Abstract:  In multi-target tracking, the presence of non-zero mean Gaussian noise can lead to measurement offsets (or system biases) that result in imprecise target state estimations. To more accurately model system biases, Bernoulli variables are employed to determine whether there is a system bias at the current time for pre-detection, with its offset modeled as a Gaussian distribution. Analytically solving for the target state, Bernoulli variables, and offsets is challenging; thus, variational Bayesian approximation is utilized to iteratively update the parameters of each variable and derive the likelihood function. This likelihood function is then utilized in updating the PHD filter, leading to the introduction of a variational PHD filter that accounts for unknown system biases. Simulation results demonstrate that the proposed algorithm surpasses the GM-PHD and extended SMC-PHD filters in tracking performance when system biases are unknown.