Probabilistic Bounds for a Class of Filtering Algorithms in the Scalar Case

We focus on the estimation error of a type of filtering algorithm in the scalar case, which is applicable to both linear and nonlinear systems. Under some regularity conditions, we construct a surrogate process that has a moment dominance property with respect to the true filtering error process. Then, moment-based probability inequalities can be used to compute probabilistic bounds for the filtering error. The sharpness of the bounds is tested on a simulated epidemic model with both Gaussian and non-Gaussian noise.