Error covariance analysis of a Karhunen-Loeve random field estimator

An error covariance analysis of a two-dimensional Karhunen-Loeve random field estimator (KLE) for gridded gravity data has been carried out without actually using the data. The analysis is based on the KLE developed by Bose (1983) for gravity compensation in an inertial measurement navigation system. The continuous gain coefficients Beta(mnj) and the continuous KL gain vector K(mn) were calculated using continuous measurements and the orthogonality relations of the KL eigenvectors in a continuous domain. A discrete version of the KLE was obtained to evaluate the discrete KL gain vector K(mn) by keeping the continuous Beta(mnj) and computing the KL eigenvectors on the two-dimensional grid configuration. The sensitivity of the KLE due to mismodeling, (in which the estimator is designed using a signal model other than the one used for the original signal) is examined in the case of a KL signal; a Markov signal; or attenuated white noise (AWN). Autocorrelation and cross correlation functions for the KL signal are given in an appendix.