For nonlinear non-Gaussian stochastic dynamic systems with inequality state constraints, this technical note presents an efficient particle filtering algorithm, constrained auxiliary particle filtering algorithm. To deal with the state constraints, the proposed algorithm probabilistically selects particles such that those particles far away from the feasible area are less likely to propagate into the next time step. To improve on the sampling efficiency in the presence of inequality constraints, it uses a highly effective method to perform a series of constrained optimization so that the importance distributions are constructed efficiently based on the state constraints. The caused approximation errors are corrected using the importance sampling method. This ensures that the obtained particles constitute a representative sample of the true posterior distribution. A simulation study on vehicle tracking is used to illustrate the proposed approach.