A cauchy system for on-line estimation in two-dimensional stochastic fields

Linear least-squares estimation problems of stationary and nonstationary continuous signals in the presence of white measurement noises in two-dimensional (2-D) stochastic fields are considered in this paper. An initial-value solution is presented for the solution to a 2-D Fredholm integral equation with a symmetric semi-degenerate covariance kernel. The solution technique is an invariant imbedding. Introducing auxiliary functions, a new linear least-squares estimator in 2-D stochastic fields based on the covariance information is constructed from the resultant initial-value solution.