论文标题
$ \ mathrm {so}（3）\ times \ times \ mathbb {r}^n $的矩阵Fisher-gaussian分布
Matrix Fisher-Gaussian Distribution on $\mathrm{SO}(3)\times\mathbb{R}^n$ for Attitude Estimation with a Gyro Bias
论文作者
论文摘要
在本文中，在非线性歧管$ \ mathrm {so}（3）（3）\ times \ times \ mathbb {r}^n $上提出了一个新的概率分布，称为矩阵Fisher-Gaussian（MFG）分布。它是通过从环境欧几里得空间中调节（9+n） - 变量高斯分布到$ \ mathrm {so}（3）\ times \ times \ mathbb {r}^n $的，同时对相关项施加了一定的几何解释，以避免过度参数化。独特的功能是，它可能代表态度，任意维度的线性变量以及它们之间的角度线性变量的大量不确定性以及它们之间的角度线性相关性，它们以全球方式没有与局部参数化相关的奇异性。开发了各种随机特性和MFG的近似最大似然估计量。此外，通过代表态度运动学的随机微分方程，开发了两种方法来传播不确定性。基于这些，提出了贝叶斯估计量，以同时估算态度和时变陀螺偏见。数值研究表明，针对两个有挑战性的情况，提出的估计量针对完善的乘法扩展滤波器表现出更好的准确性。
In this paper, a new probability distribution, referred to as the matrix Fisher-Gaussian (MFG) distribution, is proposed on the nonlinear manifold $\mathrm{SO}(3)\times\mathbb{R}^n$. It is constructed by conditioning a (9+n)-variate Gaussian distribution from the ambient Euclidean space into $\mathrm{SO}(3)\times\mathbb{R}^n$, 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.
