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.

Continuous-Discrete High-Gain Extended Kalman Filter for Mobile Robots with Asynchronous Outputs

“…1a. As in [11], the measurements of angles φ 1 , φ 2 and distance ρ 1 are taken into account. The associated output model, where x B denotes the abscissa of B in the reference frame, is:…”

“…For a thorough definition of this observer, and a complete exposure of its proof of convergence, interested readers may refer to [11].…”

“…The present paper builds on [10] and [11] where the Kalman filter algorithm has been considered for continuous-discrete systems with asynchronous measurements. In particular, we proposed a definition of asynchronous systems that doesn't require any specific structure or regularity for the measurement procedure.…”

“…In particular, we proposed a definition of asynchronous systems that doesn't require any specific structure or regularity for the measurement procedure. On this basis, the global convergence of the observer has been demonstrated, in [10] for linear, observable, time-varying asynchronous systems, and in [11] for nonlinear systems, under appropriate observability assumptions, in the framework of high-gain observers.…”

“…Therefore, system (Σ N ) is not a faithful model of the robot's dynamics. As such, following the formalism proposed in [11], this section presents an asynchronous version of (Σ N ) together with the ad hoc high-gain extended Kalman filter. In other words, the general context of the above cited article is adapted to the system (Σ N ) in terms of state space and sensor output variables.…”