Lowa prioristatistical information model for optimal smoothing and differentiation of noisy signals
Sandro Fioretti, Leopoldo Jetto · International Journal of Adaptive Control and Signal Processing · 1994
Abstract 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 littlea prioristatistical 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.