METHOD FOR DETERMINING THE INVERSE OF GRAVITY CORRELATION TIME

Abstract

The present invention discloses a method for determining an inverse of gravity correlation time. During data processing on gravity measurement of moving bases, a gravity anomaly is considered as a stationary random process in a time domain, and is described with a second-order Gauss Markov model, a third-order Gauss Markov model or an m.sup.th-order Gauss Markov model, and the inverse of gravity correlation time is an important parameter of the gravity-anomaly model, and according to a gravity sensor root mean square error, a Global Navigation Satellite System (GNSS) height root mean square error, an a priori gravity root mean square, and a gravity filter cutoff frequency during the gravity measurement of the moving bases, an inverse of gravity correlation time of the second-order, third-order or m.sup.th-order Gauss Markov model is determined. According to the method for determining an inverse of gravity correlation time provided in the present invention, a forward and backward Kalman filter during data processing on gravity measurement of moving bases can be adjusted, to obtain a high-precision and high-wavelength-resolution gravity anomaly value.

Claims

1. A method for determining an inverse of gravity correlation time, comprising the following steps: (1) for a gravity anomaly of an m.sup.th-order Gauss Markov model, according to a gravity sensor root mean square error σ.sub.f, a GNSS height root mean square error σ.sub.h, an a priori gravity root mean square σ.sub.g, and a gravity filter cutoff frequency ω.sub.c during gravity measurement of moving bases, performing iterative calculation by using Formula (1), to obtain an inverse of gravity correlation time β, $\begin{array}{cc}\beta ={\left[{\left(1+{\beta }^2\text{/}{\omega }_c^2\right)}^m\frac{{\omega }_c^{2m}}{C_m}\left[\frac{{\sigma }_f^2}{{\sigma }_g^2}+{\omega }_c^4\frac{{\sigma }_h^2}{{\sigma }_g^2}\right]\right]}^{\frac{1}{2m-1}},\mathrm{where}{C}_m=\frac{2\left(2m-2\right)!!}{\left(2m-3\right)!!};& \left(1\right)\end{array}$ (2) assuming that βω.sub.c, and simplifying Formula (1) as: $\begin{array}{cc}\beta \approx {\left[\frac{{\omega }_c^{2m}}{C_m}\left[\frac{{\sigma }_f^2}{{\sigma }_g^2}+{\omega }_c^4\frac{{\sigma }_h^2}{{\sigma }_g^2}\right]\right]}^{\frac{1}{2m-1}},& \left(2\right)\end{array}$ where Formula (2) is an explicit expression, and the inverse of gravity correlation time β on the left can be obtained by calculating known quantities on the right.

2. The method for determining an inverse of gravity correlation time according to claim 1, comprising: when m=2, performing iterative calculation by using Formula (3), to obtain the inverse of gravity correlation time β: $\begin{array}{cc}\beta ={\left[{\left(1+{\beta }^2\text{/}{\omega }_c^2\right)}^m\frac{{\omega }_c^4}{4}\left[\frac{{\sigma }_f^2}{{\sigma }_g^2}+{\omega }_c^4\frac{{\sigma }_h^2}{{\sigma }_g^2}\right]\right]}^{\frac{1}{3}},& \left(3\right)\end{array}$ and when βω.sub.c, simplifying Formula (3) as: $\begin{array}{cc}\beta ={\left[\frac{{\omega }_c^4}{4}\left[\frac{{\sigma }_f^2}{{\sigma }_g^2}+{\omega }_c^4\frac{{\sigma }_h^2}{{\sigma }_g^2}\right]\right]}^{\frac{1}{3}},& \left(4\right)\end{array}$ where Formula (4) is an explicit expression, and the inverse of gravity correlation time β on the left can be obtained by calculating known quantities on the right.

3. The method for determining an inverse of gravity correlation time according to claim 1, comprising: when m=3, performing iterative calculation by using Formula (5), to obtain the inverse of gravity correlation time β: $\begin{array}{cc}\beta ={\left[{\left(1+{\beta }^2\text{/}{\omega }_c^2\right)}^m\frac{3{\omega }_c^6}{C_m}\left[\frac{{\sigma }_f^2}{{\sigma }_g^2}+{\omega }_c^4\frac{{\sigma }_h^2}{{\sigma }_g^2}\right]\right]}^{\frac{1}{5}},& \left(5\right)\end{array}$ and when βω.sub.c, simplifying Formula (5) as: $\begin{array}{cc}\beta ={\left[\frac{3{\omega }_c^6}{16}\left[\frac{{\sigma }_f^2}{{\sigma }_g^2}+{\omega }_c^4\frac{{\sigma }_h^2}{{\sigma }_g^2}\right]\right]}^{\frac{1}{5}},& \left(6\right)\end{array}$ where Formula (6) is an explicit expression, and the inverse of gravity correlation time β on the left can be obtained by calculating known quantities on the right.

