TOA estimation via cross-correlation-based atomic norm minimization

Abstract

This paper proposes a novel Cross-Correlation-based Atomic Norm Minimization method (CC-ANM) to estimate Time-of-Arrival (TOA) parameters with enhanced accuracy. It leverages a gridless approach based on atomic norm to address the cross-correlation model, which is effective in mitigating the impact of non-independently and identically distributed (non-i.i.d.) Gaussian noise. A new optimization framework is formulated to tackle this challenge, and its dual problem expressed through a Semi-Definite Programming (SDP) is derived. By utilizing the characteristics of dual problem, the proposed method can estimate TOA parameters without the need for prior information of the path count under high Signal-to-Noise Ratio (SNR) conditions. To overcome the constraints imposed by traditional root polynomials in low SNR scenarios, the proposed method develops a derivative-based root-finding algorithm to extract TOA parameters from the dual polynomial. It can not only significantly reduce the estimation errors introduced by the discretization process, but also address the performance limitations under low SNR conditions. Simulation results demonstrate that the proposed CC-ANM method closely approximates the Cramer–Rao Lower Bound (CRLB) and outperforms existing methods across a range of SNR levels and path configurations.