- Jian Gao

# Distributed Mean-Field-Type Filter for Vehicle Tracking

Updated: Mar 11, 2018

**A new kind of distributed mean-field-type filter is proposed to solve the filtering problem in large-scale traffic networks. To deal with noisy and high-dimensional observed data, the filter incorporates a mean field term into the system model and decomposes the state space into highly independent parts; filtering is performed in each part and then integrated. To achieve accurate estimations, the procedure iterates over four steps: prediction, sampling, decomposition and correction. Theoretical analysis suggests the global error has a linear bound, which is independent of the network’s cardinality. The proposed approach is tested in aircraft and vehicle tracking scenarios. Both simulation and real experiment results demonstrate the advantage of this filter over traditional mean-field-free filters. **

Particle filter is an effective tool for vehicle tracking. However, we need to maintain a large number of particles to keep a reasonable tracking accuracy for multi-target tracking in large scale state space. This paper proposes a new distributed mean-field-type filter to handle those noisy, partial-observed and high-dimensional data. The state space is decomposed and the particles are deployed locally and updated independently in the simplified sub-spaces. The filtering framework contains four operations: sampling, prediction, decomposition and correction. A mean-field term is included in the system dynamic so that the prediction is based on the previous state as well as its statistic distribution, which is estimated by a multi-frame learning procedure. The experiment on real data shows that our approach can achieve accurate tracking results with a small number of particles.

**I. INTRODUCTION **
Vehicle tracking is a fundamental problem in Intelligent Traffic Systems (ITS). With the development of sensor technology, the observation data can be easily collected from
many sources, such as inductive loops, video cameras and radars. However, those data are often noisy and partially observed, which could make fatal conflicts and deteriorate
the quality of ITS. Therefore, new learning, filtering and data assimilation techniques are required to process the noisy data collected from large scale traffic networks.

*Map of the surveillance region *

Vision-based vehicle tracking is a challenging problem because the quality of the video data is generally very poor. The observation data is often contaminated by the noise from background interference, low resolution, lighting change, motion blur, and occlusion. Early work on filtering and signal estimation assumes Gaussian noise and linear systems. Kalman filter uses a linear time-invariant dynamic model to estimate the optimal state, which can yield the exact conditional probability estimate with that assumption. The extensions EKF, UKF, EnKF and particle filters were designed to deal with nonlinear models and non Gaussian noise.

**II. CONTRIBUTION**
A dynamical system that involves the probability measure of the state variable in the transition kernel to the next state is called a mean-field-type system. The contribution of this paper can be summarized as:
(i). We propose a distributed mean-field-type filter (DMF) for vehicle tracking. The state space is decomposed into independent sub-spaces based on the foreground detection result. Particles are initialized as some good hypotheses and updated independently in each subspace.

(ii). We provide a generic methodology to estimate the filtering distribution in four steps: sampling, prediction, decomposition and correction. This methodology can be applied to other high-dimensional networked systems with mean-field-type dynamic models and noisy observations.

(iii). The mean-field ter

m of system state is combined in the dynamic model to provide robust and accurate state prediction. A multi-frame learning procedure is designed to estimate the prior state distribution. The experimental results on real data have verified the usefulness and effectiveness of our approach.

**III. IMPLEMENTATION AND EXPERIMENTAL RESULTS**
The experiment results demonstrate the improvements in both accuracy and efficiency compared with the standard particle filters. We compare our approach with a modified version of particle filter. The particle number is set to be N = 1000, while in our algorithm we assign N = 10 particles in each zone. The processing speed is around 0.6 frame per second, with MATLAB i

mplementation on a PC with 3.50-GHz Intel Core E5-1650 CPU. Most computational load is in foreground detection. Our algorithm can be easily accelerated by parallel computing.

**Vehicle Tracking in a single camera's view**

The surveillance region is a subarea of the entire traffic network in Maryland, which covers about 30,000 square miles and contains 411 video cameras. For simplicity, we conducted the experiment on 12 cameras in this local area. The highway traffic sequences captured by these 12 video cameras are put together and generate a video with resolution 1920*1080. It contains 1376 frames at 15 frames per second. Our goal is to track multiple vehicles simultaneously in the surveillance regions and count the vehicle number on the road.

*Tracking result in 12 camera views*

**IV. CONCLUSION **

This work proposed a new distributed mean-field type filtering framework for vehicle tracking on highways. The filter has four components: sampling, prediction, decomposition and correction. By decomposition of the entire state space, the distributed filters perform locally and focus on their simplified subspace. Based on the foreground detection result, particles are initially deployed near some good hypotheses, which is better than random guessing. A multi-frame learning procedure is added before the tracking task to estimate the prior state distribution. A mean-field term is combined in the system dynamic so that the state prediction depends on not only the previous state but also the statistics of the process. The mean-field filter performs well with small ensembles in the vehicle tracking task.

*This paper has been published at American Control Conference (ACC) in 2017 and won the Student Travel Award. *