Motion modeling and state estimation in range-Doppler plane

The problem of motion modeling in range-Doppler (R-D) plane as well as range and Doppler estimation is investigated. The time evolving equations of target range and Doppler are formulated, for two common Cartesian motions, nearly constant velocity (NCV) and constant turn (CT). This builds the foundation for target tracking based on multisensor data fusion using only range and Doppler measurements and other applications. The R-D state vectors are constructed by range, Doppler and the derivative of the product of range and Doppler with respect to time. The state equations corresponding to these motions are derived by explicit substitutions according to the relationship between R-D states and Cartesian states. The unscented Kalman filter (UKF) is employed to extract R-D states from range and Doppler measurements. The filter initialization is derived by two-point differencing methodology where the correlation among the state components is handled properly. At last, the posterior Cramer-Rao Lower Bound (PCRLB) for state estimation in R-D plane is provided, and the performance of the proposed method is compared against the PCRLB and the existing methods using approximate models in the numerical experiments. The simulation results demonstrate the effectiveness of the proposed models and filtering methods. The enhancement of estimation accuracy benefits the data fusion using range and/or Dopper estimates.