance, etc. Technician Intranet 7 Pharmacists' station Medical order reception and review, medicine dispensing, statistics, etc. Pharmacist Intranet 8 General management workstation 1 Healthcare quality control, financial management, data collation, report generation, etc.
Administrative staff Intranet 9 General management workstation 2 Administrative affairs, information release and transmission, official document circulation and approval, etc.
Administrative staff Internet 10 Phone-assisted health care Doctors used a mobile phone to check medical records and to communicate with patients Doctor and patient Internet encounter a paper jam or need to replace the toner cartridge, the medical staff could also do it by themselves. For the IT department, there were no on-site maintenance tasks in the cabin hospital.

Efficient and diverse means of troubleshooting
Remote maintenance software was installed on each computer. When the medical staff in the cabin encountered a problem, an engineer from the IT department could log in to the computer remotely and solve the problem quickly. For any doubts relating to the use of computers inside the cabin, the user could consult the user manual placed on each computer. They could also use a mobile phone or ultra-long-distance walkie-talkie to consult the engineer. We also created a WeChat group to answer various doubts. During our communication with users, should any reasonable demands be raised or any problems be found with the software, we would immediately arrange the development or optimization thereof and then automatically upgrade the software through remote access.

Reduced chance of cross infection
No medical card, virtual card, or bracelet was required for identification in the cabin, so there was no need to equip peripherals such as card readers or barcode scanners. Information circulation was all electronic and paper was rarely used. The nurse only needed to print the summary sheet when following doctor's order to check the patients. Still, the paper was in the hands of the nurses. All these efforts helped reduce the frequency of the medical staff's contact with the patient, reduce the chance of infection caused by the circulation of relevant medium and paper, and minimize the chance of cross-infection.

Effective saving of protective medical supplies
There were few network and information devices in the cabin. These were plug and play and basically not interconnected. The information system was maintained remotely. All system failures could be resolved online. Multiple means of communication also significantly reduced operational problems caused by insufficient training. So far, the entire network and information system has been operating stably, and engineers from the IT department have not entered the quarantine zone once. By minimizing the amount of entry into the quarantine zone, we effectively saved the protective medical supplies and indirectly contributed to the fight against the epidemic.

CONCLUSION
We creatively worked out the 5G þ VPN solution and completed the deployment of an all-wireless network system for a cabin hospital within 48 hours, wirelessly connecting it to the host hospital. The deployment of a tailor-made lightweight hospital information system also enabled the online provision of auxiliary medical services. In this important fight against the epidemic, during which we must race against time to save more lives, IT engineers have made their own contributions with their IT weapons. So far, Wuhan Jianghan Cabin Hospital, the Cabin Hospital we are running, has been operating for more than 30 days to date. Our solution has proven to be completely feasible in practice and is worthy of replication by other cabin hospitals. During the deployment of the 5G allwireless network (which covered installation, configuration, testing, and activation), 6 network units were set up within 1 hour. This networking mode is suitable for either indoor or outdoor applications in any emergency scenarios in which it is necessary to set up an intranet connected to the host organization within a short time. Our successful experience points to the bright prospect of 5G wireless network to dwarf the conventional wired network when communication cost is not a constraint. In addition, the solution can also be used for multihospital network interconnection and rapid network recovery during the failure of wired network.

AUTHOR CONTRIBUTIONS
BZ designed the network and information system of the cabin hospital, and drafted the article. QW designed, tested and implemented the 5G all-wireless network solution. XZ and WZ developed and tested the information system of the cabin hospital. WW tested and implemented the 5G all-wireless network system. ZG contributed the conceptual design, network architecture diagram, and functional table of the information system.


Development and evaluation of a 3D annotation software for interactive COVID-19 lesion segmentation in chest CT

Segmentation of COVID-19 lesions from chest CT scans is of great importance for better diagnosing the disease and investigating its extent. However, manual segmentation can be very time consuming and subjective, given the lesions' large variation in shape, size and position. On the other hand, we still lack large manually segmented datasets that could be used for training machine learning-based models for fully automatic segmentation. In this work, we propose a new interactive and user-friendly tool for COVID-19 lesion segmentation, which works by alternating automatic steps (based on level-set segmentation and statistical shape modeling) with manual correction steps. The present software was tested by two different expertise groups: one group of three radiologists and one of three users with an engineering background. Promising segmentation results were obtained by both groups, which achieved satisfactory agreement both between- and within-group. Moreover, our interactive tool was shown to significantly speed up the lesion segmentation process, when compared to fully manual segmentation. Finally, we investigated inter-observer variability and how it is strongly influenced by several subjective factors, showing the importance for AI researchers and clinical doctors to be aware of the uncertainty in lesion segmentation results.

