Performance analysis of α- β- γtracking filters using position and velocity measurements

Abstract

This paper examines the performance of two position-velocity-measured (PVM) α-β-γ tracking filters. The first estimates the target acceleration using the measured velocity, and the second, which is proposed for the first time in this paper, estimates acceleration using the measured position. To quantify the performance of these PVM α-β-γ filters, we analytically derive steady-state errors that assume that the target is moving with constant acceleration or jerk. With these performance indices, the optimal gains of the PVM α-β-γ filters are determined using a minimum-variance filter criterion. The performance of each filter under these optimal gains is then analyzed and compared. Numerical analyses clarify the performance of the PVM α-β-γ filters and verify that their accuracy is better than that of the general position-only-measured α-β-γ filter, even when the variance in velocity measurement noise is comparatively large. We identify the conditions under which the proposed PVM α-β-γ filter outperforms the general α-β-γ filter for different ratios of noise variance in the velocity and position measurements. Finally, numerical simulations verify the effectiveness of the PVM α-β-γ filters for a realistic maneuvering target.

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

“…To evaluate the performance of the tracking filter, steady state errors for the reduction of measurement noise and the tracking of accelerating targets are used [11,12]. 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]).…”

“…(see [11,12]), where x ts,k is the true target position, used to evaluate the smoothing performance and E[ ] denotes the mean. The quantity σ 2 p is called the smoothing performance index.…”

“…This provides an index of the tracking performance for an accelerating target. When the true target position x tt,k = a c (kT) 2 /2 (a c denotes a constant acceleration) and measurement errors are not considered, the steady state predicted error is expressed as [11]:…”

“…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]:…”

“…Thus, the number of matrix operations is small compared with the Kalman filter and its variants [11].…”