Bathymetric and oceanographic applications of Kalman filtering techniques

Ocean currents and seamounts (underwater mountains) can be mapped by analyzing data from satellite radar altimeters. This paper describes the application of Kalman filtering techniques to the analysis of such data acquired during the SEASAT mission. The altimeter data are modeled as samples from autoregressive random processes. Based on these models, matched filters are used to detect the characteristic nonstationarities in the altimeter data caused by seamounts and ocean currents such as the gulf stream. The geostrophic velocities of detected ocean currents are then estimated using Kalman smoothers. A useful formula is derived, which expresses the error power spectrum of the optimal fix lag smoother as a function of the lag and the error spectra of the optimal filter and the optimal infinite-lag smoother.