Introduction
Since the end of 2019, a new coronavirus disease  has started spreading across the world, leading to a pandemic that still represents a global health crisis. Up to January 10th, 2021, almost 90 million COVID-19 cases have been reported across 223 countries and territories, and 1 926 625 of these cases represent confirmed deaths [1].
The most common clinical manifestations of COVID-19 consist of fever, cough and dyspnea [2][3][4]. Such respiratory problems are often reflected in the outcome of chest X-ray and thoracic CT exams, which reveal pneumonia either bilaterally in both lungs or-less commonly-unilaterally. Pneumonia is most often identified as a ground-glass opacity in the X-ray or CT scan. However, other types of features can also be identified from the images, such as mixed ground-glass opacities and mixed consolidation lesions, reticulations, and crazy-paving patterns, especially in the later stages of the disease [5][6][7][8][9][10]. These image features are more evident in CT scans, which, compared to X-rays, have the advantage of providing a three-dimensional-and thus more informative-view of the lungs. Therefore, the use of CT for detecting the presence, type and extent of COVID-19 lesions is particularly promising, not only for diagnostic purposes, but also for better understanding the disease progression and possible treatment responses [11]. However, COVID-19 lesions are often diffuse and can vary in shape, size and position [12]. Thus, the manual delineation of such lesions from CT scans can be an extremely challenging and time-consuming task, as well as strongly affected by inter-rater variability. These issues are particularly problematic when studying a disease that is as new and rapidly spreading as COVID-19, since the international research effort to deal with the pandemic is moving at an extremely fast pace.
In recent years, deep learning-based methods have shown very good results within the field of medical image segmentation. Therefore, a few studies published this year have also employed such architectures to perform COVID-19 lesion segmentation automatically [6,[12][13][14][15][16][17][18], which would overcome the issues of time inefficiency and subjectivity that come with manual segmentation. Most deep learning-based segmentation methods are usually trained in a supervised fashion, i.e. they require a sufficiently large training dataset that already includes ground-truth segmentation masks. However, as previously discussed, the availability of manually delineated ground-truth is still largely lacking for COVID-19 lesions. Thus, some deep learning-based studies have tried to tackle this issue by proposing computer-assisted alternatives to the standard manual segmentation process.
In the work by Shan et al. [12], a combination of a V-Net [19] with a bottleneck structure [20] was employed to perform automatic lesion segmentation. The problem of ground-truth generation was here approached by adopting a human-in-the-loop strategy: only a limited batch of training data is delineated fully manually, while the rest of the ground-truth segmentations is created by manually correcting the outputs provided by the proposed segmentation network. These iterative manual corrections were shown to lead to a better segmentation accuracy, as well as a significantly reduced annotation time compared to a fully manual approach. On the other hand, in the study by Fan et al. [6] a semi-supervised learning strategy was used for training their proposed Inf-Net. This approach is similar to the one used by Shan et al. [12], but it avoids the manual correction steps of the network's output: the training set is iteratively enlarged by training the architecture with bigger and bigger batches that are generated by the segmentation network itself. Another method for alleviating the burden of ground-truth creation was recently proposed by Yao et al.: NormNet [17], a pixel-level anomaly model that synthesizes normal CT images from abnormal ones by removing COVID-19 lesions. This model is trained to learn a decision boundary between normal healthy tissue and lesions added synthetically in the training images.
The performance of such model was comparable to other supervised models. Finally, weakly supervised methods constitute another alternative to deal with unavailability of large scale labeled dataset. By embedding generative adversarial training into a segmentation network, GASNet [18] was developed to strengthen the performance of the segmentation network with only very small labeled data. While the generator synthesizes healthy images from unhealthy ones, the discriminator is trained to distinguish them, and the adversarial signals are integrated into a segmentation network.
The above-mentioned studies showed promising results, while also proposing interesting ways to integrate the radiologists' knowledge with automated AI systems. However, machine learning-based approaches have two main drawbacks: (1) a preliminary fully manual segmentation of a relatively large number of images is necessary for starting to train the networks; (2) programming skills are required in order to properly re-train and implement these models.
In our work, we developed a novel interactive tool for COVID-19 lesion segmentation, implemented within the software Mialab (http://mialab.org). The proposed tool aims at segmenting first the lungs and later the lesions from input CT scans, by alternating automatic steps (based on the use of level-set segmentation, as well as the integration of statistical shape models) with manual correction steps. This semi-automatic pipeline does not require any previous training using manually segmented CT scans. Moreover, the creation of a simple user interface facilitates the use of our tools for any user.
Our proposed pipeline aims at speeding up and facilitating the creation of ground-truth lesion segmentation masks by providing a user-friendly tool that does not require any additional programming effort. On the other hand, the ground-truth segmentations created with our method could also be employed as training datasets for later training more complex deep learning models in a supervised fashion. For each step, the graphic interface of Mialab is shown using an example thoracic CT scan as input to be segmented.

Materials and methods
The semi-automatic pipeline presented in this paper (see Figure 1) aims at identifying and segmenting COVID-19 lesions from chest CT scans. The workflow combines automatic segmentation methods with interactive editing and refinement, and it can be divided into four different sequential sections. The first one takes the chest CT scan as input and automatically produces a lung segmentation mask. The second section allows the user to refine manually the lung mask, and the third one takes the refined lung mask and performs an automatic segmentation to produce the COVID-19 lesion mask as output. Finally, the fourth section allows the user to perform a final editing of the COVID-19 lesions mask.

Automatic lung segmentation
The first section of the pipeline aims at producing a lung segmentation (volumes including both normal and abnormal lung parenchyma) and it can itself be divided into five main steps presented below: preprocessing, lung field estimation, initial model registration, right and left lung segmentation based on shape model fitting.

Pre-processing
Initially, a sequence of pre-processing operations is performed in order to transform the input CT image into a standard pre-defined image orientation and voxel resolution.
First, the image orientation is fixed according to the RAI matrix orientation (i.e. X axis: Right to Left; Y axis: Anterior to Posterior; Z axis: Inferior to Superior). Then, the image is down-sampled to a 3x3x3 mm voxel spacing, using a triangle convolution. Lastly, a 1x1x1 isotropic resampling is performed, using linear interpolation.

Lung field estimation
The down-sampled image is then automatically segmented into the two lungs. A threshold-based level set segmentation method [21] is used for this purpose. The present method requires some parameters to be specified in order to automatically run the segmentation: • A set of threshold values, which specify the voxel regions in which the segmentation is propagated. In this work, the lung regions to be segmented are identified in the range [-860, -200] HU. • A curvature factor, which constitutes an internal constraint that determines the degree of smoothness and regularization in the level-set curve. Such curvature factor was set to 0.6. The produced output is a lung distance map, defining the lung region estimation. A distance map represents the signed distance of each image voxel to the closest boundary of the segmented region, where 0 values indicate the segmentation boundaries, negative values are for the voxels outside the region and positive values are for the voxels inside.

