The Marine Safety Simulation based Electronic Chart Display and Information System

and Applied Analysis 3 2.2. Universal Kriging for Computing Water Depth in Any Position The basic premise of Kriging interpolation is that every unknown point can be estimated by the weighted sum of the known points: Z∗ 0 n ∑ i 1 λi Zi, 2.1 where Z∗ 0 represents the unknown point, Zi refers to each known point, and λ 0 i is the weight given to it. The Kriging algorithm body is involved in the appropriate weights selection. For the details about the Kriging interpolation theory, readers may refer to 11, 12 . Universal Kriging assumes a general linear trend model. It includes the drift functions to calculatem x , which is the expectation of Z x . Considering m x a0 a1u a2v a3u a4uv a5v, 2.2 where u, v are the coordinates of point x. Then, we can get ∑ i λi ( a0 a1xi a2yi a3x i a4xiyi a5y 2 i ) a0 a1x0 a2y0 a3x 0 a4x0y0 a5y 2 0 . 2.3 In order to set up 2.3 , the following equations can be gotten ∑