Passive Doppler-bearing tracking using a pseudo-linear estimator

In this paper an explicit pseudo-linear estimator for Doppler-bearing tracking is proposed. It overcomes the problems with the bias of earlier pseudo-linear estimators and with the nonlinear frequency measurement equation by using another representation than the Cartesian one and by using the logarithm of the frequency, respectively. It is fast, inherently stable, and easy to implement. The Doppler shift is, for a nonmoving own-ship, determined by the target velocities, while the bearing rate is determined by the same velocities divided by the range. The special representation in this paper uses this difference in behavior to give fast and bias free estimation of the range. Instead of iterating a weighted feast squares problem using bearing and frequency measurements simultaneously, the true bearings and the course are estimated in a bearings only step followed by a frequency only step, which estimates range and frequency. The range estimate then gives the speed estimate. Modifications for scenarios with multiple emitted frequency lines and/or for frequency lines that disappear during parts of a scenario are shown