What do Kalman filter and particle filter mean?

Kalman filtering is different from traditional filtering (Qualcomm, bandpass, etc.). Kalman filter is actually an estimation of the target state, and it is a target state estimation method. Taking a moving target as an example, the target has its own motion equation, such as X=AX+Bu, but in reality, the motion of the target does not completely follow his motion equation, and there will be more or less deviations (for example, when you drive at a constant speed, the speed cannot always be constant). These deviations are the so-called noise, that is, the motion equation of the target is actually X=AX+Bu+q, where q stands for noise. Similarly, when you want to know the state of the target, you should measure the state of the target (that is, observe). As an observer, it is impossible to observe or measure the state of the target without bias, and there is noise, so the observation equation can be written as Z=AX+r, where r obeys Gaussian distribution, indicating observation noise. We can get the observation directly. The purpose of Kalman filter is to estimate the state of the target through noisy observations, and continuously estimate the state of the target according to the measured values during the movement of the target. Of course, Kalman filtering is only applicable to linear systems. When the target model is nonlinear, extended Kalman filter, colorless Kalman filter and particle filter can be used. In a word, the filtering in Kalman filter is equivalent to removing noise according to the observed value, thus obtaining the estimated value of the target state, which is a target state estimation method. I recommend you a book "Optimal State Estimation: Kalman H∞ and Nonlinear Filtering". Kalman filter is widely used! Many respondents have said what filtering is, so I will briefly talk about the example of using Kalman filter in high-energy physics experiments. After the particle collider accelerates the particle collision, a large number of new particles will be produced. These particles will fly around and hit the surrounding detectors, and each unit of the detector will receive the impact information of the particles.