Initial model registration
Before running the model-based level set segmentation, an affine registration is performed to register and match a lung shape model with the input image. The shape model is represented by a mean image and a set of images describing the Principal Components of Variation. It was generated by performing Principal Component Analysis (PCA) on a dataset of 14 lung distance maps, which were derived from lung segmentations from the VISCERAL challenge dataset [22]. The lung shape model's mean image is registered against the obtained lung segmentation distance map (see Section 2.1.2) and the affine transform is saved and used in the following steps of the model-based segmentation.

Right and left lung segmentation
The lung segmentation is performed in two sequential steps for each of the two lungs. The segmentation method used in this step is a model-based level set segmentation, presented in [23]. The method combines the threshold-based level set segmentation, described in Section 2.1.2, with a lung model fitting step. This latter step attempts to find the best match of the shape model into the voxel region defined by a previously-set lung look-up table, while also considering a level set curvature constraint. The relative influence in the segmentation between the model and the curvature factor is balanced by using a set of curvature and model weights, which were respectively set to 0.3 and 0.1 in the present work. Moreover, before fitting the model, the previously-computed affine transform (see Section 2.1.3) is used to obtain a rough and preliminary alignment between the shape model and the input CT image to be segmented. Once the model-based level set segmentation is performed, its two outputs (i.e. one for the left and one for the right lung) are saved as mesh files that can be used as inputs to the subsequent manual editing section of the pipeline.

Manual editing of the lung masks
After automatically segmenting the lungs, a set of manual and interactive segmentation editing tools are available for visual inspection, manual editing and refinement of the lung masks. The two lung regions are loaded as meshes that can be subsequently edited using five available tools, which are presented in the sections below. Two of them operate directly on the mesh points, while the other three work on the corresponding lung mask image. When working on the mask image, the lung meshes are first converted into a lung mask that, after the editing, is converted back into a mesh.

Magnet tool
This tool operates directly on the mesh points by displacing them according to the user's mouse clicks. A smooth transition of the displacement of the neighboring points is achieved by modulating the translation of points with a Gaussian function that takes into account the distance between the mouse click and each mesh point: the farther the point is, the smaller its displacement will be. The user can adjust the sigma parameter of the Gaussian function to change the size of the neighborhood that will be affected at each click.

TPS polyline tool
This tool operates in a similar way as the magnet tool mentioned above. Only it allows the users to simultaneously use multiple points to deform the mesh. The user can draw one or several polylines defining the 3D profiles where the mesh boundaries should be attracted onto, and the algorithm automatically interpolates and performs the best matching mesh points displacement. These polylines can be drawn in different slices and different views. They are used to create a 3D deformation field using the Thin Plate Spline (TPS) algorithm [24].

Poly-spline interpolation tool
When using this tool, the user can create a closed region from scratch by drawing several 2D splines in 3D space. The splines are then automatically interpolated to define a 3D closed surface using a radial basis function approach [25] that is then merged with the existing regions defined by the lung meshes.

Brush tool
The brush tool functions as an ordinary painting brush, except it works in 3D. Every mouse click will generate a 3D sphere of a size specified by the bush size. Unlike most other software, the 3D brush in our implementation operates on a distance map instead of binary mask, to ensure smoothness of the resulting mesh after editing. The user can then directly click and drag to paint over the lung mask in order to add or remove lung regions.

Click-and-drag smart painting tool
The click-and-drag tool is based on a real-time interactive level set segmentation method, which learns a discrimination function of the object region by analyzing image features around the line segment drawn by the user and the extended line segment beyond the mouse cursor. From the user's perspective, this tool may feel similar to some region-growing tool built in commercial image analysis software. However, since our solution is based on a level-set function, it guarantees local smoothness at the same time. More explanation of this smart painting tool can be found in [26].

COVID-19 lesion segmentation
After manually editing the lung mask, the input resampled image is masked, setting the background value to -2000 HU. Then, another threshold-based level set segmentation is performed to segment the COVID-19 lesions from the masked lungs. However, unlike what was described in Section 2.1.2, a multi-resolution approach was chosen to speed up the global computation time required by this segmentation step.
First, a lower resolution image (down-sampled with an isotropic rescaling of 0.5) is segmented. Then, the segmentation is run again in the high-resolution image by using the low-resolution output as seed region. The threshold range used to identify the COVID-19 lesion regions within the image voxels is -700 to 200 HU. The curvature factor is set to 0.6. The user can also adjust these parameters for each case to achieve a segmentation result that is more visually satisfactory.
Similar to what was performed for the two lung regions, the output lesion segmentations can also undergo a final interactive editing step by following the exact same procedure described in Section 2.2.

Method evaluation
The pipeline presented in this paper was tested on the 10 COVID-19 cases of the open access COVID-19 CT Lung and Infection Segmentation Dataset [27]. We excluded the 10 cases from Radiopaedia because their characteristics differ significantly from regular CT images; they have an 8-bit intensity range (instead of X-bit), 3D reconstructed image from these volumes turn out distorted.
Six different annotators were recruited to test the pipeline. They were split into two groups according to their different levels of expertise: a group of three radiologists, which we will refer to as the Expert Group, and a group of three annotators with a technical background which we will refer to as the Novice Group . All six annotators manually segmented the 10 CT exams using the present tool. Prior to the annotation, all annotators were trained by watching a 15 minutes-long video demo on two COVID-19 cases that are outside the 10 testing cases. The annotators were instructed to include ground-glass opacities, consolidations, reticulation and crazy paving sign in the segmentation, and to include the diffuse part surrounding the lesion.

