Gravity field interpolation method and device, and storage medium

A gravity field interpolation method, comprising:

• step S1, generating, by a server, sampling points in a grid corresponding to a satellite orbit;
• step S2, obtaining, by the server, coefficients of a polynomial based on measured values of the sampling points;
• and
• step S3, converting, by a client, an Earth-centered inertial (ECI) coordinate at a reference time into a radial-transverse-normal (RTN) coordinate corresponding to a grid cell, and normalizing the RTN coordinate to obtain a normalized RTN coordinate;
• and substituting the normalized RTN coordinate into the polynomial, calculating a gravitational acceleration before a J2 term of a spherical harmonic gravity field by using a spherical harmonic method, and calculating a gravitational acceleration after the J2 term of the spherical harmonic gravity field by using a polynomial interpolation method;
• wherein the step S1 comprises:
• step S11, determining the grid corresponding to the satellite orbit;
• and
• step S12, designing the sampling points xi in the grid according to a Chebyshev node distribution;
• wherein a sampling equation is expressed as follows:
• x
• i
• =
• cos
• ⁢
• (
• 2
• ⁢
• i
• -
• 1
• 2
• ⁢
• m
• ⁢
• π
• )
• ,
• i
• =
• 1
• ⁢
• …
• ⁢
• m
• ;
• wherein m3 represents a total number of the sampling points, and m points are taken in each dimension;
• wherein the step S2 comprises:
• step S21, generating a candidate polynomial as follows:
• Q
• d
• =
• ∑
• a
• =
• 0
• d
• ∑
• b
• =
• 0
• a
• ∑
• c
• =
• 0
• a
• -
• b
• C
• σ
• ⁢
• y
• 1
• a
• -
• b
• -
• c
• ⁢
• y
• 2
• c
• ⁢
• y
• 3
• b
• ;
• wherein y1, y2 and y3 represent three components of a normalized coordinate of a point to be calculated respectively, C represents a polynomial coefficient, Cσ represents an element in C, σ represents a total cumulative loop counter, d represents a total degree of the polynomial, and a, b and c represent variables in a summation process;
• step S22, obtaining a selected polynomial based on the candidate polynomial;
• step S23, obtaining the coefficients of the polynomial based on the measured values of the sampling points and the selected polynomial;
• and
• step S24, verifying whether an internal conformity accuracy for the sampling points meets a standard;
• in response to the internal conformity accuracy meeting the standard, storing the coefficients of the polynomial, in response to the internal conformity accuracy not meeting the standard, increasing an order of the polynomial and repeating the step S21 through the step S23;
• wherein in the step S3, the spherical harmonic gravity field U is expressed as follows:
• U
• =
• U
• J
• 1
• +
• U
• J
• 2
• +
• U
• F
• ;
• wherein UJ1 and UJ2 each represent the gravitational acceleration before the J2 term of the spherical harmonic gravity field, and Up represents the gravitational acceleration after the J2 term of the spherical harmonic gravity field;
• wherein analytical solutions for UJ1 and UJ2 are as follows:
• U
• J
• 1
• =
• -
• μ
• r
• ;
• U
• J
• 2
• =
• -
• μ
• r
• [
• J
• 2
• (
• R
• e
• r
• )
• 2
• ⁢
• P
• 2
• (
• sin
• ⁡
• (
• φ
• )
• ]
• ;
• wherein μ represents a reference gravitational constant, Re represents an Earth radius, r represents a magnitude of a position vector, φ represents a geocentric latitude, and P2 represents a second-order Legendre polynomial;
• and
• wherein UF is obtained by using polynomial fitting.