Particle Filter versus PHD Multi-Target Tracking: A Comparative Analysis

In the field of target tracking, the Particle Filter (PF) and the Probability Hypothesis Density (PHD) filter are two mainstream algorithms, each with distinct strengths and weaknesses, especially in multi-target scenarios. This article compares their performance based on a three-target tracking experiment.

The core concept of the Particle Filter: It approximates the posterior probability distribution through a randomly sampled set of particles, making it suitable for nonlinear and non-Gaussian systems. Its advantages include straightforward implementation and robustness to changes in the number of targets. However, computational load increases significantly as the target count rises. In multi-target scenarios, joint state-space modeling or data association strategies are typically required, which can lead to reduced tracking accuracy. In code implementation, the PF algorithm involves steps like particle initialization, prediction based on motion models, weight update using measurement likelihood functions, and systematic resampling to avoid degeneracy.

The theoretical foundation of the PHD filter: The PHD filter propagates the probability density of target existence rather than individual target states, avoiding explicit data association. Its Marginal PHD version further simplifies computations and is suitable for unknown and time-varying target numbers. Experiments show that for three-target crossing scenarios, the Marginal PHD filter effectively suppresses false alarms but may miss targets under low signal-to-noise ratio conditions. Algorithmically, the PHD filter recursively updates the intensity function through prediction and update steps, often implemented using Gaussian Mixture (GM-PHD) or Sequential Monte Carlo (SMC-PHD) methods, with key functions handling birth, death, and spawning of targets.

Performance comparison conclusions: Computational efficiency: Particle Filters offer better real-time performance when the number of targets is small, but the resampling step becomes a bottleneck as targets increase; the computational complexity of PHD filters remains relatively stable. Tracking accuracy: PHD filters exhibit lower association error rates in dense target crossing scenarios, while Particle Filters respond faster to abrupt motions (e.g., sharp turns). Scalability: PHD filters natively support changes in the number of targets, whereas Particle Filters require additional logic (e.g., birth/death models).

In practical applications, if the environment has high noise and frequent target interactions, the Marginal PHD filter holds an advantage; if high-frequency updates or complex target motions are required, the Particle Filter may be more suitable. Future directions could explore hybrid architectures to balance real-time performance and robustness.