Kriging and Conditional Simulation of Gaussian Field

A Gaussian discrete field is considered, whose mean field and covariance matrix are known a priori. When a sample observation set contaminated with noise at some finite points is obtained, the best estimators are evaluated at observation points as well as at interpolation points, based on an unbiased least error covariance procedure. To visualize a sample field, a method to simulate the Gaussian field conditional on observation, is investigated. A special case is considered, in which the observation is free of noises and an effective method of simulation is proposed, which is a step by step expansion procedure to avoid the Cholesky or modal decomposition of the covariance matrix. This method is based on the orthogonality property between the best estimator and the corresponding error. Numerical examples are demonstrated to show the potential usefulness of the simulation method, and to show that the updating procedure by observation is identical to the Kalman filter algorithm when plural sets of observation are processed.