Some initial-value methods for sequential estimation problems via invariant imbedding

Abstract Under the assumption that the noise processes are either additive white or colored Gaussian, some Cauchy systems suitable for real-time calculation are presented for the solution of the Fredholm integral equation of linear least squares estimation theory when the signal processes are nonstationary by use of the invariant imbedding approach and the nonminimal covariance factorization technique. It is shown that filtering and fixed-point smoothing equations for the class of ‘degenerate’ or ‘semi-degenerate’ kernel in the Fredholm equation can be easily obtained from the derived Cauchy systems.