Nonlinear System Identification and Parameter Estimation

Nonlinear system identification and parameter estimation encompass the formulation of mathematical models and the determination of their coefficients so as to capture the dynamic behaviour of systems whose responses depend nonlinearly on inputs and states. By analysing measured data, these techniques extract model structure and quantify unknown parameters, enabling prediction, control and optimisation across disciplines. Traditional approaches rely on parametric structures such as polynomial or basis‐function expansions, employing time- and frequency-domain criteria to fit models via optimisation. Contemporary advances have introduced machine-learning frameworks, sparse regression and Bayesian inference to tackle high dimensionality, noise and uncertainty. Hybrid methodologies integrate physical laws with data-driven components, improving interpretability and robustness. Key challenges include selecting an appropriate model architecture, ensuring convergence in the presence of measurement noise and adapting to time-varying dynamics. Practical applications range from fault detection in rotating machinery and adaptive control of unmanned vehicles to environmental monitoring and biomedical signal analysis. Recent innovations in real-time-capable algorithms and probabilistic estimation have extended the field’s reach, offering enhanced accuracy, uncertainty quantification and computational efficiency in complex nonlinear settings.

Research from Nature Portfolio

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Research from all publishers

Recent work has refined projection-based identification for systems with time-varying parameters by generalising finite-window algorithms to balance tracking performance against computational cost. This approach selects an optimal data window length to minimise estimation error while maintaining robustness to noise. Parallel efforts have developed gradient-based iterative schemes for stochastic dynamical systems, introducing multi-innovation updates that leverage successive measurement innovations to accelerate convergence and improve estimation accuracy under uncertainty. A comprehensive review of state-estimation techniques has highlighted the shift from purely model-driven filters, such as extended and unscented Kalman filters, towards hybrid-driven methods that fuse physics-based models with data-driven components. This synthesis enhances estimator performance when facing nonlinearities or evolving system dynamics, and charted future directions for combining deep-learning architectures with classical observers.

Nonlinear System Identification and Parameter Estimation publication trend

The graph below shows the total number of articles in nonlinear system identification and parameter estimation across all publications each year (not limited to Nature Index journals).

Technical terms

Nonlinear system identification: The process of determining a mathematical model of a system exhibiting nonlinear input–output relationships using observed data.

Parameter estimation: The numerical determination of unknown coefficients in a chosen model structure to best fit measured system responses.

Stochastic gradient algorithm: An iterative optimisation method that updates parameter estimates by following the gradient of a cost function computed from random subsets of data.

Kalman filter: A recursive state-estimation algorithm that uses a model and sequential measurements to produce optimally filtered estimates under Gaussian noise assumptions; extended and unscented variants handle nonlinearities.

Hybrid-driven method: An estimation approach that combines physics-based modelling with data-driven techniques to improve adaptability and robustness in complex or partially known systems.

References

1. Performance analysis of the generalised projection identification for time‐varying systems. IET Control Theory and Applications (2016).
2. The New Trend of State Estimation: From Model-Driven to Hybrid-Driven Methods. Sensors (2021).
3. Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data. Mathematics (2019).