The Time Difference of Arrival Estimation Method Utilizing an Inexact Reconstruction Within the Framework of Compressed Sensing

Abstract

The time difference of arrival (TDOA) estimation plays a crucial role in emitter localization and time synchronization applications. When time among multiple sensors is synchronized, the TDOAs between the sensors and the emitter can be measured to achieve hyperbolic positioning of the emitter. Conversely, if the positions of both the sensors and the emitter are known, TDOAs can be utilized to synchronize the clocks across the sensors. Given that compressed sensing (CS) can reduce both the sampling rate and data volume, thereby enhancing the efficiency of TDOA estimation, there has been growing interest among researchers in exploring TDOA estimation within the CS framework. In scenarios such as passive positioning, the signals received by sensors are often non-cooperative, and the underlying signal system is unknown, making it difficult to obtain a sparse representation of the signal. This paper introduces an incomplete reconstruction-based TDOA estimation method along with an improved variant. By selecting a partial Fourier transform matrix as the measurement matrix and a Fourier transform matrix as the projection matrix, the orthogonal matching pursuit (OMP) algorithm is employed to reconstruct the compressed measurement data. Through subsequent processing steps, such as conjugate mirroring, TDOA estimation between two signals can be performed. Although the reconstructed signal may substantially differ from the original, the accuracy of TDOA estimation remains reliable. Simulation results demonstrate that when the signal-to-noise ratio (SNR) of the received signal is at least 0 dB and the compressed sampling length exceeds one-tenth of the original signal length, the TDOA estimation error of the proposed method is nearly identical to that of the cross-correlation method.

Keywords

• compressed sensing
• time difference of arrival
• inexact reconstruction