Optimal subspace-based parameter estimation

Many important parameter estimation problems in time series modeling and sensor array processing using state-space models can be reduced to finding a solution to the equation U/sub 1/ F approximately=U/sub 2/, where noises in both sides of the equation are highly correlated because of a nonlinear transformation (the SVD) of the data matrix. Least squares or even total least squares solutions are not optimal and the complicated covariance structure in U/sub 1/ and U/sub 2/ does not allow a weighted total least squares procedure to be carried out. The authors propose an optimal subspace estimation method (OSE) to solve this equation in an approximate maximum likelihood sense. Instead of solving the equation directly, OSE first gets a maximum likelihood estimate of the structured subspace represented by U/sub 1/ and U/sub 2/. Parameters are then extracted from the estimated subspace. An array processing example shows that the performance of OSE achieves the Cramer-Rao bound.<>