Timothy S. Murphy, L3Harris Technologies; Waqar Zaidi, L3Harris
Keywords: Dempster-Shafer, JPDA, Estimation, SSA, Data Association
Abstract:
Abstract:
Space situational awareness and space domain awareness by necessity must be built on a solid framework of data association, data integrity, and timeliness to support orbit estimation and mission success. Data association is complicated by the often thousands of simultaneous observations and objects being processed at any given time. It is particularly challenging for tracking and custody of multiple objects with similar orbits. The data association problem can result in false and missed detections due to uncertain dynamics, maneuvering objects, closely space objects, and association over long propagation intervals between observations. Orbit estimation is further complicated by the scale of intelligently operating a system with thousands of objects which challenges most processing platforms. This paper proposes a framework to address these issues based on Dempster-Shafer theory and joint probabilistic data association to better express how well objects are being tracked. In particular, the belief and plausibility of an object being actively tracked are derived in this paper and directly incorporated into the data association equations. These two measures are shown to provide contextual information on if an object is being actively tracked, while solving some problematic data association situations. The value is demonstrated by representative use cases based on an actual live data collection and processing system.
Overview:
Estimation and tracking of a space object in a standard Bayesian framework assumes the object is explicitly within a defined probability distribution [1]. Any space situational awareness (SSA) system tasks sensors to acquire observations on those objects, uses obtained measurements to update those estimates, and therefore continues to track the objects [2], [3]. Most such systems, at some point in their processing, attempt data association is such a way to assure the observations used for estimation are consistent with the estimate itself; observations don’t have license plates so the system itself must determine the association. The most popular such system is joint probabilistic data association (JPDA) which computes the conditional probabilities between n observations and m space objects based on Mahalanobis distance [4], [5]. In reality, resident space object can be affected by unmodeled dynamics such as high area-to-mass ratio (HAMR) objects and active maneuvering. From a data standpoint, estimation is muddled by closely-spaced objects, weather, sensor failure, noise and more. This means that a SSA system will invariably be hampered by objects being lost or simply not seen for long periods of time.
This paper acknowledges three states of estimation for a space object: 1) an object is being actively tracked, 2) the object has been lost and the system knows it, and 3) the object is not being actively tracked but the system doesn’t know if its been lost. The case for 1) is fairly clear, 2) occurs when the system tasks on an object and doesn’t find it. Case 3) can happen due to coverage gaps in a sensor network, weather, sensor failures, or a system operator choosing not to look for a low priority object. Dempster-Schafer theory (DST) is a non-Bayesian alternative to estimation which explicitly accounts for the ambiguity described in these three states [1], [6], [7]. In DST, probability is replaced with two metrics, belief and plausibility. Belief is more analogous to probability as it is effectively the “belief” that something is true. Plausibility is inversely the “belief” that something is not true. DST goes on to define ignorance as the gap between belief and plausibility, a metric by which a system can measure what it does not know. Applying this framework to the above three cases, 1) corresponds to high belief and plausibility and 2) corresponds to low belief and plausibility. Case 3) corresponds to low belief (we aren’t actively tracking the object) but high plausibility (our propagated state knowledge could be perfectly accurate). The framework being proposed is this: dynamically estimating both belief and plausibility of custody on a per object basis. This paper provides a derivation for directly estimating belief and plausibility of custody within the standard JPDA and Kalman filter framework.
One interesting result of this logic is achieved within the new data association equations. An object that is not being actively tracked should not be updated by a Kalman filter. This is best exemplified by a dim and hard to detect object: such an object may pass through a field-of-view of a sensor but produce no observations. A standard JPDA system would erroneously associate this object to noise and incorrect objects. By including belief of custody in JPDA, objects with no belief of custody default to no update; noise is rejected as the evidence of false detection is overwhelming. Instead, the mathematics require enough observations to build up belief in custody before updating the underlying state. This process has greatly reduced the number of cross tags and erroneous associations in the L3Harris SpaceSentry system.
The final paper will provide a derivation of the update equations for belief and plausibility and the JPDA equations that directly use belief. Examples will be shown demonstrating the efficacy of the algorithms on multiple closely spaced objects.
References:
[1] Glenn Shafer. Dempster-shafer theory. Encyclopedia of artificial intelligence, 1:330–331, 1992.
[2] Travis Blake, M S´anchez, J Krassner, M Georgen, and S Sundbeck. Space domain awareness. In Advanced Maui Optical and Space Surveillance Technical Conference, 2011.
[3] Barry Schiff, James Foster, William McShane, and Kameron Simon. Attaining situational understanding in the space domain. 2017.
[4] Thomas E Fortmann, Yaakov Bar-Shalom, and Molly Scheffe. Multi-target tracking using joint probabilistic data association. In 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, pages 807–812. IEEE, 1980.
[5] Seyed Hamid Rezatofighi, Anton Milan, Zhen Zhang, Qinfeng Shi, Anthony Dick, and Ian Reid. Joint probabilistic data association revisited. In Proceedings of the IEEE international conference on computer vision, pages 3047–3055, 2015.
[6] Arthur P Dempster. A generalization of Bayesian inference. Journal of the Royal Statistical Society: Series B (Methodological), 30(2):205–232, 1968.
[7] Glenn Shafer. A mathematical theory of evidence, volume 42. Princeton university press, 1976.
Date of Conference: September 15-18, 2020
Track: SSA/SDA