Passive localization using time delay estimates with sensor positional errors

Abstract

Target localization in a passive sonar system involves bearing and range estimation. These estimates may be determined using (1) the differential time delays of the source-signal arrivals at spatially separated sensors and (2) knowledge of the sensor geometry. When the sensor positions are known exactly, the accuracy of the bearing and range estimates depends on the accuracies of the differential time delays. The time delay errors depend on the signal-to-noise ratio (SNR) and on other signal and noise parameters such as bandwidth, center frequency, observation time, and spectral slopes. A critical factor in bearing and range estimation is the sensor positional errors. Here, the combined effect of time delay errors due to finite SNR and sensor positional errors on the bearing and range estimates of the acoustic source are investigated. For low-input SNR, the analysis indicates that localization errors are heavily dependent on the SNR at the individual sensors. For high SNR, sensor positional errors are the dominant factor in the localization errors. Also, the effects of the nonlinear transformation of differential time delays and sensor positions on bearing and range estimates are investigated. It is shown that the bias due to the nonlinear transformation introduced in bearing estimation is negligible for sources close to broadside, and the bias in the range estimation is always positive. The mean square range error, which includes standard deviation and bias, is then evaluated and discussed in terms of true range, variances of bearing, and unbiased range errors.