Over-all volumetric analysis
The obtained lesion segmentations were first analyzed by computing the overall lesion volumes for each of the 10 images. These results were compared across the different annotator groups as well as with the available segmentation mask provided by Ma et al. as part of the downloaded dataset [27,28], which we will refer to as reference segmentation. Such volumetric measures allow to preliminary investigate the discrepancy in the results both between and within groups. The discrepancy between groups is indeed proportional to the difference in their mean lesion volumes, while the one within groups is proportional to the standard deviation within the same group.

Comparison between the Expert and the Novice Group
We then further compared the Expert and the Novice Groups by following both a volume-wise and a voxel-wise strategy.
As part of the volumetric analysis, we computed the intra-class correlation coefficient (using the ICC(A,1) model) [29], which evaluates the agreement in the volumetric measures of the lesions. This index was calculated for (1) the six annotators together, (2) the Expert Group only and (3) the Novice Group only. Moreover, both the mean absolute and the mean relative lesion volume differences were computed between and within groups. Finally, the linear correlation between the mean volumes and their standard deviations was analyzed.
On the other hand, to perform a voxel-wise comparison, we generated a Novice Group's and an Expert Group's consensus segmentation. These consensus segmentations were derived by performing voxel-wise majority voting with a vote of at least two annotators out of three for each of the two annotator groups. Once the consensus segmentations were obtained, we computed the Dice coefficient [30], the 95 th percentile Hausdorff distance [31] and the Jaccard similarity coefficient [32] between them. A further analysis of the spatial overlap between the lesions was then performed by calculating the generalized conformity index (GCI) [29]. Similarly to what was done for the ICC, the GCI was computed both globally and within each annotator group.

Comparison with the reference segmentation
The results from both the Expert and the Novice Group were compared also with the available reference segmentations. A Bland-Altman plot was first used to investigate the general volumetric agreement between the reference and the present annotators' segmentations. Moreover, their voxel-wise agreement was analyzed by computing Dice coefficient, Jaccard coefficient and 95 th percentile Hausdorff distance. The means and standard deviations of these evaluation metrics were calculated across the segmentation results from all annotators together, as well as separately for each of the two expertise groups.

Required annotation time
As a final metric for evaluating the usefulness and validity of the proposed tool, all annotators were asked to provide the time spent using the annotation tool for each of the ten cases. We then analyzed the mean and standard deviation of the time spent to annotate the images, as well as whether it changes according to the level of expertise.

Volumetric analysis of the segmented lesions
For each of the ten segmented images, we computed the lesion volumes according to all six annotators, as well as to the already provided reference segmentation. The means and standard deviations of such measurements were computed also within each of the two annotator groups, i.e. Expert and Novice (see Table S1 in the Supplementary Material). The plot in Figure 2 represents the volume distribution across groups for every case.
From Figure 2, it can be observed that the discrepancy in the volume measurements between and within groups varies across the different cases. It can be noticed that case 3 and 10 result in a relatively high disagreement both between and within groups. Case 2 and 4, instead, show a particularly higher disagreement within the Expert Group compared to the Novice Group. On the other hand, a higher disagreement within the Novice Group only can be observed for cases 1 and 8. Figure 3 shows the comparison of the consensus segmentations in some example slices from cases 2 and 10, which resulted, respectively, in a high and a low discrepancy between the results from the Expert and Novice Groups. In case 10, a general tendency of the Novice Group to underestimate the lesion segmentations can be observed.

Figure 2.
For each of the ten segmented cases (x axis), their lesion volume (y axis) is presented according to each of the annotators (colored dots). The solid lines connect the mean volumes computed within each of the three analyzed group, i.e. the Expert Group (in black), the Novice Group (in red) and the reference segmentation alone (in green). The 10 segmented cases are presented from the lowest (left of the x axis) to the highest (right) lesion volume according to the reference segmentation.

Comparison between the two rater groups
The agreement within and between the two annotator groups of the present study was further investigated in order to identify the importance and influence of the radiologists' knowledge to obtain reliable segmentation results. The comparison between the two groups was performed in both a volumewise and voxel-wise fashion.

Volume comparison
The volumetric agreement within and between the two annotator groups of the present study was investigated by computing the intra-and inter-group absolute volume differences, relative volume difference related to the group mean and the ICC coefficient. Table 1 shows that the highest agreement was obtained within the Expert Group (i.e. 0.955), and the lowest within the Novice Group (0.886).
In Figure 4, the relative standard deviations of each group's volumetric measures are plotted against their respective means, showing a correlation between the two. In particular, the two measurements resulted in a linear correlation coefficient of 0.96 for the Novice Group. On the other hand, within the Expert Group, one outlier can be observed (corresponding to case 4), where the standard deviation is higher than the mean (i.e. a relative standard deviation greater than 1 in Figure 4). Such outlier affects the linear correlation coefficient, which results to be equal to 0.58.

Voxel-wise comparison
The voxel-wise analysis of the agreement between the two annotator groups was first carried out by using the two consensus segmentations obtained through majority-voting. In particular, such segmentations showed a Dice coefficient of 0.845 ± 0.113 (expressed as mean ± standard deviation), a 95 th percentile Hausdorff distance of 44.714 ± 21.5 mm, and a Jaccard coefficient of 0.746 ± 0.164. Furthermore, the GCI was computed to further analyze the degree of spatial overlap between lesions within each of the investigated annotator groups (see Figure 5). A GCI of 0.588 ± 0.155 when performing a global analysis, i.e. considering all six annotators together. On the other hand, the Expert group and Novice Group alone showed a GCI of 0.650 ± 0.195 and 0.545 ± 0.149, respectively. As represented in Figure 6, the resulting GCIs within the two groups do not show a relevant correlation with the lesion volumes. The results are shown for cases 2 (top) and 10 (bottom), which resulted, respectively, in a high and a low agreement between Expert and Novice Groups. For each case, both the original CT image slice and its overlaid segmentation masks are reported. Green areas correspond to regions labeled as lesions only in the Expert consensus segmentation, red areas are labeled as lesions only by the Novice Group consensus, while yellow regions correspond to an intersection between the two groups. Table 1. Summarized volume measurements across all annotators ("Global" column), across the annotators with a medical background ("Expert Group"), across the annotators with a technical background ("Novice Group"), as well as between the Expert and Novice groups ("Inter-group"). The intra-class correlation coefficient (ICC) and its confidence interval were calculated using the ICC(A,1) model. Figure 4. The relative standard deviation (y axis) of each of the 10 volumetric measurements within every annotator group (Expert in black and Novice in red) is plotted against its respective mean (x axis) within the same group. The relative standard deviation value was computed by dividing the standard deviation by the respective mean.

