A transform-based covariance differencing approach for some classes of parameter estimation problems

A method of parameter estimation is presented for a class of problems in which the desired signal is embedded in colored noise with unknown covariance. The proposed algorithm does not require multiple estimates of the signal covariance matrix; instead, it uses a priori knowledge of the structure of the noise covariance matrix to transform the array covariance matrix in a way that leaves its noise component unchanged while the signal component is transformed in some appropriate manner. The noise component is then eliminated by forming the difference of the original and transformed covariance differencing methods to be applied to a wider class of problems than was previously possible. This is illustrated by applying the algorithm to the problems of bearing estimation, resolution of overlapping echos, and transient response analysis. Simulation results demonstrate that the technique affords significant improvement in certain situations over conventional methods.>