Consistent State Estimation for Very Long Range Radars
MIT Lincoln Laboratory Lexington United States
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Consistent state estimation for very long range radars is difficult because the true radar measurement noise covariance deviates significantly from the Gaussian ellipsoid approximation used in most track filters. Ad hoc inflation of the radar range covariance can improve inconsistency at long range, but usually at the expense of significant range accuracy. Here we present a new converted measurement extended Kalman filter algorithm CM3EKF for accurately estimating target states at very long ranges. It uses a third-order Taylor series approximation of the converted measurement noise covariance to calculate automatically the minimal range covariance inflation necessary to maintain track consistency without sacrificing range accuracy. In addition, the state covariance is automatically adjusted to compensate for approximation errors introduced by linearizing about a noisy track state. As the filter settles with time, the range inflation and state covariance compensation automatically decay to zero. In a systematic comparison with six other commonly used filters including the unscented Kalman filter UKF and regularized particle filter RPF, we show that the CM3EKF is the most consistent and has only slightly worse convergence than the RPF but is five orders of magnitude less computationally expensive and is less sensitive to tuning parameters.