The unavailability of excitation measurements poses challenges of application of many structural identification methods due to dealing with two typical types of inverse problems of parameter and force identification simultaneously. To address this issue, four different identification methods are proposed based on correlation function to identify structures subjected to multiple unknown ambient excitations, namely gradient search, genetic algorithm, particle swarm optimization (PSO), and effective combination of PSO and gradient search. Numerical studies on a cantilever beam and an eight-story frame, experiments verification on the ASCE benchmark frame are carried out to test the performance of proposed methods. In addition, effect of selection of the reference point, number of data points, unknown initial conditions and modelling errors on accuracy of identification results are also investigated. The numerical and experimental results show that the proposed methods are capable of accurately identifying the unknown structural parameters. In particular, the hybrid method of PSO and gradient search, with approach of producing solutions close to the optimal by PSO and then taking as initial values in gradient search to quickly identify structural unknown parameters, achieves the best performance for overall consideration of identification accuracy and computational efficiency.