Description

DETAILED DESCRIPTION

[0030] The present invention is further described below with reference to specific embodiments.

[0031] This embodiment discloses a method for determining an inverse of gravity correlation time, including the following steps:

[0032] S1. According to gravity measurement data of moving bases, a gravity sensor root mean square error σ.sub.f=5.0×10.sup.−5 m/s.sup.2, a GNSS height root mean square error σ.sub.h=0.05 m, an a priori gravity root mean square σ.sub.g=0.001 m/s.sup.2, and a gravity filter cutoff frequency ω.sub.c=π/50 are given.

[0033] S2. An inverse of gravity correlation time of a gravity anomaly of an m.sup.th-order Gauss Markov model is determined. According to S1, the gravity measurement data of the moving bases is calculated by using Formula (15), to obtain the inverse of gravity correlation time β.

[00011]$\begin{array}{cc}\beta ={\left[{\left(1+{\beta }^2\text{/}{\omega }_c^2\right)}^m\frac{{\omega }_c^{2m}}{C_m}\left[\frac{{\sigma }_f^2}{{\sigma }_g^2}+{\omega }_c^4\frac{{\sigma }_h^2}{{\sigma }_g^2}\right]\right]}^{\frac{1}{2m-1}},\mathrm{where}{C}_m=\frac{2\left(2m-2\right)!!}{\left(2m-3\right)!!}.& \left(15\right)\end{array}$

[0034] According to S1, the gravity measurement data of the moving bases is calculated by using a simplified Formula (16), to obtain the inverse of gravity correlation time.

[00012]$\begin{array}{cc}\beta \approx {\left[\frac{{\omega }_c^{2m}}{C_m}\left[\frac{{\sigma }_f^2}{{\sigma }_g^2}+{\omega }_c^4\frac{{\sigma }_h^2}{{\sigma }_g^2}\right]\right]}^{\frac{1}{2m-1}}.& \left(16\right)\end{array}$

[0035] S3. An inverse of gravity correlation time of a gravity anomaly of a second-order Gauss Markov model is determined. According to S1, the gravity measurement data of the moving bases is performed with iterative calculation by using Formula (17), to obtain the inverse of gravity correlation time β=0.005365

[00013]$\begin{array}{cc}\beta ={\left[{\left(1+{\beta }^2\text{/}{\omega }_c^2\right)}^2\frac{{\omega }_c^4}{4}\left[\frac{{\sigma }_f^2}{{\sigma }_g^2}+{\omega }_c^4\frac{{\sigma }_h^2}{{\sigma }_g^2}\right]\right]}^{\frac{1}{3}}.& \left(17\right)\end{array}$

[0036] According to S1, the gravity measurement data of the moving bases is calculated by using Formula (18), to obtain the inverse of gravity correlation time β=0.005339,

[00014]$\begin{array}{cc}\beta \approx {\left[\frac{{\omega }_c^4}{4}\left[\frac{{\sigma }_f^2}{{\sigma }_g^2}+{\omega }_c^4\frac{{\sigma }_h^2}{{\sigma }_g^2}\right]\right]}^{\frac{1}{3}}.& \left(18\right)\end{array}$

[0037] S4. An inverse of gravity correlation time of a gravity anomaly of a third-order Gauss Markov model is determined. According to S1, the gravity measurement data of the moving bases is performed with iterative calculation by using Formula (19), to obtain the inverse of gravity correlation time β=0.013907.

[00015]$\begin{array}{cc}\beta ={\left[{\left(1+{\beta }^2\text{/}{\omega }_c^2\right)}^3\frac{3{\omega }_c^6}{16}\left[\frac{{\sigma }_f^2}{{\sigma }_g^2}+{\omega }_c^4\frac{{\sigma }_h^2}{{\sigma }_g^2}\right]\right]}^{\frac{1}{5}}.& \left(19\right)\end{array}$

[0038] According to S1, the gravity measurement data of the moving bases is calculated by using Formula (20), to obtain the inverse of gravity correlation time β=0.013514.

[00016]$\begin{array}{cc}\beta \approx {\left[\frac{3{\omega }_c^6}{16}\left[\frac{{\sigma }_f^2}{{\sigma }_g^2}+{\omega }_c^4\frac{{\sigma }_h^2}{{\sigma }_g^2}\right]\right]}^{\frac{1}{5}}.& \left(20\right)\end{array}$

[0039] Details not described in this specification belong to the well-known technology of a person skilled in the art. It should be noted that a person of ordinary skill in the art may further make several improvements and equivalent replacements to the present invention without departing from the principle of the present invention. The technical solution with improvements and equivalent replacements in claims of the present invention shall fall within the protection scope of the present invention.