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Signal Analysis by Recursive Local Model Fitting

Signal analysis by local model fitting seems to be an obvious idea. However, apart from the classical Savitzky-Golay filter, this idea seems to have remained largely unexplored until recently.

My first steps with this approach began with the observation that using models with two segments ("past" and "future"), each with its own recursive algorithm, opens interesting possibilities, e.g.:

S. Graf, Smart Fire Detection,
Semester project at ISI/ETH, 2006.
(In this project with an industry partner, we used onset detection based on recursively fitting two connected straight-line models.)
H.-A. L., L. Bolliger, S. Korl, and C. Reller,
Localizing, forgetting, and likelihood filtering in state-space models,
2009 Information Theory and Applications Workshop, UCSD, La Jolla, CA, Feb. 8-13, 2009.
PDF

However, the full power of this approach (using multi-segment polynomial models) was discovered by Reto Wildhaber, who has been developing it far beyond my imagination and has been using it for amazing feats of real-world engineering:

R.A. Wildhaber, N. Zalmai, M. Jacomet, and H.-A. L.,
Windowed state space filters for signal detection and separation,
IEEE Trans. Signal Proc., vol. 66, pp. 3768-3783, July 2018.
IEEE Xplore / Preprint
R.A. Wildhaber, D. Bruegger, N. Zalmai, H. Malmberg, J. Goette, M. Jacomet, H. Tanner, A. Haeberlin, and H.-A. L.,
Estimation of the cardiac field in the esophagus using a multipolar esophageal catheter,
IEEE Trans. Biomed. Circuits and Systems, vol. 12, pp. 791-800, Aug. 2018.
IEEE Xplore / Preprint
R.A. Wildhaber, E. Ren, F. Waldmann, and H.-A. L.,
Signal analysis using local polynomial approximations,
28th European Signal Processing Conference (EUSIPCO 2020), Amsterdam, NL, January 18-22, 2021.
IEEE Xplore / Preprint
E. Ren, G. Cid Ornelas, and H.-A. L.,
Real-time interaural time delay estimation via onset detection,
2021 IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), Toronto, Canada, June 6-11, 2021.
IEEE Xplore / Preprint
F. Waldmann, C. Baeriswyl, R. Andonie, and R. Wildhaber,
Onset detection of pulse-shaped bioelectrical signals using linear state space models,
Current Directions in Biomedical Engineering, vol. 8, no. 2, 2022, pp. 101-104.
PDF
C. Baeriswyl, F. Waldmann, A. Bertrand, and R. A. Wildhaber,
Multi-resolution autonomous linear state space filters for N-dimensional signals,
IEEE Transactions on Signal Processing, vol. 73, pp. 5303-5318, 2025.
IEEE Xplore

For a concise summary of this approach, see Chapter 7 of the Lecture Notes of my course Model-Based Estimation and Signal Analysis (held at ETH until 2025).

Pertinent software (mostly developed by Reto Wildhaber) is available here here .

Last modified: March 28, 2026