Ship navigation for geophysical applications using Kalman‐filtered GPS fixes

Abstract

Based on a state vector representation of ship position and velocity, we have developed a Kalman filter that provides accurate navigation from position fixes supplied by a Global Positioning System (GPS) receiver. Quasi‐constant position offsets occurring for fixes associated with switches in observed satellite constellation are modeled by including constellation biases as state vector components. A proper choice of statistics for state propagation and measurement noise leads to improved positioning. However, it may also increase the statistical dependence of Kalman estimates over characteristic time periods. Since a quantitative measure of this dependence is generally important for further processing, we have derived general expressions for the autocovariance of state vector Kalman estimates. These expressions contain products of propagation matrices and Kalman gains and, hence, relate directly to stability properties of the filter. For many applications, only certain components of the state vector are of interest. We show that autocovariances for state vector projections can be computed from corresponding projections of propagation matrices and Kalman gains, provided the state transition and measurement matrices satisfy certain reducibility conditions. Application of the filter and of the autocovariance expressions is illustrated using GPS and gravity measurements collected on board the Scripps Institution of Oceanography’s R/V Thomas Washington during Leg 1 of the Roundabout expedition.