The performances of three classical adaptive cubature Kalman filters (ACKFs) for nonlinear stochastic discrete-time system with unknown process noise are investigated. First, filtering theories of the ACKFs are discussed, and then stability analysis and accuracy comparison simulations are performed. It is proved that cubature H-infinity filter (CH∞F) can provide an extra positive-definite matrix to improve its stability and other two ACKFs both need a good choice of process noise initial covariance for better stability. Simulation results also show that all the three ACKFs can have better accuracy than the traditional CKF with unknown process noise. Furthermore, CH∞F can most quickly follow the process noise change in high dimension case but it do the worst of three ACKFs in one dimension filtering, cubature Kalman filter-strong tracking filtering (CKF-STF) can keep good accuracy in all examples, adaptive cubature Kalman filter based on maximum a posterior estimation (ACKF-MAP) is prone to deterioration in high dimensions filtering, whereas it has good performance in one dimension cases.