Continuous time system identification using subspace methods

An alternative method was proposed for identification of linear continuous time system with noisy output. Using Gaussian modulating filters, by numerical integration, a discrete equivalent identification model that was parametrized directly in continuous time model parameters was obtained, and the LS estimation algorithm was developed. The LS estimator is biased even with white measurement output noise, and the bias is determined by variance of output noise. On the basis of obtained output measurement noise variance, the bias was compensated and the consistent estimates of system parameters were given. Simulation which compares the standard LS with BCLS algorithm indicates that the proposed algorithm is an efficient method for noisy output continuous time system identification.

Subspace-based identification for continuous-time stochastic systems via distribution-theoretic approach

This paper discusses and documents the algorithms of SsfPack 2.2. SsfPack is a suite of C routines for carrying out computations involving the statistical analysis of univariate and multivariate models in state space form. The emphasis is on documenting the link we have made to the Ox computing environment. SsfPack allows for a full range of different state space forms: from a simple time-invariant model to a complicated time-varying model. Functions can be used which put standard models such as ARMA and cubic spline models in state space form. Basic functions are available for filtering, moment smoothing and simulation smoothing. Ready-to-use functions are provided for standard tasks such as likelihood evaluation, forecasting and signal extraction. We show that SsfPack can be easily used for implementing, fitting and analysing Gaussian models relevant to many areas of econometrics and statistics. Some Gaussian illustrations are given.

A criterion is introduced for determining the optimum sampling interval for the identification of system parameters. It increases the accuracy and stability in identification procedures. This is done by employing a bilinear transformation from the z-plane to the w-plane. Some results of simulations are also included. These reveal the usefulness of the suggested algorithm even in the presence of measurement noise.

A new online modelling method for aircraft engine state space model

Identification of continuous-time nonlinear systems: The nonlinear difference equation with moving average noise (NDEMA) framework

Both the plant parameter4 and delay time of the system may vary in the time-varying system, which makes system identification relatively complex. In this paper, a new system identification algorithm based on subspace method and cross-correlation function is proposed to identify system parameter and time-delay simultaneously. The time delay is identified with the calculation of the cross-correlation function between pre-processed input data that processed through initial plant parameters and original output data. Then, the time delay in the output data can be deleted with the time delay identified before and the parameters can be achieved by subspace identification algorithm. Therefore, the process parameters and time delay identification can be performed online by through above two alternative operations. The validity of the proposed identification algorithm is verified by the simulation study.

It is shown how genetic algorithms can be applied for system identification of both continuous and discrete time systems. It is shown that they are effective in both domains and are able to directly identify physical parameters or poles and zeros. This can be useful because changing one physical parameter might affect every parameter of a system transfer function. The estimates of poles and zeros are then used to design a discrete time pole placement adaptive controller. Simulations for minimum and nonminimum phase systems and a system with unmodeled dynamics are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Identification of continuous-time systems using arbitrary signals

A general framework for modeling of a time-varying continuous-time SISO system from its sampled input and output while retaining the system parameters with their physical interpretation is presented. The theory can be specialized to the Poisson moment functional approach, the integrated sampling approach, the instantaneous sampling approach or the use of state variable filters. In all methods, the initial conditions can be removed by applying an appropriate discrete-time operator. Digital filtering is used to explicitly or implicitly reconstruct the time-derivatives of the sampled continuous-time signals involved. A thorough study of the approximations resulting from converting the continuous-time model to a discrete-time version is presented. It is shown how these errors can be controlled and that system parameter estimates can be obtained with an arbitrary accuracy. The digital filtering approach to integrated sampling and instantaneous sampling exhibit optimal properties among all methods that fit in the general framework. Moreover, using digital filter designs instead of numerical integration allows slower sampling. A maximum likelihood estimator is derived for time-invariant systems in an errors-in-variables stochastic framework. Finally, the theory is verified through simulations.

Abstract A smoothness priors modeling of time series with trends and seasonalities is shown. An observed time series is decomposed into local polynomial trend, seasonal, globally stationary autoregressive and observation error components. Each component is characterized by an unknown variance–white noise perturbed difference equation constraint. The constraints or Bayesian smoothness priors are expressed in state space model form. Trading day factors are also incorporated in the model. A Kalman predictor yields the likelihood for the unknown variances (hyperparameters). Likelihoods are computed for different constraint order models in different subsets of constraint equation model classes. Akaike's minimum AIC procedure is used to select the best model fitted to the data within and between the alternative model classes. Smoothing is achieved by using a fixed-interval smoother algorithm. Examples are shown. Key Words: Bayesian modelingBox-JenkinsSmoothingSeasonal adjustmentKalman filterLikelihoodTrading day adjustment

A nonlinear state space approach to the smoothing of time series is developed. The time series is expressed in state space model form where the system model or the observation model contains nonlinear functions of the state vector. Recursive formulas for prediction, filtering and smoothing for the nonlinear state space model are shown. The performance of the method is illustrated by the analyses of both a one dimensional and a two dimensional example that have been previously considered in the literature. These examples require numerical approximations of the relevant densities and numerical computations for the nonlinear transformations of variables, the convolution of two densities, Bayes formula, and normalization. Results for the one dimensional example are compared and contrasted with those obtained by the extended Kalman filter method, by a second moment approximation method and also by the Monte Carlo filter method. An empirical study of the numerical accuracy is also shown. A more complete treatment of this material is in Kitagawa (1991).

State Space Model to Detect Cycles in Heterogeneous Agents Models

Modeling mobile robots is crucial to odometry estimation, control design, and navigation. Classical state-space models (SSMs) have traditionally been used for system identification, while recent advances in deep learning, such as Long Short-Term Memory (LSTM) networks, capture complex nonlinear dependencies. However, few direct comparisons exist between these paradigms. This paper compares two multivariate modeling approaches for a differential drive robot: a classical SSM and an LSTM-based recurrent neural network. Both models predict the robot’s linear (v) and angular () velocities using experimental data from a five-minute navigation sequence. Performance is evaluated in terms of prediction accuracy, odometry estimation, and computational efficiency, with ground-truth odometry obtained via a SLAM-based method in ROS2. Each model was tuned for fair comparison: order selection for the SSM and hyperparameter search for the LSTM. Results show that the best SSM is a second-order model, while the LSTM used seven layers, 30 neurons, and 20-sample sliding windows. The LSTM achieved a FIT of 93.10% for v and 90.95% for , with an odometry RMSE of 1.09 m and 0.23 rad, whereas the SSM outperformed it with FIT values of 94.70% and 91.71% and lower RMSE (0.85 m, 0.17 rad). The SSM was also more resource-efficient (0.00257 ms and 1.03 bytes per step) compared to the LSTM (0.0342 ms and 20.49 bytes). The results suggest that SSMs remain a strong option for accurate odometry with low computational demand while encouraging the exploration of hybrid models to improve robustness in complex environments. At the same time, LSTM models demonstrated flexibility through hyperparameter tuning, highlighting their potential for further accuracy improvements with refined configurations.

This paper presents a novel deterministic approach for the identification of linear continuous-time systems. The approach is based on the projection of measured signals onto the finite dimensional signal subspace whose basis is determined by the parameter structure of the target system model. In this paper, we describe the basic concept and implementation of the proposed identification framework, and develop the methodology to deal with multi-variable input and/or output case. In addition, the initial state estimation technique, which enables us to use the truncated I/O data for identification, is introduced. The important features of the proposed approach are (i) the ability to handle both open and closed loop systems in a unified way and (ii) the robustness against the measurement noise. These features are demonstrated through a numerical example.