Papers › Matrix Fisher-Gaussian Distribution on SO(3)×ℝⁿ for Attitude Estimation with a Gyro Bias
Matrix Fisher-Gaussian Distribution on SO(3)×ℝⁿ for Attitude Estimation with a Gyro Bias
Weixin Wang, Taeyoung Lee
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In this paper, a new probability distribution, referred to as the matrix Fisher-Gaussian (MFG) distribution, is proposed on the nonlinear manifold SO(3)×ℝⁿ. It is constructed by conditioning a (9+n)-variate Gaussian distribution from the ambient Euclidean space into SO(3)×ℝⁿ, while imposing a certain geometric interpretation of the correlation terms to avoid over-parameterization. The unique feature is that it may represent large uncertainties in attitudes, linear variables of an arbitrary dimension, and angular-linear correlations between them in a global fashion without singularities associated with local parameterizations. Various stochastic properties and an approximate maximum likelihood estimator of MFG are developed. Furthermore, two methods are developed to propagate uncertainties though a stochastic differential equation representing attitude kinematics. Based on these, a Bayesian estimator is proposed to estimate the attitude and time-varying gyro bias concurrently. Numerical studies indicate that the proposed estimator exhibits a better accuracy against the well-established multiplicative extended Kalman filter for two challenging cases.
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