# A Particle PHD Filter for Dynamic Grid Map Building towards Indoor Environment
## 1 Introduction
However, the PHD filter is based on the framework of RFS, the number of elements in an RFS should be random, and the clutter should satisfy Poisson distribution. The paper [20] proposed limiting the response of the target in only one resolution cell in the image observation and set a threshold value for the measurements to make it meet the two basic requirements of PHD filter. On the basis of [20], the paper [21] analyzed the problem of overestimating the number of targets theoretically and proposed a clustering method to solve the problem of overestimating the number of targets instead of limiting the response of target in one cell. However, they all assume that the physical size of the object is less than the resolution cell. For example, setting the grid size to 1 m is obviously not suitable for an indoor navigation environment. [PERSON] et al. [22] proposed an object tracking method based on a dynamic grid map. This method utilizes the feedback from these object tracks to the cell-level representation, and then the occupied grid cell can be individually associated with the object tracks without the need to use clustering methods for the objects that have been tracked. The object track is modeled as an oriented rectangular box. When calculating the size and reference position of the rectangular box, not only the relevant occupancy grid cells is considered, but also the measured free space evidence adjacent to each object box is considered, making the estimation more robust and accurate. In the paper [23], the dynamic object is represented as a modified occupancy grid map. Unlike traditional occupancy grid representation, the modified grid map is only used to keep track of the grids that may be occupied at the next moment. Then, GM-PHD is used to track the grid map, which can complete the tracking and shape estimation of multiple dynamically extended objects. This method can achieve a 20% improvement in the OSPA metric error compared to the baseline GM-PHD filter. [PERSON] et al. [24; 25] proposed combining MIB filters on the basis of PHD filters (PHD/MIB filter) and gave a strict mathematical definition for the building of dynamic grid maps based on random finite set (RFS) theory. This algorithm uses parallel acceleration to build dynamic grid maps in real time. However, multi-target estimation based on PHD/MIB filter uses a fixed number of particles to resample, which makes the efficiency very low. Since the new particle generation method is based on the Bernoulli filter method in each grid (under DS evidence theory, the mass value is greater than zero) and the constant velocity model is used, the system has a poor estimation effect on the maneuvering target and when the target just enters the field of view. In summary, the combination of PHD filter and grid map for dynamic object estimation shows promising results. However, they usually set the range of the dynamic grid map to a fixed size, which is very inflexible and cannot gradually expand the sensing range with the movement of the robot. At the same time, they are mainly aimed at outdoor environments. For indoor environments, due to the small space, filters are required to estimate the state of dynamic objects with faster speed and accuracy. The main contributions of this article are as follows: First, 2D Lidar is used to estimate the state of dynamic objects in indoor environments and the dynamic environment is represented by a dynamic grid map, which simplifies the problem of data association between measurements and targets in the PHD filter. The dynamic grid map is bound to the robot coordinate system, so that the size of the dynamic grid map remains unchanged with the movement of the robot, and the update equation of the particle state with the movement of the robot is deduced. Second, the CV and CS motion models are fused, which improves the system's perception speed and accuracy of maneuvering objects and reduces the fluctuations in the estimation of constant-velocity moving objects.