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Synchronization through extended Kalman filtering. (English) Zbl 0927.93053

Nijmeijer, Henk (ed.) et al., New directions in nonlinear observer design. International workshop, Geiranger Fjord, Norway, June 24–26, 1999. London: Springer. Lect. Notes Control Inf. Sci. 244, 469-490 (1999).
A nonlinear discrete-time system of the form \(x(k+1)=f(x(k))+w(k)\) with linear observations \(y(k)=Hx(k)+v(k)\) is considered. The estimate \(\widehat{x}(k) \) of the state \(x(k)\) is produced by the extended Kalman filter which consists of using the classical Kalman filter equations for the first-order approximation of the nonlinear system about the last estimate. The authors investigate the error \(e(k)=x(k)-\widehat{x}(k)\) and establish conditions for its boundedness for large \(k\).
For the entire collection see [Zbl 0915.00063].

MSC:

93E11 Filtering in stochastic control theory
93C10 Nonlinear systems in control theory
93C55 Discrete-time control/observation systems
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