A Real-Time Maximum Correlation Matching Based on Approximated Local Gravity Map

Abstract

Firstly, the limitations of the traditional maximum correlation matching algorithm is analyzed and the new algorithm to approximate local grid gravity anomaly map with the tensor product of Gauss spline function is proposed to get the continuous analytic expression of local gravity anomaly map. Then, the mathematical model of maximum correlation matching algorithm is redesigned based on this unified analytic expression and the BFGS Quasi–Newton method is adopted to solve this non-linear model. With respect to the bad real-time performance of traditional maximum correlation matching algorithm, the way fixing the length of sample sequence is adopted to improve sampling structure and the conversion formula between two rigid transformations centered with different points is derived. Finally, the real-time maximum correlation matching algorithm based on continuous analytic expression of local gravity anomaly map is realized. Two simulations have been done based on 2′ × 2′ gravity anomaly database from satellite altimetry inversion for the comparative analysis. From the simulation results, we can see that the matching results of new algorithm can track the actual path with high precision in case of relatively big observation noise and initial position errors.