This paper presents a model that closely approximates the Generalized Maxwell-Slip (GMS) model, a multistate friction model known to describe all essential friction characteristics in presliding and sliding motion. In contrast to the GMS model, which consists of a switching structure to accommodate for its hybrid nature, the new model, referred to as the Smoothed GMS (S-GMS) model, consists of an analytic set of differential equations. Such a model is well suited for gradient-based state and parameter estimation, as in the Extended Kalman Filter (EKF) or in Moving Horizon Estimation (MHE). Similar to the GMS model, the S-GMS model is a multi-state model that also describes all essential friction characteristics. Moreover, the S-GMS model description includes the single-state LuGre model and Elasto-Plastic model as special cases. This paper discusses the implementation of the EKF estimator for the S-GMS friction model and compares its performance to the LuGre model in joint state and parameter estimation.