Statically Fused Converted Position and Doppler Measurement Kalman Filters

The work presented in this paper makes two contributions for exploiting Doppler (range rate) measurements in tracking systems. First, a new linear filter, the converted Doppler measurement Kalman filter (CDMKF), is presented to extract nonlinear pseudostates from converted Doppler measurements (i.e., the product of the range measurements and Doppler measurements). The pseudostates are constructed from the converted Doppler and its derivatives. The linearly evolving equations of the pseudostates are derived for common target motion models. The second contribution of this paper is using the CDMKF along with the converted position measurement Kalman filter (CPMKF), in which only the position measurements are used, to establish a new filtering structure, statically fused converted measurement Kalman filters (SF-CMKF). The resulting states of CPMKF and CDMKF are combined by a static minimum mean squared error (MMSE) estimator, where the nonlinearity and correlation between the pseudostates and the Cartesian states are handled simultaneously, to yield the final state estimates. The dynamic nonlinear estimation problem is converted into dynamic linear estimation followed by static nonlinear fusion. The estimation accuracy can be enhanced by incorporating the Doppler measurements via the linear CDMKF, while the filtering stability can be improved by dealing with nonlinearity outside the filtering recursions. Monte Carlo simulations and comparison with the posterior Cramer-Rao bound demonstrate the effectiveness of the CDMKF and SF-CMKF.