MAP-based estimation of the parameters of non-stationary Gaussian processes from noisy observations

The paper proposes a modification of the standard maximum a posteriori (MAP) method for the estimation of the parameters of a Gaussian process for cases where the process is superposed by additive Gaussian observation errors of known variance. Simulations on artificially generated data demonstrate the superiority of the proposed method. While reducing to the ordinary MAP approach in the absence of observation noise, the improvement becomes the more pronounced the larger the variance of the observation noise. The method is further extended to track the parameters in case of non-stationary Gaussian processes.