Skilled at representing the chirp signal, Radon-Wigner distribution (RWD) plays an important role in parameters estimation for moving targets. By searching for the best time-frequency angle, the conventional RWD estimation method suffers from the tradeoff between the estimation accuracy and computation complexity. In this paper, an efficient RWD estimation method is proposed by exploiting the geometry information in the RWD domain, and extensive parameters searching is replaced by only two parameters computation, then the computation complexity is effectively reduced from O(MN) to O(2N). The proposed efficient RWD method is applied in moving targets velocity estimation, which is emerging issue for smart city. The non-ideal factors in real circumstance are considered, and three robust methods are proposed to improve the estimation accuracy by exploiting the geometry information in the RWD domain further. A clutter suppression RWD (CSRWD) method is proposed to cancel the clutter but preserve the moving target in the RWD domain, and a learned RWD (LRWD) method is proposed to minimize the estimation error caused by measurement error. Then, CSRWD is combined with LRWD to obtain a unified robust RWD (URRWD), which possesses the advantages of CSRWD and LRWD simultaneously. Simulation and real data processing results validate the proposed methods, and lower implementation complexity is proven under the same accuracy assumption. It can be considered as the geometry information opens a window for the searching-based estimation method to make the original bleak searching process suddenly bright. The concept can also be expanded to the other searching-based estimation methods, such as Radon transform, fractional Fourier transform and so on.
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