Automatic Parameter Setting Method for an Accurate Kalman Filter Tracker Using an Analytical Steady-State Performance Index

Abstract

We present an automatic parameter setting method to achieve an accurate second-order Kalman filter tracker based on a steady-state performance index. First, we propose an efficient steady-state performance index that corresponds to the root-mean-square (rms) prediction error in tracking. We then derive an analytical relationship between the proposed performance index and the generalized error covariance matrix of the process noise, for which the automatic determination using the derived relationship is presented. The model calculated by the proposed method achieves better accuracy than the conventional empirical model of process noise. Numerical analysis and simulations demonstrate the effectiveness of the proposed method for targets with accelerating motion. The rms prediction error of the tracker designed by the proposed method is 63.8% of that with the conventional empirically selected model for a target accelerating at 10 m/s 2 .

Performance Analysis and Design Strategy for a Second-Order, Fixed-Gain, Position-Velocity-Measured (α-β-η-θ) Tracking Filter

“…The α-β-η-θ filter (and the α-β filter) is equivalent to steady state Kalman filters [31]. Thus, we derive the optimal gains for the motion model under consideration from the Kalman filter equations [4]…”

“…However, this filter is not optimal for other models, such as the frequently-used random-velocity model [9] and the diagonal Q, which does not include correlations in process noise [1,2]. Other process noise can be incorporated using arbitrary process noise; see [4]. The performance of this α-β-η-θ filter was evaluated in [31] only in terms of several simple numerical calculations, and strategies for designing tracking indices were not discussed.…”

“…These indices are more effective in evaluating steady state tracking accuracy than the error covariance matrix in the Kalman filter equations, as discussed by Ekstrand (see Section 9.8 of [12]). Moreover, a comprehensive performance index for measurement-error smoothing and tracking of an accelerating target based on these indices is presented in [4]. This comprehensive index is used for our proposed gain design strategy.…”

“…However, there are trade-offs between these indices. To consider these trade-offs and practical performance evaluations, a comprehensive performance index in smoothing and tracking was proposed and its effectiveness for the Kalman filter verified in [4]. This index corresponds to the root-mean-square (RMS) prediction error for a constant-acceleration target (considering sensor noise) and is calculated as:…”

“…Adaptive tracking techniques such as Kalman and extended Kalman filters [1][2][3][4][5] and particle filters [6,7] are commonly used for this purpose because of their accuracy. An alternative option is fixed-gain tracking filters, which have also been studied and used extensively for two reasons [8][9][10][11][12]:…”