## 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