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Underwater Target Localization and Synchronization for a Distributed SIMO Sonar With an Isogradient SSP and Uncertainties in Receiver Locations

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Underwater Target Localization and Synchronization for a Distributed SIMO Sonar With an Isogradient SSP and Uncertainties in Receiver Locations

Chaofeng He et al. Sensors (Basel).

Abstract

A distributed single-input multiple-output (SIMO) sonar system is composed of a sound source and multiple underwater receivers. It provides an important framework for underwater target localization. However, underwater hostile environments bring more challenges for underwater target localization than terrestrial target localization, such as the difficulties of synchronizing all the underwater receiver clocks, the varying underwater sound speed and the uncertainties of the locations of the underwater receivers. In this paper, we take the sound speed variation, the time synchronization and the uncertainties of the receiver locations into account, and propose the underwater target localization and synchronization (UTLS) algorithm for the distributed SIMO sonar system. In the distributed SIMO sonar system, the receivers are organized in a star topology, where the information fusion is carried out in the central receiver (CR). All the receivers are not synchronized and their positions are known with uncertainties. Moreover, the underwater sound speed is approximately modeled by a depth-dependent sound speed profile (SSP). We evaluate our proposed UTLS algorithm by comparing it with several benchmark algorithms via numerical simulations. The simulation results reveal the superiority of our proposed UTLS algorithm.

Keywords: clock synchronization; distributed sonar; localization; sound speed profile; uncertainties of locations.

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
The schematic diagram of target localization by single-input multiple-output (SIMO) sonar systems.
Figure 2
Figure 2
The feasible locations of the receivers.
Figure 3
Figure 3
The scheme to calculate the coordinate [xi,yi].
Figure 4
Figure 4
Description of the time series.
Figure 5
Figure 5
Root mean square errors (RMSEs) of the estimation of the clock skews of the receivers via the underwater target localization and synchronization (UTLS), the weighted least squares (WLS)-nonlinear weighted least squares (NWLS), the approximated WLS (AWLS)-NWLS and the NWLS-UTL algorithms, respectively, with 10log(1/σμh2)=10log(1/σμi2)=96 dB and 10log(1/σx2)=10 dB.
Figure 6
Figure 6
RMSEs of the estimation of the clock skews of the receivers via the UTLS, the WLS-NWLS, the AWLS-NWLS and the NWLS-underwater target localization (UTL) algorithms, respectively, with 10log(1/σμh2)=10log(1/σμi2)=80 dB, and 10log(1/σi2)=10log(1/σh2)=68 dB.
Figure 7
Figure 7
RMSEs of the measurements and the estimations of the locations of the receivers via the UTLS algorithm. In the upper subplot, we assume 10log(1/σx2)=10 dB and 10log(1/σμh2)=10log(1/σμi2)=96 dB. In addition, we assume 10log(1/σi2)=10log(1/σh2)=68 dB in the lower subplot.
Figure 8
Figure 8
RMSEs of the estimation of the offsets of the receivers via the UTLS, the WLS-NWLS and the AWLS-NWLS algorithms, respectively, with 10log(1/σμh2)=10log(1/σμi2)=96 dB and 10log(1/σx2)=10 dB.
Figure 9
Figure 9
RMSEs of the estimation of the offsets of the receivers via the UTLS, the WLS-NWLS and the AWLS-NWLS algorithms, respectively, with 10log(1/σμh2)=10log(1/σμi2)=96 dB, and 10log(1/σi2)=10log(1/σh2)=68 dB.
Figure 10
Figure 10
RMSEs of localization via the UTLS, the WLS-NWLS, the AWLS-NWLS, the ANWLS, the NWLS-UTL and the NWLS-RP algorithms, respectively, with 10log(1/σμh2)=10log(1/σμi2)=96 dB and 10log(1/σx2)=10 dB.
Figure 11
Figure 11
RMSEs of localization via the UTLS, the WLS-NWLS, the AWLS-NWLS, the ANWLS, the NWLS-UTL and the NWLS-RP algorithms, respectively, with 10log(1/σμh2)=10log(1/σμi2)=80 dB and 10log(1/σi2)=10log(1/σh2)=68 dB.

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