The Improved Kriging Interpolation Algorithm for Local Underwater Terrain Based on Fractal Compensation

Abstract

The interpolation-reconstruction of local underwater terrain using the underwater digital terrain map (UDTM) is an important step for building an underwater terrain matching unit and directly affects the accuracy of underwater terrain matching navigation. The Kriging method is often used in terrain interpolation, but, with this method, the local terrain features are often lost. Therefore, the accuracy cannot meet the requirements of practical application. Analysis of the geographical features is performed on the basis of the randomness and self-similarity of underwater terrain. We extract the fractal features of local underwater terrain with the fractal Brownian motion model, compensating for the possible errors of the Kriging method with fractal theory. We then put forward an improved Kriging interpolation method based on this fractal compensation. Interpolation-reconstruction tests show that the method can simulate the real underwater terrain features well and that it has good usability.

The Real-Time and Realistic Rendering for 3D Sea Terrain Based on Electronic Chart

“…We test the performance of our DIBNS method by making comparisons with other classical methods, such as IDW [1] , Kriging [2] and improved Kriging [7] .…”

“…Therefore we compare the interpolation algorithms by the smoothness. Figure 10 shows the difference between the improved Kriging [7] and our method on grids. We can see that the gird constructed with our algorithm has smoother effect.…”

“…Comparison of interpolation results between improved Kriging [7] (top) and our method (bottom). Figure 11.…”

“…There are some classical interpolation algorithms, such as inverse distance weighting (IDW) [1] , Kriging [2] , splines [3] and fractional Brownian motions [4] . In recent years, some interpolation algorithms [5][6][7][8][9] are proposed by modifying the above methods. The IDW algorithm realizes the interpolation by counting the mean of weighted elevations around the point to be interpolated.…”

“…It gets high accuracy, but gets low computing speed because of the matrix interpolation computation. Algorithms [6][7] add the fractal theory into Kriging to improve the accuracy of interpolation. However, more calculation for interpolation results in a slower interpolation speed.…”