Probabilistic Robot chapter II Recursive state estimation (Bayesian filter) _ Probabilistic robot

After learning Gaobo's "Slam 14", basic understanding of slam frame structure, and then looked at some Orb-slam code, ran a few models, read several papers, feel still a lot of questions about state estimation is not very clear, and then in the know about the slam recommended books, There is a state estimation and probability robot, but the state estimate is only available in English, the probability robot has a Chinese version, so I bought a probabilistic robot. Although the quality of translation may not be too good, but still can read, some places still need to read English. Thanks for translating probabilistic robot authors to save time. Recently, the entire probability of the robot's first part of the reading, I made a little note, or posted it. Take notes just to deepen their understanding, there may be some places to understand not in place, you are welcome to criticize.
The whole book is divided into 4 parts, namely basic knowledge, positioning, map construction and planning and control. Basic knowledge altogether 6 chapters. The first chapter of the introduction does not say, the remaining five chapters are recursive state estimation (Bayesian filter), Gaussian filter, Nonparametric filter, Robot Motion (state equation), robot perception (observation equation). Next I will put the six chapters of the notes are posted to deepen their understanding.
Then start with the second chapter of the notes.
This chapter mainly introduces the basic idea of Bayesian filtering algorithm in robot. This chapter establishes a coupled dynamic system model for the interaction of robots and their environments, which is the establishment of two equations, observation equations and control equations. The robot influences the environment by controlling the equation, and the observation equation only observes the environment change without affecting it.
In probabilistic robots, robots and environments are linked by the two equations, which can also be seen as two distributions, i.e., state-transfer distributions and observational distributions. The state transfer distribution describes the characteristics of how states change over time (governing equations). The observed distribution describes the characteristics of the measurement state (state change caused by the control equation). Because these two are described in terms of probability, they form the cornerstone of a probabilistic robot.
The robot confidence level is a posteriori distribution of all past sensor measurements and all past control environmental states. Bayesian filter is the basic algorithm of the human confidence of the computer, it is a recursive, T-time confidence is calculated by the confidence of the t-1 moment. Confidence response is the robot's internal information about the state of the environment, such as robot posture, in general, the robot is not aware of its own posture, it must through the external observation data to infer their posture, that is, from the internal confidence to identify their real state. In the probability robot, the confidence degree is expressed by the conditional probability distribution. For a true state confidence distribution, a probability can be allocated for each possible hypothesis. The confidence distribution is a posteriori probability of the state variable in terms of the observed data obtained.

Before the measurement of T time has been done, only based on the measurement before the t-1 moment and the control before T time, we can get a prediction probability, namely:

It is a posteriori based on the previous state, predicting the state of the T moment before the measurement of the integrated time t. The Predictive Computing Bel (x_t) is called the measurement update.
Bayesian filter has a very important assumption, that is, Markov hypothesis, it assumes that the current state is the sum of all past states, that is, the next state is only determined by the current state, and the previous state has nothing to do.
Bayesian filtering algorithm
The Bayesian algorithm consists of two basic steps:
1. Calculation forecasts, that is, based on the previous state and current control to predict the current state.
2. Measurement update, according to the current measurement results to revise the previous step of the forecast results. This step is mainly based on the Bayes law to achieve, that is, conditional probability.

The whole algorithm is as follows:

This is the Bayesian filter algorithm, now you want to finish the notes, and then over time to try to write the code of each algorithm.