Matrix algorithm for Doppler sonar navigation

The software for precision navigation systems with Doppler velocity logs is typically based on the standard Janus equations. In the absence of significant error sources, these equations provide a simple solution to the Doppler sonar equation. This paper presents a more accurate algorithm for solving the Doppler sonar equation, which accounts for the error sources ignored in the standard Janus equations but retains their simplicity. This new matrix algorithm is based on a classical least-squares solution to an overdetermined linear system. The majority of the matrices in the system are time-invariant direction cosine and rotation matrices, which can be computed prior to the mission. The accuracy of this new algorithm has been verified during several at-sea tests. An improvement of almost 275 feet can be observed for a typical mission of five hours at five knots