Robot control algorithm-Bayes Filter Bayesian filter

Some content comes from: Mobile Sensing and Robotics. Link: Bayes Filter .

Probabilistic Approaches.

Mainly use probabilistic methods to describe and update the current state of the robot. Need to know the total probability formula, the Bayes formula. Other related knowledge, if you don’t understand, make up.

1. Uncertainty in robot motion and observations.
2. Use of probability theory to explicitly represent the uncertainty.

几条特性：
$$\begin{gathered} 0\le P(A)\le 1 \\ P(True)=1,P(False)=0 \\ P(A+B)=P\left(A\right)+P(B)-P(AB) \\ P(A|B)=\frac{P(AB)}{P\left(B\right)}=\frac{P(B|A)P(A)}{P\left(B\right)} \end{gathered}$$

Recursive Bayes Filter.

Pay attention to the meaning of several notations:

1. belief($x_t$): in $x_t$The probability of the position (state) of the robot at the moment.
2. $x_t$: state at step $t$, where the robotic are. $At$ time$t$ , the position of the robot.
3. ${with}_{1:t}$: observation, measurement. t t Observed value at time$t$ .
4. $u_{1:t}$: control, action. $t$ the action taken.

Prediction and Correction Step.

Bayes Filter can be written as two steps:

1. Prediction Step.

Motion Model.

2. Correction Step.

Observation Model.

Derivation notes

The following are the deduced notes I made (in order to prevent ambiguity, I provide the scanned version and the original version). The conversion of each step, including the full probability formula and Markov hypothesis, is not explained in detail. If you don’t know, check it. The theory used in each step of the update is marked. If you have any questions, please raise them under the comments.

1. Scan documents:

2. Original image file: