The Bayesian filtering quickly understand Kalman filter Kalman Filter (KF)

Reprinted: https: //blog.csdn.net/varyshare/article/details/97891376
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Fast hardware algorithms often comes from a very simple idea that evolved, if you do not know this idea and understand that evolution can not talk fast hardware algorithm

Intuitive understanding

What first Kalman filter to solve the problem? I estimate the robot away from the obstacle distance himself as an example
A: First robot known "the last obstacle between the robot from a distance", "robot sensor measures the distance from the obstacle (we call it the observations , such as direct measurement radar robot obstacle distance from 7m) "and" speed "their current time of these three data. According to the "last obstacle between the robot from a distance" and "speed of their current time" we can estimate the distance from the current robot obstacle (we call it an estimate ). For example: the last second obstacle from 10m, speed is 4m / s, so now this second estimate on the distance from the barrier 6m yes. So the question is, the distance from the obstacle robot now both observations 7m, there are a estimated value of 6m. I believe in the end what? Simply believe that the observations in case the sensor is broken it? I believe that in case of a simple estimate of the distance in time or speed estimates are not allowed to do? So, we want to get the ultimate robot based on the accuracy of the observations and the estimated value of the distance from the obstacle estimates. High accuracy on the final result of the high proportion of low accuracy on low proportion. 7m if the radar measurement accuracy is 90% according to the estimated speed of 6m accuracy that is 80%, then the final result of the distance estimation is


intuitively understood that finished, more

However, 90% and 80% of both the accuracy of the above is how calculated ? The man in the end is how the Kalman invention Kalman Filter ? What thought process of the invention Kalman algorithm is ? Kalman filter algorithm in the end have anything to do with Bayesian filtering algorithm ? I think these must be lingering in your mind, not only from the intuitive understanding answer these questions.

Kalman filter (Kalman filter) algorithm and Bayesian filtering (bayes filter) What is the connection between the algorithms?

A: The Bayesian filtering is an idea , it tells how we know how to calculate the final estimated value reliability when the reliability of the observations command and control of these two values. But Bayesian filtering does not tell us how to calculate the observed values of credibility, how to control model (issued after the robot control command is executed in accordance with what the model) modeling. The Kalman filter algorithm is a Bayesian filtering algorithm for the specific implementation . Kalman filter observations confidence that a normal distribution model, a control model is normal.

So Kalman filter algorithm is derived from the further evolution of Bayesian filtering algorithm, I hope in this article you can have pre-school understanding of Bayesian filtering. If you do not know how Bayesian filtering done? You can look at this article [understanding and derivation of Bayesian filter (Bayes Filter) algorithm] (https://blog.csdn.net/weixin_44088559/article/details/105389194).

Recall Bayesian filtering algorithm:

Why Bayesian filtering algorithm requires a probability value?

Kalman filtering Bayesian filtering done?

Kalman filtering Bayesian filtering is how to achieve?

I guess the state of the robot as an example.

Assume Kalman filter observation and control of the robot made

Kalman filter in the end how to solve a problem? What amount is known, eventually wanted to ask what results?

In the end what kind of ideas are derived from Kalman filter algorithm inventor's point of view?

How to simplify deduced Kalman gain? And how to derive the mean recursion expression to get X