Data Denoising Based on Hadamard Matrix Transformation and Rayleigh Quotient Maximization: Application to GNSS Signal Classification

Global navigation satellite system (GNSS) signal type classification based on machine learning is an effective way to improve urban positioning performance. However, GNSS signal type features extracted are unrelated, and the number of features is limited, referred to as nonlocal- and few-feature issues, which limits the classification performance. This article presents a new data denoising theory to boost the classification performance based on concepts of Hadamard matrix transformation and Rayleigh quotient maximization. Hadamard matrix transformation increases the distance between different classes, i.e., interclass distance, by projecting the data into a new space, thereby increasing the classification performance. To improve the signal-to-noise ratio (SNR) of features, we maximize the Rayleigh quotient of the interclass distance. The proposed denoising approach is, in particular, effective for nonlocal- and few-feature signals. We applied the proposed data denoising theory to the GNSS signal type classification problem. Results indicate that GNSS signal type classification performance (microaveraging recall, i.e., Recallμ ) can be improved by about 5% ~ 10% in a static test. For the dynamic test, about 1.5% ~ 3.5% improvement is achieved.