Sequential nonlinear tracking filter with range-rate measurements in spherical coordinates

The three-dimensional CMKF-D with only position measurements is extended to solve the radar target tracking problem with range-rate measurements, where the errors between range and range-rate measurements are correlated. Firstly, a pseudo measurement is constructed by the product of range and range-rate measurements to reduce the high nonlinearity of the range-rate measurements with respect to the target state; then the consistent first two moment estimates of the converted measurement errors are derived by the nested conditioning method; finally, since the pseudo measurement is quadratic in the target state, the second-order EKF is used to implement the nonlinear tracking filtering, where the Cholesky factorization is used to decorrelate the converted position and pseudo measurement errors, thus the position and pseudo measurements can be sequentially processed to reduce the approximation error in the second-order EKF further. Monte-Carlo simulation results show that performance of the new tracking filter is improved greatly.