Research And Analysis On Moving Target Localization In Multistatic Sonar

The problem of moving target localization is a fundamental application in multistatic sonar.To identify the location and velocity of a potential target,numerous attempts have been made to explore the multiple measurements,the environmental parameters and the acoustic characteristics in order to improve the accuracy,computational efficiency and robustness of target positioning.In view of the literature over the years,the time delays between the direct and echo signals together with the bearing angles are often used to locate a stationary target.When the target is moving,Doppler shifts between the direct and echo signals are present and they can be exploited for position and velocity estimation.This paper considers the joint use of time delays,Doppler shifts and angle measurements to locate a moving target in the typical multistatic sonar localization geometry and provides theoretical and experimental analysis for localization performances.To begin with,this paper will focus on the performance analysis of moving target localization in multistatic sonar.We examine the contribution of Doppler shifts and arrival angles to improving the positioning accuracy,as well as the effects of sensor position errors on target position and velocity estimation through the Cramér-Rao lower bound(CRLB)study.It can be shown in both theory and simulations that the addition of Doppler measurements would significantly improve the localization accuracy when the target is closer to the transmitters or receivers.Incorporating the angle measurements can greatly improve positioning accuracy,especially when the time delay and Doppler noise levels become large.The presence of transmitter and receiver position errors is able to obviously deteriorate the localization performance,especially in the small noise region.Next,we develop an explicit algebraic solution with multiple steps of linear regression via the transformation of nonlinear measurement equations as well as the introduction of nuisance parameters.The weighted least square(WLS)technique is involved in each stage.By exploring the pseudo-linear relationship between WLS estimators and unknowns through successive stages,we reduce the number of nuisance variables to reach the final solution.Not only the proof but also the simulation results are provided to show that the mean square error(MSE)of the proposed solution matches the CRLB well under small measurement noise conditions.Last but not least,the proposed method can be simplified by estimating the error of the first estimator and refining it in the second stage directly.The squared relationship or Taylor series expansion would be used to construct the pseudo-linear functions.In this way,we reduce the number of stages in the closed-form solution while achieving the purpose of deducing the computation time.The newly proposed technique is also shown to be able to attain the CRLB accuracy under small Gaussian measurement noise.It is worth to notice that the above algorithms can be extended to the scenarios with sensor position uncertainty as well.