1. Field of the Invention
The present invention relates to fault detection and isolation in any system whose system state is observed with an overdetermined set of measurements. More particularly, the present invention relates to fault detection and isolation in navigation systems.
2. Description of the Related Art
Navigation systems, such as those used in aircraft, determine position through the use of ranging systems. Ranging systems ascertain an aircraft's position by simultaneously determining the aircraft's distance from several transmitters, where the location of each transmitter is known.
The ranging systems can be either passive or active. An active ranging system uses distance measuring equipment (DME) to determine a distance from a ground based transmitter. The DME transmits a signal to the ground station and then after a fixed delay, the ground station transmits a signal to the DME. By measuring the round trip time of the signal, the DME determines the aircraft's distance from the ground station.
An example of a passive ranging system is the global positioning system (GPS). In this system the aircraft GPS equipment passively receives transmissions from a global positioning satellite to determine the aircraft's distance from the satellite. The distance from the satellite is determined by the amount of time that it takes for the signal to travel from the satellite to the aircraft. The GPS system in the aircraft is not synchronized to the satellite, and therefore does not know precisely when the satellite transmitted its signal. As a result, the range measured by the aircraft's GPS equipment contains an offset that corresponds to the amount of time by which the satellite and aircraft GPS equipment are out of synchronization. The range measurements containing this offset are called pseudorange measurements. The offset as well as the position is determined by taking several pseudoranges and solving the resulting simultaneous algebraic equations in accordance with well known procedures.
Whether using an active or passive ranging system, the navigation system uses the range measurements to determine the aircraft's position. The range measurements are used to determine lines of position (LOP), where each LOP is a portion of a circle having the satellite or ground station at its center. In a two dimensional navigation system a LOP defines a line, and in a three dimensional navigation system a LOP defines a surface. In the case of an active system, the radius of the circle is equal to the aircraft's distance from the satellite or ground station. In a passive system the radius measurement includes the above described offset. FIG. 1 illustrates three LOPs. LOPs 2, 4 and 6 were determined by calculating the distance from the aircraft to three different transmitters. Point 8 corresponds to the intersection of the three LOPs and indicates the aircraft's position.
FIG. 2 illustrates three LOPs that do not intersect in a single point. The three LOPs do not intersect in the same point because one of the LOPs contains an error resulting from an incorrect determination of the aircraft's distance from the ground station or satellite transmitter. This error could result from an excessive delay in the retransmit from a ground based transmitter or it could result from a satellite transmitter being out of synchronization with other satellite transmitters. In reference to figure two, LOP 12, 14 or 16 could be incorrect. This results in three possible aircraft positions shown by intersecting points 18, 20 and 22. Since it is not known which LOP is incorrect, the aircraft's position is estimated to be somewhere within area 24 which is bounded by the three LOPs. The distances from the estimated position to the several LOPs are called error residuals. In the past, the integrity of this type of navigation system was monitored by measuring the size of the residuals. When the RMS (root means square) of the residuals became greater than a threshold, an integrity alarm was sent to a pilot. Unfortunately, there was no fault isolation to identify the LOP that was in error.