Optimal evaluation in dynamic systems having waveform disturbances (Q1061079)

For a linear stochastic system \(dz/dt=D(t)z+A\delta (t-\tau)+G(t)\xi (t)\) (where the deterministic matrices D and G describe the systems dynamics and the noise dynamics, the random vector A models the pulse intensities for a \(\delta\)-pulse occuring at random time \(\tau\), and \(\xi\) (t) is Gaussian white noise) consider the linear observation \(y(t)=H(t)z(t)+\eta (t)\) (\(\eta\) (t) being Gaussian white noise). The article presents filter equations for an optimal rms estimate of the state z(t) using methods of conditional Markov processes, see e.g. \textit{R. S. Liptser} and \textit{A. N. Shiryayev} [Statistics of random processes I (1977; Zbl 0364.60004) and II (1978; Zbl 0369.60001)]. The optimal design of a one-dimensional filtering circuit provides an example.