The authors analyze the error behavior for the discrete-time extended Kalman filter for general nonlinear systems in a stochastic framework. In particular, it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough. This result is verified by numerical simulations for an example system.

Stochastic stability of the discrete-time extended Kalman filter

Feedback systems: Input-output properties

Technical communique: Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough

Given the square matrices $A, B, D, E$ and the matrix $C$ of conforming dimensions, we consider the linear matrix equation $A{\mathbf X} E+D{\mathbf X} B = C$ in the unknown matrix ${\mathbf X}$. Our aim is to provide an overview of the major algorithmic developments that have taken place over the past few decades in the numerical solution of this and related problems, which are producing reliable numerical tools in the formulation and solution of advanced mathematical models in engineering and scientific computing.

/pdf/computational-methods-for-linear-matrix-equations-29c8rmvfvt.pdf

Computational Methods for Linear Matrix Equations

This paper is concerned with the distributed set-membership filtering problem for a class of general discrete-time nonlinear systems under event-triggered communication protocols over sensor networks. To mitigate the communication burden, each intelligent sensing node broadcasts its measurement to the neighboring nodes only when a predetermined event-based media-access condition is satisfied. According to the interval mathematics theory, a recursive distributed set-membership scheme is designed to obtain an ellipsoid set containing the target states of interest via adequately fusing the measurements from neighboring nodes, where both the accurate estimate on Lagrange remainder and the event-based media-access condition are skillfully utilized to improve the filter performance. Furthermore, such a scheme is only dependent on neighbor information and local adjacency weights, thereby fulfilling the scalability requirement of sensor networks. In addition, an optimization algorithm is developed to minimize the trace of the estimated ellipsoid set, and the effect from the adopted event-triggered threshold is thoroughly discussed as well. Finally, a simulation example is utilized to illustrate the usefulness of the proposed distributed set-membership filtering scheme.

A Set-Membership Approach to Event-Triggered Filtering for General Nonlinear Systems Over Sensor Networks

https://hal.archives-ouvertes.fr/hal-00098113/document

Brief Extension of minimum variance estimation for systems with unknown inputs

A new method for designing a Kalman filter for linear discrete-time systems with unkown inputs is presented. The algorithm recently developed for stochastic singular systems is applied to obtain a linear estimation of the state and unkown inputs. The necessary and sufficient conditions for the existence and stability of the filter are derived and proved. An illustrative example is included.

ltering with unknown inputs via optimal state estimation of singular systems

Brief paper: State estimation in the presence of bounded disturbances

https://hal.archives-ouvertes.fr/hal-00105181/document

Solution to Sylvester equation associated to linear descriptor systems

In this paper, the class of bilinear systems subjected to unknown inputs for which there exists a disturbance decoupled observer with linear error dynamics is characterized. It is shown that the design of this kind of observer is equivalent to the design of a disturbance decoupled observer for a linear system. This result simplifiers considerably the observer design compared to those proposed in the literature, and the observer existence conditions can be easily deduced. As a corollary of this result, necessary and sufficient conditions for the existence of disturbance decoupled linear observers for bilinear systems subjected to unknown inputs are derived. This approach is extended to the fault detection of bilinear systems.

/pdf/on-disturbance-decoupled-observers-for-a-class-of-bilinear-3myp617kin.pdf

Mohamed Darouach

Papers

Brief Extension of minimum variance estimation for systems with unknown inputs

ltering with unknown inputs via optimal state estimation of singular systems

Brief paper: State estimation in the presence of bounded disturbances

Solution to Sylvester equation associated to linear descriptor systems

On Disturbance Decoupled Observers for a Class of Bilinear Systems