Author: Zen and the Art of Computer Programming
Particle Filter is a target tracking method based on probability theory, which was originally applied in the field of drones. In recent years, with the development of sensor technologies such as computer vision, more and more systems have been applied to augmented reality. So, how to use the particle filter algorithm of computer processing image data to track target objects? This article will introduce the principle, application and evolution process of this algorithm in detail.
2. Explanation of basic concepts and terms
2.1 Probability Density Function
An important assumption in the particle filter algorithm is that the observation value returned by each sensor (Sensor) has a certain probability distribution. That is to say, suppose there is a variable X whose value is x, and the probability density function f(x) represents the probability that the random variable X falls in a certain interval [a, b]. Then, according to Bayes' theorem, the joint probability distribution P(X=x|Y) can be obtained, where Y represents the system output observation value, which is equal to the conditional probability of the observation value. In the particle filter algorithm, assuming that the state variable of each perceptron is x, then the state variable of the particle is a set {xi} composed of multiple particles, where xi obeys the probability distribution f(x). Through iterative calculation, the state variable of each particle can be updated, making the error smaller and smaller, and finally achieving the purpose of tracking the target.
2.2 Particle Filter (Particle Filterer)
The particle filter is a state space model, consisting of a series of discrete particles, and uses this model to simulate system behavior. The particle filter is divided into two parts: initialization phase and iteration phase.
- Initialization stage: First, based on the initial estimate, the initial position, velocity and other parameters of the particles are set.
- Iterative stage: Based on the current system state estimate, weight and signal-to-noise ratio information are used to weight the particles to obtain a new particle set. Then, the particles are corrected, sampled and other operations are performed, and the state and position of the particles are updated, in order to achieve the purpose of estimating the real system state. Particle filters operate in two main ways:
- Localizer mode: Each iteration only updates the status of a single particle to maintain the stability of the particle set. The advantage of this mode is that the calculation speed is fast, but the positioning accuracy is not high enough, and it requires a long period of training to achieve better results.