Maximum-likelihood estimation of range, velocity, and acceleration using a linear FM train radar waveform

An efficient implementation of the maximum likelihood estimator (MLE) is presented for the estimation of target range, radial velocity and acceleration when the radar waveform consists of a wideband linear frequency modulated (LFM) pulse train. Analytic properties of the associated wideband ambiguity function are derived; in particular the ambiguity function, with acceleration set to zero, is derived in closed form. Convexity and symmetry properties of the ambiguity function over range, velocity and acceleration are presented; these are useful for determining region and speed of convergence for recursive algorithms used to compute the MLE. In addition, the Cramer Rao bound is computed in closed form which shows that the velocity bound is decoupled from the corresponding bounds in range and acceleration. A fast MLE is then proposed which uses the Hough transform (HT) to initialize the MLE algorithm. Monte Carlo simulations show that the MLE attains the Cramer-Rao bound for low to moderate signal-to-noise depending on the a priori estimates of range, velocity and acceleration.