Maximum Likelihood Estimation of Range of Polynomial Amplitude Modulated Complex Scatterers

We analyze the maximum likelihood estimator (MLE) of range from frequency samples of a radar return consisting of a superposition of complex scatterers whose amplitude have a polynomial amplitude dependence in frequency. Such scatterers arise from target components that contain edges, like flat plates, dihedral and trihedral reflectors, cones, cylinders and other basic geometric shapes. When the MLE of the linear prediction coefficients is used to estimate the scatterer's range, assuming constant amplitude, very closely spaced roots arise from the linear prediction polynomial. The mean square error (MSE) of the multiple root, corresponding to polynomial amplitude dependence, is computed in closed form in the presence of noise. A better approach is to constrain the linear prediction coefficients to account for the multiple roots while doing maximum likelihood estimation of these coefficients. Its mean square error performance is given by the corresponding Cramer-Rao bound (CRB), is computed for the repeated root sinusoids and is shown to be significantly more accurate than the MSE of the distinct(non-repeated) roots model.