A generalized maximum likelihood estimation algorithm for passive Doppler-bearing tracking

Estimation of the trajectory of a target from a passive sonar´s bearings and frequency measurements in the presence of multivariate normally distributed noise, with unknown inhomogeneous general covariance, is modelled as a nonlinear multiresponse parameter estimation problem. It is shown that maximum likelihood estimation in this case is identical to optimizing a determinant criterion which has a concise form and contains no elements of unknown covariance matrix. An effective Gauss-Newton type algorithm, using only the first-order derivatives of the model function, is presented to implement such estimation. The simulation shows that the proposed approach is superior to the traditional estimation methods especially under the condition of strong inhomogeneity of noise covariance and high correlation between different types of measurement noises