Maximum Likelihood Estimates and Cramer-Rao Bounds for Map-Matching Based Self-Localization

We describe a method to determine (x, y, z) position of a platform located in a region where a reference bathymetry map is available. The platform can be considered an autonomous undersea vehicle (AUV) equipped with a multi-beam high frequency sonar. Estimates of the heading, pitch and roll are available through the onboard inertial navigation systems (INS). An estimate of the AUV depth from the ocean surface, altitude from a Doppler velocity logger (DVL) as well as the sound speed at the AUV depth are also available. The position (x, y, z) is determined based on these estimates as well as time delay estimates from the beam time series. The maximum likelihood estimate (MLE) is derived and connections between previous approaches are made. Theoretically based performance predictions are compared against MLE performance in real data. The new estimator is directly linked with the relief (or information) of the map and therefore allows for a direct estimate of accuracy. This insight is critical for integrated map-matching navigation systems but has hitherto been unavailable. The new estimator of location can constrain the error growth of a purelyINS-based system and lead to improved navigation.