Multistatic Sonar Localization with a Transmitter

This paper focuses on the problem of multistatic sonar localization with a transmitter where the known signal transmission speed, the transmitter and receiver positions are all contaminated by Gaussian noise. The Cramer-Rao lower bound (CRLB) are derived for the object position and the localization parameters. The analysis in CRLB shows that the localization parameters have a chance to be updated to more accurate ones. Two solutions are then proposed to estimate the object position using the time measurements and angle measurements. One is a two-step closed-form solution based on weighting least squares and the other is a generalized trust region subproblem (GTRS) solution using Newton's method. A recursive MLE is also proposed to update the localization parameters and a more accurate propagation speed can be obtained from the proposed MLE especially when the propagation speed noise is large. Simulations show that the two localization solutions and the propagation speed updated from the proposed MLE can reach their CRLBs.