Self-consistent statistical models for the gravity anomaly, vertical deflections, and undulation of the geoid

Mathematical relationships exist between the anomaly, deflections, and undulation that constrain the models for the autocorrelation and cross-correlation functions of these processes. In previous work, constraints between the anomaly and deflections have been recognized, but constraints relating to the undulation have been ignored. In this paper, new models are proposed that take these constraints into account. One of these new models, the ‘third-order Markov undulation model’ is suggested for the analysis of inertial navigation system errors caused by uncertainties in the gravity field.