Nicola Forti

Distributed finite element Kalman filter

This paper addresses state estimation for spatially distributed systems governed by linear partial differential equations from discrete in-space-and-time noisy measurements provided by sensors deployed over the spatial domain of interest. A decentralised and scalable approach is undertaken by decomposing the domain into overlapping subdomains assigned to different processing nodes interconnected to form a network. Each node runs a local finite-dimensional Kalman filter which exploits the finite element approach for spatial discretisation and the parallel Schwarz method to iteratively enforce consensus on the estimates and covariances over the boundaries of adjacent subdomains. The effectiveness of the proposed distributed consensus-based finite element Kalman filter is demonstrated via simulation experiments concerning a temperature estimation problem modelled by the bi-dimensional heat equation.

A Bayesian approach to joint attack detection and resilient state estimation

The paper deals with resilient state estimation of cyber-physical systems subject to switching signal attacks and fake measurement injection. In particular, the random set paradigm is adopted in order to model the switching nature of the signal attack and the fake measurement injection via Bernoulli and/or Poisson random sets. The problem of jointly detecting a signal attack and estimating the system state in presence of fake measurements is then formulated and solved in the Bayesian framework leading to the analytical derivation of a hybrid Bernoulli filter that updates in real-time the joint posterior density of the detection attack Bernoulli set and of the state vector. Exploiting a Gaussian-mixture implementation of the filter, a simulation example is developed in order to demonstrate the effectiveness of the proposed method.

Point source estimation via finite element multiple-model Kalman filtering

Point source estimation consists of detecting and localizing a concentrated diffusive source as well as estimating its intensity and induced field from pointwise-in-time-and-space measurements of sensors deployed over the area of interest. The spatiotemporal dynamics of the diffused field is modeled by a partial differential equation (PDE) and a finite element (FE) method is employed for spatially discretizing the PDE model. Source identifiability, i.e. the possibility of detecting the source and uniquely identifying its location and intensity, is analysed in a system-theoretic framework. Further, a novel multiple model filtering approach to source estimation is presented and its effectiveness is demonstrated via a simulation experiment.

Distributed Joint Attack Detection and Secure State Estimation

The joint task of detecting attacks and securely monitoring the state of a cyber-physical system is addressed over a cluster-based network wherein multiple fusion nodes collect data from sensors and cooperate in a neighborwise fashion in order to accomplish the task. The attack detection–state estimation problem is formulated in the context of random set theory by representing joint information on the attack presence/absence, on the system state, and on the attack signal in terms of a hybrid Bernoulli random set (HBRS) density. Then, combining previous results on HBRS recursive Bayesian filtering with novel results on Kullback–Leibler averaging of HBRSs, a novel distributed HBRS filter is developed and its effectiveness is tested on a case study concerning wide-area monitoring of a power network.

Distributed Finite-Element Kalman Filter for Field Estimation

The paper deals with decentralized state estimation for spatially distributed systems described by linear partial differential equations from discrete in-space-and-time noisy measurements provided by sensors deployed over the spatial domain of interest. A fully scalable approach is pursued by decomposing the domain into possibly overlapping subdomains assigned to different processing nodes interconnected to form a network. Each node runs a local finite-dimensional discrete-time Kalman filter which exploits the finite element approach for spatial discretization, a backward Euler method for time-discretization and the parallel Schwarz method to iteratively enforce continuity of the field predictions over the boundaries of adjacent subdomains. Numerical stability of the adopted approximation scheme and stability of the proposed distributed finite element Kalman filter are mathematically proved. The effectiveness of the proposed approach is then demonstrated via simulation experiments concerning the estimation of a bi-dimensional temperature field.

Cyber Meets Control: A Novel Federated Approach for Resilient CPS Leveraging Real Cyber Threat Intelligence

Cyber-physical systems (CPS) embody a tight integration between network-based communications, software, sensors, and physical processes. While the integration of cyber technologies within legacy systems will most certainly introduce opportunities and advancements not yet envisioned, it will undoubtedly also pave the way to misdemeanors that will exploit systems� resources, causing drastic and severe nationwide impacts. While almost all works in the literature exclusively tackled the security of one independent aspect of CPS (i.e., cyber or physical), we argue that these systems cannot be decoupled. In this context, we present what we believe is a first attempt ever to tackle the problem of CPS security in a coupled and a systematic manner. To this end, this article proposes a novel approach that federates the cyber and physical environments to infer and attribute tangible CPS attacks. This is achieved by - Leveraging real cyber threat intelligence derived from empirical measurements. - Capturing and investigating CP data flows by devising an innovative CPS threat detector. An added value of the proposed approach is rendered by physical remediation strategies, which are envisioned to automatically be invoked as a reaction to the inferred attacks to provide CPS resiliency. We conclude this article by discussing a few design considerations and presenting three case studies that demonstrate the feasibility of the proposed approach.

MAP Moving Horizon state estimation with binary measurements

The paper addresses state estimation for discrete-time systems with binary (threshold) measurements by following a Maximum A posteriori Probability (MAP) approach and exploiting a Moving Horizon (MH) approximation of the MAP cost-function. It is shown that, for a linear system and noise distributions with log-concave probability density function, the proposed MH-MAP state estimator involves the solution, at each sampling interval, of a convex optimization problem. Application of the MH-MAP estimator to dynamic estimation of a diffusion field given pointwise-in-time-and-space binary measurements of the field is also illustrated and, finally, simulation results relative to this application are shown to demonstrate the effectiveness of the proposed approach.