Nearly constant acceleration model for state estimation in the range-Doppler plane

The problem of motion modelling in the range-Doppler (R-D) plane as well as range and Doppler estimation for the Cartesian nearly constant acceleration motion, which is a common manoeuvering motion, is investigated. The temporal evolution equation is derived based on the state vector consisting of target range, Doppler and derivatives of the product of range and range rate versus time. In this way, the measurement equation of range and Doppler measurements can be maintained in a desirable linear-Gaussian structure. Based on the non-linear state equation and the linear measurement equation, the unscented Kalman filter is adopted to tackle the non-linear filtering problem. The corresponding filter initialisation method is developed based on the two-point differencing method. Explicit expressions of the initial state estimates and the initial covariance matrix are presented in analytic forms where the correlation among the state components is handled properly. The posterior Cramer-Rao lower bound (PCRLB) is provided for state estimation in the R-D plane. Comprehensive comparisons of the proposed method against the existing R-D state estimation methods using approximate models, Cartesian state estimator and PCRLB are carried out in simulations to demonstrate the validity and correctness of the proposed motion model and estimation method.