Date of final exam: 07/05/1999

E-mail: iacoviel@dis.uniroma1.it

Tutor: Prof.  C. Bruni, Università di Roma ‘La Sapienza’

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On line discontinuities identification in noisy signals   ___________________________________________________________________________________________________________

Advisor:

Prof.  C. Bruni, Università di Roma ‘La Sapienza’

Summary of the thesis

The aim of this thesis is to analyze the problem of on line identification of jump discontinuities in the output of a linear stochastic time invariant dynamical system affected by additive gaussian white noises. This occurs for instance when faults in the sensing devices give rise to a sudden unknown polarization in the measurement noise. The experimental setup we refer to consists in the real time correction of the evolution of a Kalman filter used in a stochastic state feedback control scheme. The proposed procedure is based on a multiscale analysis technique by means of a particular family of wavelets: second order derivative of gaussian with fixed variances; with respect to the chosen class of perturbations (step-like signals) an identifiability result is first established; we propose an alarm function and statistical tests are proposed to decide if an alarm is due to noise or to a discontinuity. To test the limitations and the potentiality of the proposed procedure simulated data were analyzed; in particular the influence of the signal to noise ratio and the effect of successive discontinuities is discussed. The procedure was compared with another one based on the analysis of the sample mean of the signal on sliding windows.
 

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