IEEE Transactions on Aerospace and Electronic Systems · 1979 · 468 citations · 8 references
ComputingRobotics EngineeringGlobal Navigation Satellite SystemsSensor FusionUncertainty QuantificationBayesian FilteringKalman FilteringState EstimationTracking SystemsBearing-only TrackingCovarianceExtended Kalman FilterExtended Kalman FilteringFilter StabilityInitializationState Vector EstimationTarget Tracking
The extended Kalman filter for bearings‑only target tracking is theoretically analyzed. The study proposes and discusses candidate methods to improve filter stability. The authors derive closed‑form state and covariance expressions and use them to show how bearing‑range error interactions can cause filter instability, and they propose candidate methods to mitigate this. The study finds that conventional initialization causes filter instability, that these findings are underutilized, and that alternative initialization and relinearization can substantially improve stability.
The extended Kalman filter applied to bearings-only target tracking is theoretically analyzed. Closed-form expressions for the state vector and its associated covariance matrix are introduced, and subsequently used to demonstrate how bearing and range estimation errors can interact to cause filter instability (i.e., premature covariance collapse and divergence). Further investigation reveals that conventional initialization techniques often precipitate such anomalous behavior. These results have important practical implications and are not presently being exploited to full advantage. In particular, they suggest that substantial improvements in filter stability can be realized by employing alternative initialization and relinearization procedures. Some candidate methods are proposed and discussed.
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Ridge Regression: Biased Estimation for Nonorthogonal Problems
Arthur E. Hoerl, Robert W. Kennard · Technometrics · 1970 · 1.9K citations