Low a priori statistical information model for optimal smoothing and differentiation of noisy signals

A novel approach is proposed to the optimal smoothing and differentiation problem of unknown one-dimensional signals corrupted by additive white Gaussian noise. State space techniques are used. the main feature of the method is that very little a priori statistical information about the signal generation process is required. Starting from the basic assumption that the actual waveform does not show relevant discontinuities, a state space representation is derived by defining a state vector composed of the signal and its derivatives. All parameters of this representation are analytically derived except two: a multiplicative scalar of the input noise covariance matrix and the variance of the measurement noise. A procedure for the optimal estimation of these parameters from noisy data is proposed. Application of a fixed-lag Kalman smoother provides the simultaneous estimate of the signal and its derivatives. Numerical results confirm the validity of the approach.

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