Inverse Gravity Correlation Time Determination for Moving Base Gravity Measurement
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Solution Overview
Problem
Current methods for determining the inverse of gravity correlation time related to filtering cutoff frequency in gravity measurement of moving bases are not reported in literature, hindering high-precision and high-resolution gravity field data processing.
Innovation Solution
A method involving gravity-anomaly Fourier transform, power spectral density analysis, and iterative calculations using specific formulas to determine the inverse of gravity correlation time based on gravity sensor, GNSS height errors, and filter cutoff frequency, applicable to second-order, third-order, and mth-order Gauss Markov models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional filters (FIR or IIR) are used for gravity data processing, then filtering can be implemented, but the relationship between filtering cutoff frequency and gravity correlation time parameters is not established
Solution Approach 1:
The patent establishes a feedback mechanism by deriving the relationship between filter cutoff frequency and gravity correlation time parameters. The power spectral density function incorporates the inverse gravity correlation time parameter, allowing the filter design to feedback into the statistical characterization of gravity anomalies, and vice versa. This closed-loop relationship enables optimized filter design based on actual gravity field statistics.
Solution Approach 2:
The patent transforms the filter design approach by changing from fixed filter coefficients to parameter-based design where the cutoff frequency is directly related to the inverse gravity correlation time. By expressing the power spectral density in terms of the Markov model parameters (inverse correlation time), the filter characteristics can be dynamically adjusted based on the statistical properties of the gravity anomalies being processed.
2Reliability
If gravity anomalies are modeled using Gauss Markov models, then statistical characterization is achieved, but the inverse gravity correlation time parameter cannot be determined
Solution Approach 1:
The patent replaces direct measurement of the inverse gravity correlation time parameter with an equivalent approach using filter cutoff frequency. Instead of attempting to measure the correlation time directly from gravity anomaly data, the method substitutes this with the measurable filter cutoff frequency parameter, which has a direct mathematical relationship with the inverse correlation time through the power spectral density function.
Solution Approach 2:
The patent introduces the filter cutoff frequency as an intermediary parameter that connects the statistical model (Gauss Markov) with measurable quantities. The cutoff frequency serves as a bridge between the theoretical inverse correlation time parameter and actual filter design parameters, allowing determination of the correlation time characteristics through the intermediary of filter frequency response.
3Measurement precision
If high-precision gravity anomaly values are obtained through filtering, then measurement quality improves, but the filter design lacks guidance from correlation time parameters
Solution Approach 1:
The patent applies preliminary action by establishing the relationship between filter cutoff frequency and inverse gravity correlation time before actual filter design. By deriving the power spectral density function and its relationship with the Markov model parameters in advance, the methodology provides pre-calculated guidance for filter design, eliminating the need for trial-and-error approaches and making the design process more straightforward.
Data Source
AI summary
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 mth-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 mth-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.