Sparse reconstruction time delay estimation algorithm based on backtracking filter
Authors: Leng Xue-Dong  , Ba Bin  , Lu Zhi-Yu  , Wang Da-Ming  ,   Institute of Information System Engineering, The PLA Information Engineering University, Zhengzhou 450001, China
Published: December 2020

The time delay estimation is widely used in wireless location field, and is the research emphasis in complex environment of this field. The current delay estimation algorithms can be classified as five methods of correlation, high-order statistics, self-adaption, maximum likelihood and subspace. However, the existing algorithms can hardly achieve an ideal performance in small sample（single snapshot) and low signal-to-noise ratio environment during wireless location. In order to solve the problem about the insufficiency of the current algorithms in the above conditions, many new methods have been introduced into the delay estimation problem. The compressed sensing sparse reconstruction method has been applied to the signal processing field as a newly-proposed algorithm in recent years. The delay estimation is realized by using the method of sparse reconstruction, in which the sparse representation of the signal is the premise. The rational construction of the measurement matrix and the design of the signal reconstruction algorithm are the core of correct estimation.The purpose of this article is to deal with the lack of measurement data in small sample（single snapshot) and low signal-to-noise ratio environment during wireless location. In the model of wireless location, the signal can be represented as a sparse matrix form by selecting suitable sparse representation matrix. The wireless multi-channel is measured in the time domain, the propagation delay varies with channel and the delay representation in the time domain is sparse, so that it can be directly constructed into the form of sparse signal. Since the necessary and the sufficient condition of the coefficient sparse matrix successfully reconstructed by the measurement matrix are the measurement matrix meeting the restricted isometry property（RIP). The orthogonal measurement matrix based on the steering vector by the method of Gram-Schmidt is proven to achieve the RIP. A novel sparse reconstruction algorithm based on backtracking filter is constructed to estimate the time delay. In order to guarantee that the first selection includes the optimal atom, several atoms are selected. And then the backtracking mechanism is introduced, and the selected atoms are approached by the method of the minimum square to sequence the obtained signals and select the optimal atom. Therefore, this method can be used to guarantee that the optimal atom is selected. The presented algorithm can achieve the delay estimation by using the corresponding relation between the time delay and the measurement matrix in a high precision. Furthermore, the Cramer-Rao bound（CRB) of this model is derived. Finally, simulations show that the proposed approach is suitable for small sample（single snapshot) and low signal-to-noise ratio environment. The proposed method can achieve a higher precision than Root-Music and improve performance at low complexity cost compared with OMP algorithm. The simulation result proves that the algorithm is stable and reliable.