# Multi-Agent-Supported Tracking Based on Hidden Markov Model with Weighted Entropy
## 1 Introduction  
With the rapid development of smart cities, the requirement for video surveillance systems has significantly increased. Visual object tracking, a fundamental task in computer vision, is divided into single-object tracking (SOT) and multi-object tracking (MOT). In recent years, MOT, aiming to locate multiple specific objects and maintain their unique identities in sequential frames, has received increasing attention due to its capability to advance video understanding, intelligent surveillance, human-computer interaction, and medical diagnostics. The tracking-by-detection (TBD) framework has recently become the dominant paradigm in MOT [1, 2, 3]. It transforms the MOT task into a frame-by-frame data association problem, typically implemented in a centralized system. Extensive research has been dedicated to addressing complex environmental conditions and target occlusion, with the aim of mitigating association failures and target loss. However, pedestrian trajectories--the primary focus of MOT--often deviate from purely deterministic models. This is due to their spatiotemporal evolution, which is jointly governedby objective physical constraints and subjective cognitive decision-making processes. To characterize pedestrian locomotion patterns, we propose a dual-phase paradigm comprising a decision phase and an action phase. The decision phase encompasses non-observable processes including destination planning, obstacle avoidance, and speed adjustment. In contrast, the action phase only contains the observable process of physical movement. This dual-phase structure presents challenges for traditional tracking methods, as it introduces significant uncertainty due to variable cognitive intentions and external environmental perturbations. The Hidden Markov Model (HMM), a kind of Probabilistic Graphical Model, provides a robust framework for modeling sequential probabilistic problems and performs efficient inference. Within this framework, latent states representing pedestrian intentions are influenced solely by the preceding state transition. This is particularly well-suited to the context of pedestrian tracking due to its ability to represent doubly stochastic processes: an unobservable decision phase governed by internal cognitive states and an observable action phase manifesting as measurement [4]. Further, target features suffer from severe uncertainties as well, influenced by changes in orientation, pose, or appearance. This variability aligns with the entropy framework, which quantifies information disorder. Leveraging this insight, we employ weighted entropy [5] to dynamically characterize feature uncertainty, enabling adaptive fusion strategies that balance noisy detections. However, the introduction of these two mechanism causes unavoidable computation loads in the traditional approach of track management, in addition to the weak adaptability of the algorithm and limited scalability of the system. Thus, we introduce a multi-agent mechanism to manage the tracking of objects. With the hypothesis that pedestrians do not exhibit abrupt large displacements between consecutive frames, we formulate each object as an agent that maintains a separate HMM-based Kalman filter and independently decide the creation, association, prediction, termination, and weight of features for tracks, which is a Markov decision process. Each agent is trained based on rewards obtained from the environment. Detections are associated based on each filter's prior prediction about the tracked object's position. And the weight of features is determined by the evaluation of entropy given by the agents. Therefore, the main contributions of this paper are as follows:  
* Decomposing pedestrian locomotion into a decision phase and an action phase according to human cognitive patterns: This addresses the analysis of dynamic moving patterns instead of objective conditions. And the dual-phase structure naturally accommodates probabilistic modeling frameworks.