Radial basis functions have the features of simple form and flexible node configuration, which can form networks to fit complex nonlinear systems. The networks composed of radial basis functions can describe nonlinear model mapping relationships. In this paper, the parameter estimation problem of a class of radial basis function-based nonlinear models with colored noises is studied. In order to suppress the influence of colored noise on the parameter estimation, the data filtering technique is used to design a filter to filter the observed data without changing the model input-output relationship, which realizes the white noise processing of the identification models with colored noises. On this basis, a filtering-based multi-innovation extended stochastic gradient algorithm is proposed for estimating this type of radial basis function-based nonlinear models by using the gradient search and combining the multi-innovation identification theory. Furthermore, considering the parameter separability of the models, in the framework of filtering identification, a three-stage filtering-based multi-innovation extended recursive algorithm is proposed for estimating this type of radial basis function-based nonlinear models by using the decomposition technique and recursive search method. The simulation results show the effectiveness and superiority of the proposed algorithms.