# Quantized Innovations Bayesian Filtering

## TL;DR

This paper derives simple Bayesian filtering formulas for linear systems using quantized innovations, improving efficiency and providing a basis for comparison with existing methods like sign-of-innovations Kalman filter and particle filtering.

## Contribution

It introduces exact recursive Bayesian filtering formulas for quantized innovations in linear systems, offering a new approach that simplifies previous methods.

## Key findings

- Provides exact recursive formulas for Bayesian filtering with quantized innovations.
- Demonstrates the approach with computational examples.
- Offers a basis for comparing different filtering techniques.

## Abstract

The paper provides simple formulas of Bayesian filtering for the exact recursive computation of state conditional probability density functions given quantized innovations signal measurements of a linear stochastic system. This is a topic of current interest because the innovations signal should be white and therefore efficient in its use of channel capacity and in the design and optimization of the quantizer. Earlier approaches, which we reexamine and characterize here, have relied on assumptions concerning densities or approximations to yield recursive solutions, which include the sign-of-innovations Kalman filter and a Particle filtering technique. Our approach uses the Kalman filter innovations at the transmitter side and provides a point of comparison for the other methods, since it is based on the Bayesian filter. Computational examples are provided.