# An optimization framework for resilient batch estimation in Cyber-Physical Systems

## TL;DR

This paper introduces a resilient set-valued estimation framework for linear time-varying systems affected by bounded process noise and potentially unbounded impulsive measurement noise, ensuring bounded estimation errors.

## Contribution

It develops a novel class of set-valued estimators that maintain bounded errors despite unbounded impulsive measurement noise, enhancing robustness in cyber-physical system state estimation.

## Key findings

- Estimator achieves resilience against unbounded impulsive noise
- Error bounds depend on system observability and performance functions
- Simulation confirms robustness and bounded error performance

## Abstract

This paper proposes a class of resilient state estimators for LTV discrete-time systems. The dynamic equation of the system is assumed to be affected by a bounded process noise. As to the available measurements, they are potentially corrupted by a noise of both dense and impulsive natures. The latter in addition to being arbitrary in its form, need not be strictly bounded. In this setting, we construct the estimator as the set-valued map which associates to the measurements, the minimizing set of some appropriate performance functions. We consider a family of such performance functions each of which yielding a specific instance of the general estimator. It is then shown that the proposed class of estimators enjoys the property of resilience, that is, it induces an estimation error which, under certain conditions, is independent of the extreme values of the (impulsive) measurement noise. Hence, the estimation error may be bounded while the measurement noise is virtually unbounded. Moreover, we provide several error bounds (in different configurations) whose expressions depend explicitly on the degree of observability of the system being observed and on the considered performance function. Finally, a few simulation results are provided to illustrate the resilience property.