Filtering in Multivariate Systems with Quantized Measurements using a Gaussian Mixture-Based Indicator Approximation

This work addresses the problem of state estimation in multivariable dynamic systems with quantized outputs, a common scenario in applications involving low-resolution sensors or communication constraints. A novel method is proposed to explicitly construct the probability mass function associated with the quantized measurements by approximating the indicator function of each region defined by the quantizer using Gaussian mixture models. Unlike previous approaches, this technique generalizes to any number of quantized outputs without requiring case-specific numerical solutions, making it a scalable and efficient solution. Simulation results demonstrate that the proposed filter achieves high accuracy in state estimation, both in terms of fidelity of the filtering distributions and mean squared error, while maintaining significantly reduced computational cost.