Comparison with the reference segmentation
The segmentation results obtained from the annotators of the present study were finally compared with the reference lesion segmentation mask that was already provided as part of the dataset. Figure 7 shows a rather high agreement between the reference segmentation volumes and both the Expert Group and the Novice Group segmentation volumes. Such agreement appears to be stronger when dealing with smaller lesions. Moreover, the biggest volume differences can be observed when comparing the reference with the Expert Group, rather than the Novice Group.
Furthermore, a voxel-wise comparison was also conducted by computing the Dice coefficient, Jaccard coefficient and 95 th percentile Hausdorff distance between the reference segmentation and the annotator groups analyzed in the present study (see Table 2). All three evaluation metrics showed a slightly better result in the Novice Group compared to the Expert Group, when the reference segmentation is assumed to be the "ground-truth".

Required annotation time
Each annotator recorded the total time spent for segmenting each case, including both the time required to run the semi-automatic pipeline and the manual editing of the annotations using the available manual tools. The overall required annotation time resulted to be equal to 23 ± 12 minutes (expressed as mean ± standard deviation across all raters and all 10 cases). Within the Expert Group, the required time was 23 ± 10 min. On the other hand, the Novice Group reported an annotation time of 22 ± 14 min.

Figure 7.
Bland-Altman plot describing the agreement between the available reference segmentation and both the Expert Group (in black) and Novice Group (in red) segmentations. Table 2. Voxel-wise agreement between the reference segmentation and (1) all six annotators ("global" column); (2) only the three annotators with a medical background ("expert" column); (3) only the three annotators with a technical background ("novice" column). Dice coefficient, Jaccard coefficient and 95 th percentile Hausdorff distance, all expressed as mean ± standard deviation.

Discussion
In this work, we propose a user-friendly and semi-automatic pipeline for COVID-19 lesion segmentation. This tool showed promising results when used by both expert radiologists and users with a technical background, suggesting the possibility of applying it in a vast range of applications within the scientific community.
Overall, we see a relatively high inter-observer variation among our annotators in our COVID-19 lesion annotation experiments, which is not surprising as COVID-19 lesions tend to have ground-glass appearance with blurry boundaries. This is reflected in both the volume comparison and voxel-wise comparison. Through a questionnaire investigation, we found that most of the annotators are rather confident (average confidence level of 7.13 out of 10) with their annotations. The relatively large disagreement seems to mostly stem from their different perception and interpretation of what a lesion is and where its boundary is defined. Spending more time on each case or using a different tool for the annotation will not likely reduce the inter-observer variation greatly. However, spending more time training the annotator to achieve better consensus on their interpretation of the lesion boundary might help to reduce the differences. On the other hand, our experiment setup with less adequate training will be closer to the clinical reality. Our reported inter-observer variation on COVID-19 lesion segmentation could provide reference for future studies that aim to build large scale annotated COVID-19 chest CT databases. Also, future AI researchers should be aware of the rather high inter-observer variation associated with their training data when using these annotated images to train AI models. Moreover, clinicians should be aware of these uncertainties when using the quantitative COVID-19 lesion burden estimation produced by automated or semi-automated software to make their clinical evaluation of the patient's status.

Comparison between the Expert and the Novice Group
One focus of our quantitative evaluation of the segmentation results is to analyze the agreement in the segmentation results between and within two groups of annotators: the Expert Group, made up of three expert radiologists, and the Novice Group, consisting of three engineers lacking of a solid radiology knowledge.
By performing a volumetric analysis of the segmented lesions, we could come to two major observations. The first one is that there is no visible and consistent trend in the segmentation results of the two groups, since the discrepancy in volume measurements varies largely across the ten tested cases. This can be particularly observed from the measurements presented in Figure 2 and Table S1, as well as from the Bland-Altman plot in Figure 7. It is indeed noticeable that none of the two groups obtains consistently larger or smaller volumes, also when compared to the reference segmentation in the latter figure.
The second observation that we could see from our volumetric analysis is that satisfactory agreement could be obtained both between and within the groups. As expected, the Expert Group showed the highest within-group agreement (with an ICC of 0.955), reflecting their common expertise and background knowledge. However, the Novice Group also showed a rather high ICC (i.e. 0.886), which suggests that the proposed tool can help even non-expert users to achieve a good level of agreement. This hypothesis is further confirmed by the high ICC observed both globally and between the two groups, i.e. the present pipeline could allow users with different levels of expertise to achieve segmentation results that are in rather good agreement with those delineated by a radiologist. On the other hand, one factor seemed to consistently affect the within group-agreements: lesions with bigger volumes were associated with a higher standard deviation within each group. This can be noted from Figure 4, which shows that the relative standard deviation (i.e. normalized by the mean lesion volume) is relatively constant with respect to the lesion volume. However, this affected both novices and experts, showing that such difficulty is hard to overcome even when solid radiologic knowledge is present.
The analysis of the agreement between the two groups was then also performed in a voxel-wise fashion by using the two consensus segmentations. We are aware of the challenges of both performing accurate lesion segmentations (especially along the lesion boundaries) and of relying on just one consensus segmentation to represent a whole expertise group. However, an average Dice coefficient of 0.845 was achieved, which we believe to indicate a very promising result and a high degree of spatial overlap between the two groups across the analyzed cases.
The voxel-wise agreement was investigated also within groups by measuring their GCIs. Similarly to what was observed for the volumetric analysis, the Expert Group showed a higher agreement than the Novice Group also in terms of spatial overlap. This was again expected due to the level of expertise of the annotators. However, in contrast to the volumetric agreement, we could notice that the level of spatial agreement is much less correlated to the lesion volume (see Figure 6). Thus, we think that the main challenges of delineating geometrically accurate lesions are more related to factors such as image quality, disease stage and the rater's personal perception than to the simple lesion volume.

