High-gain Extended Kalman Filter Research Articles

High-gain extended Kalman filter for continuous-discrete systems with asynchronous measurements

ABSTRACT This paper investigates an adaptation of the high-gain Kalman filter for nonlinear continuous-discrete system with multirate sampled outputs under an observability normal form. The contribution of this article is twofold. First, we prove the global exponential convergence of this observer through the existence of bounds for the Riccati matrix. Second, we show that, under certain conditions on the sampling procedure, the observer's asynchronous continuous-discrete Riccati equation is stable and also, that its solution is bounded from above and below. An example, inspired by mobile robotics, with three outputs available is given for illustration purposes.

Distributed Adaptive High-Gain Extended Kalman Filtering for Nonlinear systems

In this work, we propose a distributed adaptive high-gain extended Kalman filtering approach for nonlinear systems. Specifically, we consider a class of nonlinear systems that are composed of several subsystems interacting with each other via their states. In the proposed approach, an adaptive high-gain extended Kalman filter is designed for each subsystem. The distributed Kalman filters communicate with each other to exchange subsystem state estimates. First, an implementation strategy which specifies how the distributed filters should communicate is designed. Second, the detailed design of the subsystem filter is described. Subsequently, the stability of the proposed distributed state estimation is analyzed. Finally, the effectiveness and applicability of the proposed design are illustrated via the application to a chemical process example.

A Real-Time Adaptive High-Gain EKF, Applied to a Quadcopter Inertial Navigation System

The authors demonstrate the practical application of the adaptive high-gain extended Kalman filter (EKF) (AEKF) onboard a quadcopter unmanned aerial vehicle (UAV). The AEKF presents several advantages in state estimation, as it combines good filtering properties with an increased sensitivity to large perturbations. It does this by varying the high-gain parameter according to a metric called innovation. Unlike many adaptive observers, the AEKF is mathematically proven to globally converge, a significant advantage over the traditional EKF when considering robust controls. The AEKF is implemented on the UAV's inertial navigation system (INS). Full INSs can have problems when sensors are noisy and limited, particularly in the case of highly dynamically unstable systems such as a quadcopter. Simulation and experimental data show that the AEKF is suitable for this INS.

An adaptive high-gain observer for nonlinear systems

In this paper the authors provide a solution to the noise sensitivity of high-gain observers. The resulting nonlinear observer possesses simultaneously (1) extended Kalman filter’s good noise filtering properties, and (2) the reactivity of the high-gain extended Kalman filter with respect to large perturbations. The authors introduce innovation as the quantity that drives the gain adaptation. They prove a general convergence result, propose guidelines to practical implementation and show simulation results for an example.

Observability and observer design for kinetic networks

In this paper, we deal with the observability and observer design of a certain class of reactors (batch reactors) which are globally asymptotically feedback stabilisable. We show how to design two types of high-gain observers: a Luenberger-like high-gain observer and a high-gain extended Kalman filter. Results of convergence of these estimators follow from our observability analysis. We prove that the non-linear feedback controller using these high-gain observers stabilise such reactors. In fact, we develop an observer-based control structure for a non-linear model of batch reactors. Two examples of such reactors that correspond to strongly connected networks and that have zero deficiency are presented in this paper. Simulations show the good performance of such an observer-based control structure.

Output Stabilization for Kinetic Networks

This paper deals with the observability and observer design of a certain class of reactors which are globally asymptotically feedback stabilizable. We show how to design two types of high gain observers: a Luemberger-like high gain observer and a high gain extended Kalman filter. Results of convergence of these estimators follow from our observability analysis. We prove that the nonlinear feedback controller using these high-gain observers stabilize such reactors. In fact, we develop an observer-based control structure for a nonlinear model of batch reactors. We give two examples of such reactors that correspond to strongly connected networks and that have zero deficiency. Ce papier traite de l'observabilité et la synthèse d'observateurs pour une certaine classe de réacteurs qui sont globalement asymptotiquement stabilisables par feedback. Nous montrons comment construire deux types d'observateurs grand gain: observateur grand gain du type Luenberger et un filtre de Kalman étendu grand gain. Les résultats de convergence de ces estimateurs decoulent de notre analyse d'observabilité. Nous prouvons que la loi de commande par retour d'etat utilisant ces observateurs, stabilise de tels réacteurs. En fait, nous développons une structure de contrôle basée sur un observateur (i.e couplage Contrôleur-Observateur) pour un modèle non-linéaire de réacteurs fermes homogènes. Nous donnons deux exemples de tels réacteurs dont les réseaux réactionnels sont faiblement réversibles et admettant un indice de déficience nul.