Terrain matching with effective 3D Zernike moments: Spectrum analysis and algorithm

Terrain-Aided Navigation (TAN) systems have been investigated as an effective alternative to the Global Navigation Satellite System (GNSS) in the GNSS-denied environment. The core of a TAN system is a terrain matching algorithm to enable the positioning parameter determination using both the pre-existing digital elevation model and the real-time sensor data. Compared with the other terrain features, the 3D Zernike Moments (3D-ZMs) are not only orthogonal but also non-sensitive to noise, which is good for improving the performance of the terrain matching algorithm. However, there are still the 3D-ZMs insensitive to the terrain elevation fluctuation which are no good for the terrain matching and yet addressed sufficiently. Hence, a terrain matching algorithm based on the 3D-ZMs is proposed for the TAN systems. The 3D-ZMs are derived in the frequency domain for the spectrum analysis of the 3D-ZMs for the first time. The performance of the 3D-ZMs including the discrimination power and the sensitivity to noise is analyzed as the foundation for the proposed matching algorithm. With the revised 3D-ZM descriptors and feature vector by removing the 3D-ZMs vulnerable to noise and those insensitive to the terrain elevation fluctuation, the proposed terrain matching algorithm has revealed the superior matching performance to the existing ones, especially when there are noise and rotations.