# SLAM系统的滤波和优化方法笔记

1. 已知高斯变量的分布为  条件分布 的联合分布为

变量的边缘分布为

1. 已知联合概率

SLAM方法中基于滤波的方法的核心是卡尔曼滤波，基于(非线性)优化方法的核心是高斯牛顿法，经由线性化，二者可以通过迭代EKF联系在一起。包含前通和后通步骤的基于平滑的方法等价于最小二乘Cholesky分解的基于优化的方法，是一种批处理方法。

[1]."Kalman Filtering with Newton's Method"

KF的牛顿法推导：... one-step KF is given by a single Newton method on the gradients of a quadratic objective functions and with a carefully chosen initial guess. It provides a more generic recursive state estimation. can also used for EKF for non linear system.

[2].“State estimation for robotics"  Timothy D. Barfoot

[3].OKVIS:  “Keyframe-Based Visual-Inertial Odometry Using Nonlinear Optimization”

[4]."Probabilistic Robotics" 第11章关于GraphSLAM.

[5]."A Sliding Window Filter for SLAM"

... it is not surprising that marginalizing out parameters induces conditional dependencies between all the remaining parameters that the removed parameters were conditionally dependent on. 参数之间的相关性是通过被边缘化的参数建立的。

http://blog.sciencenet.cn/blog-465130-1086221.html

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