In this paper we present a "State-Based Multi-Parameter Probability Estimation" (SBMP) for Context-Based Adaptive Binary Arithmetic Coding (CABAC) which employs a two hypotheses probability estimator based on exponentially weighted moving averages. It uses a logarithmic state representation and a single subsampled transition table with only 32 elements for the probability update. This reduces the memory requirements virtually without affecting the compression efficiency, compared to corresponding approaches that use a linear state representation and a computation-based probability update. The proposed scheme is based on simple operations like table look-ups and additions. Compared to the state-of-the-art probability estimator of the video compression standard H.265/HEVC, the compression efficiency is increased by up to 1 % Bjontegaard-Delta bit rate (BD rate) when applied to draft 2 of the Versatile Video Coding (VVC) standard. Furthermore, SBMP was recently adopted to working draft 2 of the MPEG-7 part 17 standard for compression of neural networks for multimedia content description and analysis.