Characterization of Model-Based Detectors for CPS Sensor Faults/Attacks

A vector-valued model-based cumulative sum (CUSUM) procedure is proposed for identifying faulty/falsified sensor measurements. First, given the system dynamics, we derive tools for tuning the CUSUM procedure in the fault/attack free case to fulfill a desired detection performance (in terms of false alarm rate). We use the widely-used chi-squared fault/attack detection procedure as a benchmark to compare the performance of the CUSUM. In particular, we characterize the state degradation that a class of attacks can induce to the system while enforcing that the detectors (CUSUM and chi-squared) do not raise alarms. In doing so, we find the upper bound of state degradation that is possible by an undetected attacker. We quantify the advantage of using a dynamic detector (CUSUM), which leverages the history of the state, over a static detector (chi-squared) which uses a single measurement at a time. Simulations of a chemical reactor with heat exchanger are presented to illustrate the performance of our tools.Comment: Submitted to IEEE Transactions on Control Systems Technolog

Deterministic Mean-field Ensemble Kalman Filtering

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Legland etal. (2011) is extended to non-Gaussian state space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence $\kappa$ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF when the dimension $d<2\kappa$. The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which exists for both DMFEnKF and standard EnKF. Numerical results support and extend the theory

Degenerate Kalman filter error covariances and their convergence onto the unstable subspace

The characteristics of the model dynamics are critical in the performance of (ensemble) Kalman filters. In particular, as emphasized in the seminal work of Anna Trevisan and coauthors, the error covariance matrix is asymptotically supported by the unstable-neutral subspace only, i.e., it is spanned by the backward Lyapunov vectors with nonnegative exponents. This behavior is at the core of algorithms known as assimilation in the unstable subspace, although a formal proof was still missing. This paper provides the analytical proof of the convergence of the Kalman filter covariance matrix onto the unstable-neutral subspace when the dynamics and the observation operator are linear and when the dynamical model is error free, for any, possibly rank-deficient, initial error covariance matrix. The rate of convergence is provided as well. The derivation is based on an expression that explicitly relates the error covariances at an arbitrary time to the initial ones. It is also shown that if the unstable and neutral directions of the model are sufficiently observed and if the column space of the initial covariance matrix has a nonzero projection onto all of the forward Lyapunov vectors associated with the unstable and neutral directions of the dynamics, the covariance matrix of the Kalman filter collapses onto an asymptotic sequence which is independent of the initial covariances. Numerical results are also shown to illustrate and support the theoretical findings

On hybrid consensus-based extended Kalman filtering with random link failures over sensor networks

summary:This paper is concerned with the distributed filtering problem for nonlinear time-varying systems over wireless sensor networks under random link failures. To achieve consensus estimation, each sensor node is allowed to communicate with its neighboring nodes according to a prescribed communication topology. Firstly, a new hybrid consensus-based filtering algorithm under random link failures, which affect the information exchange between sensors and are modeled by a set of independent Bernoulli processes, is designed via redefining the interaction weights. Second, a novel observability condition, called parameterized jointly uniform observability, is proposed to ensure the stochastic boundedness of the error covariances of the hybrid consensus-based filtering algorithm. Finally, an example is given to demonstrate the effectiveness of the derived theoretical results

Nonlinear stability of the ensemble Kalman filter with adaptive covariance inflation

The Ensemble Kalman filter and Ensemble square root filters are data assimilation methods used to combine high dimensional nonlinear models with observed data. These methods have proved to be indispensable tools in science and engineering as they allow computationally cheap, low dimensional ensemble state approximation for extremely high dimensional turbulent forecast models. From a theoretical perspective, these methods are poorly understood, with the exception of a recently established but still incomplete nonlinear stability theory. Moreover, recent numerical and theoretical studies of catastrophic filter divergence have indicated that stability is a genuine mathematical concern and can not be taken for granted in implementation. In this article we propose a simple modification of ensemble based methods which resolves these stability issues entirely. The method involves a new type of adaptive covariance inflation, which comes with minimal additional cost. We develop a complete nonlinear stability theory for the adaptive method, yielding Lyapunov functions and geometric ergodicity under weak assumptions. We present numerical evidence which suggests the adaptive methods have improved accuracy over standard methods and completely eliminate catastrophic filter divergence. This enhanced stability allows for the use of extremely cheap, unstable forecast integrators, which would otherwise lead to widespread filter malfunction.Comment: 34 pages. 4 figure

Event-based recursive distributed filtering over wireless sensor networks

In this technical note, the distributed filtering problem is investigated for a class of discrete time-varying systems with an event-based communication mechanism. Each intelligent sensor node transmits the data to its neighbors only when the local innovation violates a predetermined Send-on-Delta (SoD) data transmission condition. The aim of the proposed problem is to construct a distributed filter for each sensor node subject to sporadic communications over wireless networks. In terms of an event indicator variable, the triggering information is utilized so as to reduce the conservatism in the filter analysis. An upper bound for the filtering error covariance is obtained in form of Riccati-like difference equations by utilizing the inductive method. Subsequently, such an upper bound is minimized by appropriately designing the filter parameters iteratively, where a novel matrix simplification technique is developed to handle the challenges resulting from the sparseness of the sensor network topology and filter structure preserving issues. The effectiveness of the proposed strategy is illustrated by a numerical simulation.This work is supported by National Basic Research Program of China (973 Program) under Grant 2010CB731800, National Natural Science Foundation of China under Grants 61210012, 61290324, 61473163 and 61273156, and Jiangsu Provincial Key Laboratory of E-business at Nanjing University of Jiangsu and Economics of China under Grant JSEB201301