同时估计状态与噪声协方差，提升参数估计精度
Joint State and Noise Covariance Estimation
- 通过最大后验与似然框架建立联合优化的凸结构
- 提出两种新算法，可无缝集成至现有非线性最小二乘求解器
- 适用于机器人、视觉定位等需要自适应噪声建模的任务
本文研究在高斯噪声污染测量数据下，同时估计状态（如位姿、点）与噪声协方差矩阵的问题，若存在先验信息则进一步利用。噪声协方差决定最小二乘问题中各测量值的权重。我们证明该联合问题具有凸结构，并在联合最大后验与似然框架及其多种变体中给出了噪声协方差最优估计的完整表征与解析解。基于此理论结果，提出两种新算法，可联合估计主参数与噪声协方差。所提BCD算法能轻松嵌入现有非线性最小二乘求解器，每次迭代开销极小。通过在多种场景下的广泛实验验证方法有效性，为机器人与计算机视觉中的姿态估计问题（尤其SLAM）提供实用指导。
原文摘要 · Abstract (English)
This paper tackles the problem of jointly estimating the noise covariance matrix alongside states (parameters such as poses and points) from measurements corrupted by Gaussian noise and, if available, prior information. In such settings, the noise covariance matrix determines the weights assigned to individual measurements in the least squares problem. We show that the joint problem exhibits a convex structure and provide a full characterization of the optimal noise covariance estimate (with analytical solutions) within joint maximum a posteriori and likelihood frameworks and several variants. Leveraging this theoretical result, we propose two novel algorithms that jointly estimate the primary parameters and the noise covariance matrix. Our BCD algorithm can be easily integrated into existing nonlinear least squares solvers, with negligible per-iteration computational overhead. To validate our approach, we conduct extensive experiments across diverse scenarios and offer practical insights into their application in robotics and computer vision estimation problems with a particular focus on SLAM.
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