Comparison with the provided reference segmentations
The dataset used in the present study included, together with the original CT scans, also their respective lung and lesion segmentations performed by a team of radiologists [28]. Therefore, we decided to compare such reference segmentations with those produced by the annotators enrolled for the present study.
Comparing the lesion volume measurements from our annotators with those from the reference segmentation, we could observe that their agreement is higher when dealing with smaller volumes. This is consistent with what was observed in Section 4.1 regarding the comparison between Expert and Novice Group in terms of lesion volumes. Thus, this further strengthens the argument that the more spread the lesions are, the less reliable their volume estimations may become.
We then computed three voxel-based evaluation metrics (Dice coefficient, Jaccard coefficient and Hausdorff distance), using the manual reference segmentation as "ground truth". All three metricsboth when computed globally on all six annotators and when computed group-wise-indicated less spatial overlap compared to the analysis between our Expert Group and Novice Group using our proposed tool. This suggests that this tool guides the annotators-no matter what their expertise is-to achieve results that are particularly consistent with each other. We indeed found particularly relevant and interesting that our enrolled radiologists produced segmentations that appear to be more in agreement with those from the Novice Group, compared to those manually produced by another group of radiologists. It is therefore important to be aware that the segmentations produced in the reference study [28] could also be influenced by the radiologists' perception and training, making it hard to point out which segmentations are the most accurate.
We believe that the above-discussed observations show how hard it is to obtain reliable and consistent lesion segmentations, even when performed by expert radiologists. This indicates how the analysis of inter-rater agreement is fundamental for these applications and that a certain bias in the segmentation results cannot be easily eliminated. However, even if results can be affected by erroneous estimations and biases, our tool was shown to succeed at least in trying to reduce the discrepancy between different levels of expertise by providing a guided and user-friendly workflow.

Applicability of the proposed tool
Given the promising results observed in this study, we believe that the present tool can be useful for analyzing chest CT images of COVID-19 patients in several ways.
First of all, the possibility of segmenting both lungs and lesions together allows for measuring also the well-aerated lung volume, which can predict adverse outcome or death in COVID-19 patients [33]. Thus, our pipeline might allow risk stratification of hospitalized patients.
Another application is the generation of annotated training data, aiming to implement new machine learning-based and deep learning-based tools. Our tool can indeed aid the further automation of new segmentation approaches by providing lesion masks that can be used as "ground-truth" during the training process. Moreover, it can also allow the training of new automated diagnostic tools by directing them towards regions presenting important image features.
Apart from COVID-19-centered applications, we also believe that the proposed tool could be adapted for analyzing other lower respiratory tract infections or other diseases affecting the lung parenchyma, such as chronic obstructive pulmonary disease, interstitial lung disease, or tuberculosis.
All above-discussed applications are facilitated by the fact that the pipeline is partially automatic and partially involves manual adjustments. The possibility of manually adjusting the segmentation results throughout the workflow allows to obtain more reliable and controlled lung and lesion masks. On the other hand, the automated steps of the pipeline have two other main advantages. The first one is to provide less-expert users with more guidance on what may actually constitute a lesion and what not. By receiving a preliminary automatic segmentation, it is indeed going to be less likely for the user to miss certain lesions or to be unsure about the lesion boundaries. The second advantage of including automated steps into the pipeline is speed, since the annotators reported an average annotation time of 23 minutes. This average value was also equal to 23 minutes for the enrolled radiologists only, who represent the expertise group that would normally be involved in the manual delineation of lesion masks. In contrast, the time spent for manually generating the reference segmentations-which were included as part of the dataset employed in the present study-had been reported to be equal to 400 ± 45 minutes per scan [28]. Thus, this suggests that the proposed tool can significantly improve annotation efficiency.

Future work
In the future, we aim to further improve the functionalities and efficiency of the proposed pipeline in order to optimize the segmentation process further.
The present version of the segmentation tool uses pre-set values for the thresholds and smoothness parameters used in the automatic segmentation steps. Such fixed values were set purely empirically and are always the same for each input image. However, in the future we would like to make the selection of such values automatic and based on the statistical distribution of the voxel intensities. This would help to reduce the amount of manual tweaking required from the user.
Another possible future extension may consist in including an automatic registration of a reference lung shape into the lung of the subject being segmented. In this way, lesion locations could be related to specific lung segments. This would allow to compare the lesion distributions between different patients and to facilitate studying disease progression over time.

Conclusions
In this work, we presented an interactive and user-friendly software for segmenting COVID-19 lesions from input chest CT scans, implemented within the software Mialab (http://mialab.org).
The use of our proposed tool, which alternates automatic segmentation steps with manual corrections, led to promising results when employed by both radiologists and users with an engineering background. The proposed pipeline was shown to aid and speed up the process of creating lesion segmentation masks.
We also evaluated the inter-observer segmentation variability and how it can be influenced by several factors, ranging from the lesion volume to the rater's personal interpretation of where the lesion boundaries should be drawn. Our analysis could provide guidance and reference for future efforts to build large COVID-19 chest CT databases for AI model training. It indeed highlights that both AI researchers and clinical doctor should be aware of the uncertainty associated with the annotated image data and the quantitative volumetric measurements.


