State estimation in range coordinate using range-only measurements

In some tracking applications, due to the sensor characteristic, only range measurements are available. If this is the case, due to the lack of full position measurements, the observability of Cartesian states (e.g., position and velocity) are limited to particular cases. For general cases, the range measurements can be utilized by developing a state estimation algorithm in range-Doppler (R-D) plane to obtain accurate range and Doppler estimates. In this paper, a state estimation method based on the proper dynamic model in the R-D plane is proposed. The unscented Kalman filter is employed to handle the strong nonlinearity in the dynamic model. Two filtering initialization methods are derived to extract the initial state estimate and the initial covariance in the R-D plane from the first several range measurements. One is derived based on the well-known two-point differencing method. The other incorporates the correct dynamic model information and uses the unscented transformation method to obtain the initial state estimates and covariance, resulting in a model-based method, which capitalizes the model information to yield better performance. Monte Carlo simulation results are provided to illustrate the effectiveness and superior performance of the proposed state estimation and filter initialization methods.