Proximal observers for secure state estimation
For control and estimation engineers, this work provides a novel method to handle sparse but arbitrary measurement noise in nonlinear systems, though the approach is incremental as it builds on existing proximal operator techniques.
This paper introduces a framework for designing robust state estimators for discrete-time nonlinear systems subject to impulsive measurement noise, using proximal operators to minimize nonsmooth convex functions. The proposed observers guarantee asymptotic convergence of the estimation error in noise-free settings and can be implemented via efficient numerical procedures or analytic relaxations.
This paper discusses a general framework for designing robust state estimators for a class of discrete-time nonlinear systems. We consider systems that may be impacted by impulsive (sparse but otherwise arbitrary) measurement noise sequences. We show that a family of state estimators, robust to this type of undesired signal, can be obtained by minimizing a class of nonsmooth convex functions at each time step. The resulting state observers are defined through proximal operators. We obtain a nonlinear implicit dynamical system in term of estimation error and prove, in the noise-free setting, that it vanishes asymptotically when the minimized loss function and the to-be-observed system enjoy appropriate properties. From a computational perspective, even though the proposed observers can be implemented via efficient numerical procedures, they do not admit closed-form expressions. The paper argues that by adopting appropriate relaxations, simple and fast analytic expressions can be derived.