Including TDMA Range Measurements in Snapshot Integrity Algorithms
Brandon Weaver, Gianluca Zampieri, and Okuary Osechas, German Aerospace Center (DLR), Germany
Location: Beacon B
Navigation systems using time division multiple access (TDMA) signals—meaning individual transmitters are allocated a finite time interval in which to transmit—must allow for a user to receive these signals sequentially. If a user in motion receives TDMA ranging signals and incorporates them into a batch processing scheme, an error is introduced in the range measurement that is referred to as the mobility error. This mobility error represents the difference in geometric user-transmitter range at the time of measurement reception and at the time of measurement application. For example, an aircraft collecting sequential TDMA range measurements that processes them in batch at a scheduled position solution update time will have range measurements that are outdated relative to the aircraft’s current position. Typically, such systems make use of sequential processing algorithms that avoid introducing a mobility error to the range measurement when computing a position. If batch processing cannot be avoided, such as in the case that a snapshot RAIM-like algorithm implementation is needed, then the mobility error must be considered when incorporating these kinds of measurements into such a scheme.
Sequential measurements are normally used in combination with some variation of Kalman filter, which easily processes measurements as received to update the estimated state vector . Operational TDMA-based navigation systems such as the JTIDS RelNav function frequently include inertial or air data sensors to propagate a user’s position with dead reckoning techniques between TDMA range signal receptions, again usually implemented with a type of Kalman filter . This type of sensor processing handles the effect of user motion between measurement reception and application seamlessly.
One application where batch processing is necessary is the snapshot fault detection approach of the Receiver Autonomous Integrity Monitoring (RAIM) algorithm that is well-established in civil aviation . This algorithm operates on the principle of checking consistency of redundant measurements to the computed position. For sequential measurements received by a user in motion, this is problematic due to each measurement only applying at the point of reception. No “snapshot” is possible because each measurement applies to a different point of reference, precluding any consistency at a single epoch. A way of characterizing the mobility error to allow sequential measurement inclusion in a RAIM-like approach is necessary for TDMA-based systems wanting to leverage this widespread method of integrity monitoring.
In order to use sequential range measurements for a user in motion in any snapshot-based fault detection method, the mobility error must be statistically characterized. This is necessary as the RAIM algorithm considers the measurement errors in determining test statistic thresholds and detection probabilities. The snapshot approach also requires that the TDMA measurements can be treated as if received at a single epoch in order for the principle of consistency among redundant measurements to apply. A method to represent the TDMA measurements at a common point of reference is therefore also necessary if they are to be used in a RAIM algorithm.
A mathematical expression for the mobility error is derived and the predicted statistical characteristics are analyzed. This information is used to develop of method of referencing the sequential measurements to a virtual epoch so that the principles of RAIM apply. The performance of the resulting RAIM algorithm is then compared via simulation to a standard, batch measurement RAIM receiver.
As navigation systems become more diverse and include more varied sensor types and operation principles, it is probable that sequential range measurements become more common. Expanding the RAIM-style use case to systems such as this allows a convenient method of targeting integrity requirements in a well-established manner, simplifying the adoption of new systems to the navigation community. Furthermore, the methods shown here could reveal additional ways of combining other non-conventional sensors to a single RAIM framework.
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