参考：
An Elementary Introduction to Kalman Filtering
之前看的一篇讲Kalman Filter的论文，觉得很不错！重读一遍。
论文的结构大致是这样的：
Section 2——
回顾基础知识，如何对估计和估计的置信度进行建模和量化？
Section 2 describes how these intuitive ideas can be quantified. Estimates are modeled as random samples from distributions,and confidence in estimates is quantified in terms of the variances and covariances of these distributions.
Section 3——
如何对标量进行估计？
Section 3 shows how to fuse scalar estimates such as temperatures optimally. It is also shown that the problem of fusing more than two estimates can be reduced to the problem of fusing two estimates at a time without any loss in the quality of the final estimate.
Section 4——
如何对矢量进行估计？
Section 4 extends these results to estimates that are vectors, such as state vectors representing the estimated position and velocity of a robot.
Section 5——
如果只有部分状态变量可以被观测，那么如何由部分估计得到完整估计？
方法就是BLUE，最佳线性无偏估计。
In some applications, estimates are vectors but only a part of the vector can be measured directly. For example, the state of a spacecraft may be represented by its position and velocity, but only its position may be observable. In such situations, how do we obtain a complete estimate from a partial estimate?
Section 5 shows how the Best Linear Unbiased Estimator (BLUE) can be used for this.
Section 6——
Kalman filter如何解决线性系统中的状态估计问题？
Section 6 uses these ideas to solve the state estimation problems for linear systems, which is the usual context for presenting Kalman filters.
Section 7——
最后再简单介绍一下如何在非线性系统中使用Kalman filter。
Section 7 briefly discusses extensions of Kalman filtering for nonlinear systems.
来看一下Introducion部分吧。
开宗明义地说，Kalman filter就是用来进行状态估计的一种方法。
Kalman filtering is a state estimation technique invented in 1960 by Rudolf E. Kálmán.
BTW，这里插入一下什么是estimation——
Estimation is the problem of reconstructing the underlying state of a system given a
sequence of measurements as well as a prior model of the system.
状态估计，是根据系统的先验模型和测量序列，对系统内在状态进行重构的问题。
——From State Estimation for Robotics
先验模型，比如已知的动力学知识。
测量序列，也就是从传感器获取到的测量量。
接下来，文中提到，在一些资料中Kalman filter被视作Bayesian inference（在噪声假设为高斯噪声时）的一种应用，这样做带来了一种误导，以为Kalman filter只能用在噪声是高斯的场景中。
Other presentations derive Kalman filtering as an application of Bayesian inference assuming that noise is Gaussian. This leads to the common misconception that Kalman filtering can be applied only if noise is Gaussian.
通俗地说，Kalman filter就是将关于某个未知量的几种近似值合并到一起，形成一个比这些近似值都更好的近似值。
Kalman filtering can be seen as a particular approach to combining approximations of an unknown value to produce a better approximation.
很容易联想到的就是加权平均的方法了。
interesting!
Filtering is weighting，滤波即加权。
本科时候，一个专业做信号处理的老院士给我们上课的时候，说过这样一句话：filtering is weighting（滤波即加权）。 滤波的作用就是给不同的信号分量不同的权重。最简单的loss pass filter， 就是直接把低频的信号给0权重，而给高频部分1权重。对于更复杂的滤波，比如维纳滤波, 则要根据信号的统计知识来设计权重。
作者：Leo Cheng
链接：https://www.zhihu.com/question/30856539/answer/50002733
来源：知乎
著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。