JOINT ESTIMATION OF STATES AND PARAMETERS OF LINEAR SYSTEMS WITH PARAMETER FAULTS UNDER NON-GAUSSIAN NOISES

Joint estimation of states and time-varying parameters of linear state space models is of practical importance for the fault diagnosis and fault tolerant control. Previous works on this topic consider the joint estimation in the Gaussian noise environment, but not in the presence of outliers. The known fact is that the measurements have inconsistent observations with the largest part of the observation population (outliers). They can significantly make worse the properties of linearly recursive algorithms which are designed to work in the presence of Gaussian noises. This paper proposes the strategy of the joint parameter-state robust estimation of linear state space models in the presence of non-Gaussian noises. The case of parameterdependent matrices is considered. Because of its good features in robust filtering, the extended Masreliez-Martin filter represents a cornerstone for realization of the robust algorithms for joint state-parameter estimation of linear time-varying stochastic systems in the presence of non-Gaussian noises. The good features of the proposed robust algorithm for joint estimation of linear time-varying stochastic systems are illustrated by intensive simulations.

INTRODUCTION
It is well known that it is very difficult to determine a large number of physical parameters which are integral part of complex systems. Despite the fact that many system parameters are available with some reasonable accuracy, a large number of parameters are known within a certain range, while some parameters are entirely unknown because manufacturers consider these data as proprietary information. For example, it is difficult to ensure precise determination of system parameters such as dimensions of certain components, leakage coefficients, friction coefficients, as well as static and dynamic friction forces due to the impossibility of their direct measurement or calculation and this causes great difficulty in control of pneumatic actuators [ [1]]. More precise knowledge of the system parameters increases the model quality, which causes better control performances. Hence, states filtering as well as parameters estimation can be key factors for performances, stability and accuracy of the systems.
Since Rudolf Kalman published his famous paper [ [2]], the Kalman filter (KF) has become the basis of many estimation processes in different application areas. In recent years, KF has encountered a renewed interest, due to an increasing range of applications [ [3], [4]]. Precise knowledge of system parameters and states is crucial for successful realization of many control techniques. Many modern engineering applications such as autonomous vehicles [ [5]], strain prediction for fatigue [[6]] or robotic manipulation tasks [ [7]] require real-time Kalman filtering framework with linear models.
It is usually too expensive to measure directly the system states. Self-applied state estimation methods assume that the system parameters are constant. In the real world, these parameters are always variable e.g. friction coefficients, temperature, pressure, or flow). The states estimation procedure with constant parameters will result in large errors when changing parameters. It is also known that the dynamic behaviour of complex systems is usually described by a linear stochastic state space model with time-varying parameters [ [8], [9]]. Therefore, methods by which parameter and state estimation can be obtained at the same time are required. A significant number of papers have been published on the theme of the Kalman filter application for parameters estimation of dynamic systems. One of the first papers dealing with this topic is [ [10]]. The convergence analysis of the extended Kalman filter for parameters estimation was analyzed in [ [11]]. The joint estimation of states and parameters using the Kalman filters is widespread [ [12], [13], [14]]. The joint estimation of states and time-varying parameters is of great practical importance for fault diagnosis and fault tolerant control [ [15]]. One of the biggest challenges in the design of flight control systems is a requirement for the flight of the aircraft to recover safely from structural damage and/or system faults. Regardless of whether the aircraft is equipped with a special control reconfiguration capability, reliable fault diagnostic information is extremely important to the pilot. The main challenge is the detection and isolation of incipient faults in the presence of modeling uncertainty and noise [ [16]]. The problem of the joint estimation in dynamic systems has been intensively studied and the basic estimation techniques are well established, but, because of the complex nature of dynamic systems, the application of techniques to these problems is not straightforward. These methods are quite popular. Inclusion of unknown parameters in the state vector allows easy implementation of the estimation algorithm, because the problem of parameters estimation in this case is solved using the standard filtering theory. In this way, a good joint estimation technique was obtained. Also, thus derived recursive estimation algorithm enables both offline and online realization.
On the other side, there is no such solution available for linear systems in the presence of non-Gaussian measurements. Because of that, in this paper, it is assumed that the measurement noise is non-Gaussian. Justification of this approach was confirmed in practice [ [17]]. Namely, the known fact is that the measurements have inconsistent observations with the largest part of the observation population (outliers). Their presence can destroy the good features of linearly recursive algorithms which are designed for estimation in the presence of Gaussian noises. Therefore, it is very important to design a robust algorithm which would be a little sensitive to outliers. The Huber's theory of robust statistics is crucial for the algorithm design whose robustness is achieved by introducing a nonlinear transformation of prediction error (Huber's function) [ [18], [19]].
The Masreliez-Martin filter is a frame for realization of the described algorithms. It is considered the case when the process noise has a Gaussian distribution, and the measurement noise has a non-Gaussian distribution. Some heuristic modifications have been made in order to improve features of the robust filters. Namely, in a posteriori filter matrix, Fisher information has been replaced with a derivative of the Huber's function. The benefits of such modified filters have been shown in [[20]]. Because of its good properties in robust filtering, the modified extended Masreliez-Martin filter represents a cornerstone for realization of the robust algorithm for the joint state-parameter estimation of linear time-varying stochastic systems in the presence of non-Gaussian noises.
Considering the unknown parameters of the dynamic system, for the purpose of pursuing the accuracy robust estimation, this paper proposes two kinds of strategies to estimate the state and parameter jointly. The state estimation and parameter identification are united by the joint parameter and state estimation. It is completely natural to put unknown, generally time-varying, parameters in the vector of states, after which the problem is reduced to the classic filtering problem. This paper considers linear state space systems with matrices which are parameter dependent. In that case, in order to obtain the robust algorithm for the joint estimation of states and parameters, we shall consequently face with a general nonlinear filtering problem. Conventionally, the joint state-parameter robust estimation problem in such systems is based on the extended Kalman filter.
The good features of the proposed robust algorithms are illustrated through intensive simulations.

