Gravity matching navigation algorithm based on multiscale search and Hadamard transformed difference

The accuracy and stability of navigation algorithms are crucial preconditions for underwater gravity matching aided navigation. To improve the matching accuracy and robustness of the matching algorithm, this paper presents a novel gravity matching navigation algorithm based on multiscale search and Hadamard transformed difference. The Hadamard transformation process was first time introduced in the new algorithm for the Walsh-Hadamard kernel function with the property of energy conservation. The gravity measurement sequences could be converted to the Hadamard domain; thus, the difference in numerical values, tendency, and spatial structure of the gravity measurement sequence were also a focus in the new algorithm, whereas only gravity statistical values were considered in classical matching algorithms. Therefore, with the proposed algorithm, the number of measurements necessary for matching can be effectively reduced, while improving the matching accuracy and success rate. In addition, a multiscale neighborhood search strategy based on contour constraints was designed to improve the matching efficiency, whereas a point-by-point global search was widely used in classical matching algorithms. Marine gravity maps of the South China Sea were used to construct the simulation tests. Simulation results show that under various conditions, the new algorithm has lower requirements for the number of measurements, measuring accuracy, and matching areas while exhibiting a higher navigation accuracy, matching success rate, and matching efficiency. Thus, the proposed algorithm could provide a new option for future practical applications of gravity matching aided navigation.