Effects of measurement unobservability on neural extended Kalman filter tracking

Stephen C. Stubberud; Kathleen A. Kramer

doi:10.1117/12.818384

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11 May 2009 Effects of measurement unobservability on neural extended Kalman filter tracking

Stephen C. Stubberud; Kathleen A. Kramer

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Proceedings Volume 7336, Signal Processing, Sensor Fusion, and Target Recognition XVIII; 733605 (2009) https://doi.org/10.1117/12.818384
Event: SPIE Defense, Security, and Sensing, 2009, Orlando, Florida, United States

Abstract

An important component of tracking fusion systems is the ability to fuse various sensors into a coherent picture of the scene. When multiple sensor systems are being used in an operational setting, the types of data vary. A significant but often overlooked concern of multiple sensors is the incorporation of measurements that are unobservable. An unobservable measurement is one that may provide information about the state, but cannot recreate a full target state. A line of bearing measurement, for example, cannot provide complete position information. Often, such measurements come from passive sensors such as a passive sonar array or an electronic surveillance measure (ESM) system. Unobservable measurements will, over time, result in the measurement uncertainty to grow without bound. While some tracking implementations have triggers to protect against the detrimental effects, many maneuver tracking algorithms avoid discussing this implementation issue. One maneuver tracking technique is the neural extended Kalman filter (NEKF). The NEKF is an adaptive estimation algorithm that estimates the target track as it trains a neural network on line to reduce the error between the a priori target motion model and the actual target dynamics. The weights of neural network are trained in a similar method to the state estimation/parameter estimation Kalman filter techniques. The NEKF has been shown to improve target tracking accuracy through maneuvers and has been use to predict target behavior using the new model that consists of the a priori model and the neural network. The key to the on-line adaptation of the NEKF is the fact that the neural network is trained using the same residuals as the Kalman filter for the tracker. The neural network weights are treated as augmented states to the target track. Through the state-coupling function, the weights are coupled to the target states. Thus, if the measurements cause the states of the target track to be unobservable, then the weights of the neural network have unobservable modes as well. In recent analysis, the NEKF was shown to have a significantly larger growth in the eigenvalues of the error covariance matrix than the standard EKF tracker when the measurements were purely bearings-only. This caused detrimental effects to the ability of the NEKF to model the target dynamics. In this work, the analysis is expanded to determine the detrimental effects of bearings-only measurements of various uncertainties on the performance of the NEKF when these unobservable measurements are interlaced with completely observable measurements. This analysis provides the ability to put implementation limitations on the NEKF when bearings-only sensors are present.

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Stephen C. Stubberud and Kathleen A. Kramer "Effects of measurement unobservability on neural extended Kalman filter tracking", Proc. SPIE 7336, Signal Processing, Sensor Fusion, and Target Recognition XVIII, 733605 (11 May 2009); https://doi.org/10.1117/12.818384