Because the state space model contains both the unknown states and the unknown parameters,and they involve the nonlinear product relations,which makes the identification problem more complicated.In order to solve this problem,this paper studies the combined state and parameter estimation methods for canonical state space systems.The interactive estimation theory is used to derive the combined state and parameter estimation algorithms by means of the recursive or iterative scheme.When computing the parameter estimates,the unknown states in the information vector of the identification algorithms are replaced with their estimates,the obtained parameter estimates are used to design the parameter estimates based observer or the parameter estimates based Kalman filtering algorithm to estimate the states of the systems.They form an interactive estimation process (a hierarchical estimation process).Along this line,from the recursive scheme or the iterative scheme,this paper presents the observer based or the Kalman filtering based stochastic gradient (SG) identification algorithm,recursive least squares (LS) identification algorithm,multi-innovation SG algorithm,multi-innovation LS identification algorithm,and the model decomposition based identification methods.Finally,the computational efficiency,the computational steps and the flowcharts of some typical algorithms are discussed.