Statically Fused Converted Measurement Kalman Filters for Phased-Array Radars

In this paper, statically fused converted measurement Kalman filters (SF-CMKF) are developed for target tracking using measurements reported by phased array radars in direction cosine coordinates. First, the conversions of position and Doppler measurements and the estimation of the mean and variance of the converted measurement errors are explicitly derived. Then, the filtering procedure of the SF-CMKF working in Direction Cosine coordinates (SF-CMKFcos) is formulated. The pseudostate vector is constructed and the pseudostate equation for the nearly constant velocity motion model in three-dimensional Cartesian coordinates is deduced. The converted Doppler measurement Kalman filter (CDMKF) and converted position measurement Kalman filter (CPMKF) are developed to extract information from position and Doppler measurements in Direction Cosine coordinates, respectively. To generate the final target state estimates, the pseudostate estimates from the CDMKF and the Cartesian-state estimates from the CPMKF are fused statically under the minimum mean squared error criterion. The nonlinear static fusion procedure is maintained outside the dynamic filtering recursions, which keeps the nonlinear approximation errors from being accumulated recursively. Finally, a comprehensive performance comparison is carried out using numerical simulations, where the proposed SF-CMKF is evaluated against several commonly used filters that incorporate Doppler measurements for tracking in Direction Cosine coordinates. Simulation results indicate that the proposed filter is superior to the existing filters, especially in extreme situations where the position measurement errors are large.