We employ the Structured Total Least Squares (STLS) framework for estimating the delays associated with multiple reflections of a chirp signal. The classical methods of using matched-filter correlation processing, originally aimed at estimating the delay of a single reflection, have poor resolution and accuracy in the presence of multiple, closely spaced reflections with overlapping correlation functions. The STLS framework offers enhanced resolution and accuracy for this problem. We provide an overview of the STLS framework for complex-valued data and parameters, showing validity of the Riemannian Singular Value Decomposition (RiSVD) approach (which is a well-established tool for real-valued STLS problems), and also offer a new STLS algorithm via Alternating Coordinates Minimization (ACM), characterized by guaranteed convergence and by an ability to account for errors in the equations, thus potentially being more robust against model mismatch (e.g., whenever the exact number of reflections is unknown). We then turn to formulate the delays estimation problem in the complex-valued STLS framework, and use simulation results to demonstrate and analyze the accuracy and convergence performance (and associated trade-offs) of the proposed approach.
- Delay estimation
- Linear FM
- Structured total least squares