# A Particle PHD Filter for Dynamic Grid Map Building towards Indoor Environment
## 1 Introduction  
At present, with more and more robots entering our life, how to make robots have the ability of safe and fast dynamic obstacle avoidance has become a hot topic of mobile robot research. In the classical robot obstacle avoidance algorithm, which introduces the relative velocity information of a robot and dynamic object, better obstacle avoidance effect can be obtained [1, 2, 3], but how to quickly and accurately obtain the dynamic object is a very important challenge. For example, because of the randomness of human motion and the limited indoor space, it is difficult to track and estimate it quickly. In the field of general target tracking, the random finite set (RFS) theory [4, 5, 6] provides a mathematical and rigorous method for multi-objective Bayesian state estimation, which can cover all the situations that the standard Bayes filter cannot, including multiple appearing/disappearing objects, imperfect detection, and non-standard measurements. After the random finite set was first proposed by [PERSON] [4, 5], several classical Bayes filters were designed and developed based on this theory. However, the filter directly estimates the posterior probability density of multiple targets based on random finite sets, which involves set integrals and is difficult to be solved analytically. In the most general setting, these random finite set-based stochastic filters can be implemented only using the sequential Monte Carlo method [7, 8], or using approximations methods such as theProbability Hypothesis Density (PHD) filter [9; 10; 11], the Cardinalized PHD filter [12; 13], and the Labeled Multi-Bernoulli filter [14; 15]. The Probability Hypothesis Density (PHD) filter, which approximates the full multi-object density using the first-order statistical moment of the RFS known as the intensity function or the PHD, is developed to alleviate the computational intractability. The PHD filter operates on the single-target state space and greatly simplifies the calculation problems. At same time, this advantage accelerates the application of random finite set theory in multi-target estimation problems. In the field of robot and autopilot, it is very important to get the position and speed of the object around it. Several approaches have been presented to combine grid mapping and multi-object tracking toward automatic driving. The classical occupancy grid maps divide the whole environment into independent grid cells and calculate the probability of occupancy of each grid separately. The classic occupancy grid maps are widely used in SLAM (simultaneous location and mapping) and are an important tool for path planning and obstacle collision avoidance for their explicit free-space estimate and ability to represent arbitrarily shaped objects. [PERSON] et al. [16; 17] proposed using particles to characterize the dynamic state of a grid cell, which greatly reduces the amount of calculation to estimate the state of the grid. In order to improve the utilization of particles, [PERSON] et al. [18] and [PERSON] et al. [19] proposed that particles only characterize the grid occupied cells by dynamic objects instead of all the occupied grid cells. However, they did not give a stochastically rigorous definition of a multi-object state estimation problem. Theoretically, any dynamic environment can be represented as a random finite set consisting of several point targets (corresponding to grid cells). Therefore, it is intuitively believed that the combination of PHD filter and grid map for multi-target tracking can achieve good results. However, PHD filter has two basic assumptions: one is that each target can only produce one measurement, and the other is that the alarm measurements conform to Poisson distribution. When using grid maps to represent the measurement model, one object will affect the whole area and make an intensity contribution to each cell. At the same time, there are fixed measurements at every moment equal to the number of all grids.