Quaternion Estimation via Modified Rodrigues Parameters
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Solution Overview
Problem
Current attitude estimation algorithms, such as Extended Kalman Filter, face limitations in estimation accuracy and stability due to truncation of higher-order terms and complex parameter settings, particularly in spacecraft attitude estimation systems, where quaternion normalization constraints and gyro drift errors are significant.
Innovation Solution
A weight and reference quaternion correction unscented quaternion estimation method (CUSQUE) is introduced, which uses unscented transformation theory to avoid Jacobian matrix calculations, sets different weights for time and measurement updates, and employs the Lagrange function method to determine the weighted mean value of the quaternion, improving estimation accuracy and stability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Extended Kalman Filter is used for attitude estimation, then the algorithm is widely applicable, but the estimation accuracy is limited due to truncation of higher-order terms
Solution Approach 1:
The patent transforms the attitude estimation problem from quaternion space to modified Rodrigues parameter (MRP) space, changing the mathematical representation parameters. This transformation allows the unscented filter to operate in a parameter space where the nonlinear constraints are relaxed, improving estimation accuracy without requiring complex normalization steps.
Solution Approach 2:
The patent replaces the traditional Extended Kalman Filter mechanism with an Unscented Filter mechanism. Instead of using linearization via Jacobian matrices, the unscented filter uses sigma points to capture the true mean and covariance through unscented transformation, providing higher-order accuracy without increased computational complexity.
2Productivity
If Unscented Quaternion Estimator is used to avoid quaternion normalization constraint, then computational burden is reduced, but reference quaternion selection and parameter setting need further revision
Solution Approach 1:
The patent changes the parameter representation from unit quaternion to modified Rodrigues parameter, which does not require normalization constraints. This parameter transformation eliminates the need for complex reference quaternion selection and simplifies the algorithm implementation while maintaining computational efficiency.
3Adaptability or versatility
If multiple parameters are set according to actual environment in unscented Kalman filter, then the algorithm can adapt to different scenarios, but the attitude estimation problem is more complicated compared to univariate model and target tracking
Solution Approach 1:
The patent develops a unified unscented filter framework that handles multiple estimation tasks (attitude quaternion, gyro drift, measurement noise covariance) simultaneously through a single algorithm structure. The modified Rodrigues parameter transformation provides a universal representation that works across different spacecraft attitude scenarios, reducing the need for scenario-specific parameter adjustments.
Data Source
AI summary
The invention relates to a weight and reference quaternion correction unscented quaternion estimation method, comprising: obtaining measurement data as quantity measurement through a gyro and a star sensor; establishing a quaternion-based discrete spacecraft nonlinear state space model; estimating an error quaternion, a gyro drift and a corresponding error covariance at a k moment by using an unscented quaternion estimator based on parameter and reference quaternion correction at a k−1 moment; and setting a filtering time as Ntime, if k<Ntime, then repeating the step 3, if k=Ntime, then finishing filtering, and outputting the attitude quaternion, the gyro drift and the corresponding error covariance.