A single observation passive location algorithm based on phase-difference and Doppler frequency rate of change

The single observation passive location is the technique used by a single observation to determine the position and velocity of an emitter from the electromagnetic wave emitted by a target. The key point is how to obtain the position and the velocity of the emitter with high speed and precision. Up to now, two popular passive location methods have been put forward. They are Bearing-only (BO) and phase-difference rate of change (PRC) respectively. With adding the information of phase-difference rate of change, the latter performs distinctly better in the precision and the speed than the former. However, the PRC method has a bad performance and high requirement for the initial value when obtaining the position and the velocity simultaneously. This paper proposes a location and tracing algorithm based on the information of phase-difference, phase-difference rate of change and Doppler frequency rate of change. The algorithm can be used to estimate not only the position and the velocity of the fixed emitter, but also those of the moving single observation and target. The observability conditions and the error of the algorithm (called PFRC) are analyzed. Moreover, the simulation based on Extend Kalman Filter (EKF) shows that PFRC is superior in precision and speed.