Model parameter estimation for reciprocal Gaussian random processes

The problem of estimating the model parameters of a discrete-index reciprocal Gaussian random process from a limited number of noisy observations is addressed. The general case of a first-order multivariate process is analyzed, stating its basic properties and deriving a linear equation set that relates the model parameters (including the unknown variance of the observation noise) to the (generally nonstationary) autocorrelation function of the observed process. It generalizes to the reciprocal processes the so-called 'high-order Yule-Walker equations' for AR processes. Based on these results, a practical estimation algorithm is proposed.