An accurate and practical traffic-state estimation (TSE) method for signalized intersections plays an important role in real-time operations to facilitate efficient traffic management. This paper presents a generalized modeling framework for estimating traffic states at signalized intersections. The framework is non-parametric and data-driven, without any requirement on explicit modeling of traffic flow. The Bayesian filter (BF) approach is the core of the framework and introduces a recursive state estimation process. The required transition and measurement models of the BFs are trained using Gaussian process (GP) regression models with respect to a historical dataset. In addition to the detailed derivation of the integration of BFs and GP regression models, an algorithm based on the extended Kalman filter is presented for real-time traffic estimation. The effectiveness of the proposed framework is demonstrated through several numerical experiments using data generated in microscopic traffic simulations. Both fixed-location data (i.e., loop detector) and mobile data (i.e., connected vehicle) are examined with the framework. As a result, the method shows good performance under the different traffic conditions in the experiment. In particular, the approach is suitable for short-term estimation, a challenging task in traffic control and operations.