Fast convex optimization method for frequency estimation with prior knowledge in all dimensions

Zai Yang, Lihua Xie

Abstract: Highlights•The frequency estimation problem is studied in all dimensions with prior knowledge;•A convex optimization approach is proposed based on the weighted atomic norm in both the 1-D and the multi-dimensional cases;•To the best of our knowledge, the proposed method is the only convex optimization method for multi-dimensional frequency estimation that can exploit the prior knowledge and work in the continuous domain;•The proposed method shares the same computational cost as the standard atomic norm method;•Numerical simulations show that the proposed method can improve the estimation accuracy compared to the standard atomic norm method;•Numerical simulations show that the proposed method can be an order of magnitude faster than an existing method with comparable accuracy in the 1-D case.