Aiming at the nonlinear system model, a central difference Kalman-probability hypothesis density filter is
proposed to track multiple targets. Multi-target tracking is fulfilled by deriving polynomial approximations with Stirling
interpolation formulas, estimating first-order statistical moment of posterior multi-target states with central difference Kalman
filter and Gaussian mixture probability hypothesis density filter, and extracting targets’ states from the recursion of probability
hypothesis density. The advantage of proposed filter is mainly that Jacobian matrix solving is unnecessary and second-order
Taylor expansion accuracy can be ensured. Simulation results show that the robustness of the algorithm is enhanced, and the
estimating accuracy of the number and states of the targets are improved.