Patent Document ID: 9965831
Application ID: 15525355
Patent Status: 1

Claim One:
1. A method of estimating a physical characteristic at a geographic location adjacent to at least one geographic location at which a measurement of the physical characteristic was made, measurements of the physical characteristic being represented as data on a data grid having a plurality of data grid points, each data grid point corresponding to a geographic location and each data grid point having a data value representing the physical characteristic at the corresponding geographic location, to provide an interpolated data value at an interpolated point offset from a data grid point by offsets x, y, the method comprising the steps of: obtaining the data value and a plurality of derivative values for each of a set of data grid points defining a sub-grid, defining a 4×4 data value matrix from the data values and derivative values, defining a plurality of 4×4 transformation matrices, calculating a 4×4 coefficient matrix from the transformation matrices and the data value matrix, defining a x vector based on the offset x and a y vector based on the offset y, and calculating the interpolated data value representing the physical characteristic at the corresponding geographic location from the x vector, y vector and coefficient matrix; wherein the data value matrix is defined by: data value matrix IV = ( P i , j P i , j x ′ P i , j y ′ P i , j xy ′ P i + 1 , j P i + 1 , j x ′ P i + 1 , j y ′ P i + 1 , j xy ′ P i , j + 1 P i , j + 1 x ′ P i , j + 1 y ′ P i , j + 1 xy ′ P i + 1 , j + 1 P i + 1 , j + 1 x ′ P i + 1 , j + 1 y ′ P i + 1 , j + 1 xy ′ ) , where P i,j is a data value with x,y coordinates in the data grid of i,j, P i,j x′ is the first order derivative in the x direction of P i,j , P i,j y′ is the first order derivative in the y direction of P i,j , and P i,j xy′ is the second-order derivative in the x-v direction of P i,j .