Range and speed estimation from frequency measurements alone

A time history of the received frequency of a sinusoidal source moving at constant velocity can determine the range and the magnitude but not the sign of the speed of the source. This paper presents an extended Kalman filter whose internal states are tailored to the observability of the problem to minimize nonlinearity within the filter. Nonlinear transformation of the internal filter states give range and speed. Simulation comparisons with Cramer Rao bounds indicate unbiased consistent estimation when the filter is initialized in a region of adequate frequency rate.