JOINT ESTIMATION ALGORITHM IN CASE OF PARAMETER DEPENDENT MATRICES
In this paper, we consider state-space systems with time-varying parameters in the following form: are unknown state and parameter vectors, respectively. From a practical point of view, it is unreasonable to make assumptions about the fault characteristics and not to consider these as unknown time functions. The general form of parameters changing of the stochastic linear system is defined as follows: in which G is a priori known nonsingular matrix which is convenient for inclusion of a priori information on the phenomenon which is identified. The stochastic process () k  is zero-mean white noise whose covariance matrix () k  has the form: Input and measured output vector of the system are () It is assumed that the process noise is the zero-mean Gaussian white noise ( ) Qk is the covariance matrix. The measurement noise () ek has a non-Gaussian distribution with approximately normal distribution classes: in which the probability density () pe represents a mixture of the primary probability density 11  In some cases, the fault (k) p f could be expressed as a change in the system parameter, for example a change in the th i row and th j column element of the matrix A, the system can then be described as (1)-(2), see Fig. 1.

Fig. 1 Open-loop system with parameter faults in the system
This approach is based on the assumption that the faults are reflected in the physical system parameters such as friction, mass, viscosity, resistance, inductance, capacitance, etc. As indicated, the linear state space model is often specified up to the value of some parameters () k  . Since matrices A, B and D are dependent of parameters () k  and due to multiplying with state vector () xk , the system (1)-(2) is nonlinear. Hence, to obtain the parameter estimation recursively, we shall consequently face a general nonlinear filtering problem.
Our goal is to derive the robust algorithm for the joint state and parameter estimation of stochastic linear systems in the presence of outliers which maintains a low sensitivity in appearance of outliers. Using the joint state-parameter formulation, a unified estimation of states and parameters has been achieved. It is completely natural to put the parameters in the vector of states, after which the problem is reduced to the classic filtering problem of k th  order unified system (where k n p  , in which n is a number of estimated states and p is a number of estimated parameters). The robust extended Kalman filter can be used to estimate states and parameters of linear stochastic systems, after the joint state-parameter formulation: The extended system is given in a more compact form: where () zk denotes the extended state vector ( ) [ ( ) Based on the extended robust filter which is proposed in [ [20]], the robust algorithm for joint states-parameters estimation of system (7)-(8) has the following form: Here ˆ() zk is the estimate of extended state vector, and generally, () Pk denotes the filter covariance matrix ˆ( ) and its derivative: in which k  is appropriately defined parameter of the Huber's function, see Fig. 2 (22) in which N  represents the standard normal cumulative distribution function.

Fig. 2 Huber's function and its derivative
It can be shown that the mathematical expectation and the covariance matrix of transformed residuals Therefore, in the case that transformation () Tk is: the covariance matrix of the transformed residuals will be I . The following block structure of the matrix gain and covariance matrices is in accordance with the joint state-parameter formulation (6): Keeping this in mind, estimates of a priori and a posteriori extended state vectors, relations (10) and (14), are given by the following relations: Now, it is easy to express the estimates of the state and parameter vectors: In this way, the robust algorithm for the joint states-parameters estimation of linear stochastic systems in case of parameter-dependent matrices, has been derived. The robust algorithm is summarized in Table 1.
Initial conditions

SIMULATION RESULTS
Since the linear state space system with parameter dependent matrices is considered, we need to apply the extended Kalman filter based algorithm. Following results demonstrate superiority of the proposed robust joint estimation algorithm in presence of non-Gaussian noises in relation to the joint estimation algorithms based on the widelyused extended Kalman filter and extended Masreliez-Martin filter. The behavior of the algorithms will be considered on: The features of the proposed robust algorithm are considered on the model whose time-varying parameter vector has an expected value: The process noise () wk is the zero-mean white noise with covariance matrix: The covariance matrix of parameters has the form: The non-Gaussian distribution of the measured noise is given by 1      The presented results have shown that the widely-used extended Kalman filter (EKF) is very sensitive to the presence of non-Gaussian noises, as opposed to the proposed robust joint estimation algorithm. In order to show the robustness of the proposed robust joint estimation algorithm for systems with parameter faults in relation to other conventional and widely-used joint estimation algorithms, the algorithms are run 30 times independently, for different contamination degrees. Furthermore, it is particularly important to note that proposed robust estimation algorithm for systems with parameter faults (REA), see Table 2, keeps high performances in relation to joint estimation algorithms based on modern filters, such as: Gaussian sum filter (GSF), particle filter (PF) or interactive multiple modelling filter (IMMF). Table 2 provides statistical data based on 1000 iterations.  Table 2, it can be seen that the worst results obtained by the proposed robust joint algorithm is even better than the best result obtained by others, at a certain contamination degree. Furthermore, from Table 2, it can be clearly seen that the superiority of the proposed robust algorithm is greater in higher degrees of contamination. Also, it is important to note that in presence of non-Gaussian noises, the proposed REA is an attractive alternative solution which outperforms other modern algorithms and, at the same time, has a reduced complexity in comparison with them.

CONCLUSIONS
In this paper, the joint state and parameter robust estimation algorithm for stochastic linear time-varying systems, in presence of non-Gaussian noises has been proposed. The proposed algorithm has been used to solve the joint estimation problem of linear stochastic models where the conventional approaches fails. Since the system is described with a stochastic model with variable parameters, the natural frame for identification were robust Kalman filters. Because of their good features in robust filtering, the modified extended Masreliez-Martin filter was used as a basis in formulating the joint robust estimator of linear stochastic systems. The benefits of the proposed robust algorithms were illustrated through intensive simulations.