Initialization and tracking using Doppler-biased multistatic time-of-arrival measurements with linear frequency modulated waveforms

We investigate the target tracking problem in a multistatic sensor configuration in which the system uses Doppler tolerant waveforms (DTW), specifically the linear frequency modulated (LFM or chirp) waveforms, for target illumination. DTW introduce a bias to the true time-of-arrival (TOA), as a result of which the corresponding range measurement accuracy is degraded when this bias is ignored. It might be thought that with N sensors measuring the time delays (which have different combinations of range and range rate vectors) one would have complete observability from a single frame. However, N such measurements do not yield the desired observability regardless of N and the sensor geometry. An important part in the design of a tracking filter using nonlinear measurements is the initialization: the initial state estimate should be unbiased and the associated covariance should be consistent with the errors. This paper presents a maximum likelihood based method as well as a simpler iterative bias cancellation method to estimate the target initial state from two observation frames. The iterative method makes it possible to obtain unbiased initial position and velocity estimates by canceling out the Doppler bias. Simulation results confirm that both estimators are efficient and the filter initialized by either estimator is statistically consistent. We also analyze the effect of the range-Doppler coupling coefficient on the performance of the filter. As is so often the case, the positive coefficient (which corresponds to upsweep) is shown to be superior to the negative one (downsweep).