Identification of continuous-time state-space model from samples of input-output data

1982 ◽  
Vol 18 (2) ◽  
pp. 50 ◽  
Author(s):  
Zhou Qi-Jie ◽  
N.K. Sinha
Keyword(s):  
State Space ◽  
Continuous Time ◽  
State Space Model ◽  
Input Output ◽  
Output Data ◽  
Space Model

State-Space Model and Kalman Filter Gain Identification by a Kalman Filter of a Kalman Filter

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Minh Q. Phan ◽  
Francesco Vicario ◽  
Richard W. Longman ◽  
Raimondo Betti
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
State Space ◽  
Kalman Filters ◽  
State Space Model ◽  
Model Structure ◽  
System State ◽  
Input Output ◽  
Output Data ◽  
Space Model

This paper describes an algorithm that identifies a state-space model and an associated steady-state Kalman filter gain from noise-corrupted input–output data. The model structure involves two Kalman filters where a second Kalman filter accounts for the error in the estimated residual of the first Kalman filter. Both Kalman filter gains and the system state-space model are identified simultaneously. Knowledge of the noise covariances is not required.

Improvement of Observer/Kalman Filter Identification (OKID) by Residual Whitening

1995 ◽  
Vol 117 (2) ◽  
pp. 232-239 ◽  
Author(s):  
M. Phan ◽  
L. G. Horta ◽  
J.-N. Juang ◽  
R. W. Longman
Keyword(s):  
Kalman Filter ◽  
Linear System ◽  
State Space ◽  
Moving Average ◽  
State Space Model ◽  
Input Output ◽  
Output Data ◽  
Space Model ◽  
Auto Regressive ◽  
Average Description

This paper presents a time-domain method to identify a state space model of a linear system and its corresponding observer/Kalman filter from a given set of general input-output data. The identified filter has the properties that its residual is minimized in the least squares sense, orthogonal to the time-shifted versions of itself, and to the given input-output data sequences. The connection between the state space model and a particular auto-regressive moving average description of a linear system is made in terms of the Kalman filter and a deadbeat gain matrix. The procedure first identifies the Markov parameters of an observer system, from which a state space model of the system and the filter gain are computed. The developed procedure is shown to improve results obtained by an existing observer/Kalman filter identification method, which is based on an auto-regressive model without the moving average terms. Numerical and experimental results are presented to illustrate the proposed method.

scholarly journals Using approximate Bayesian inference for a “steps and turns” continuous-time random walk observed at regular time intervals

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e8452
Author(s):  
Sofia Ruiz-Suarez ◽  
Vianey Leos-Barajas ◽  
Ignacio Alvarez-Castro ◽  
Juan Manuel Morales
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Time Scale ◽  
Animal Movement ◽  
State Space Model ◽  
Movement Direction ◽  
Time Intervals ◽  
Space Model ◽  
Regular Time ◽  
Approximate Bayesian

The study of animal movement is challenging because movement is a process modulated by many factors acting at different spatial and temporal scales. In order to describe and analyse animal movement, several models have been proposed which differ primarily in the temporal conceptualization, namely continuous and discrete time formulations. Naturally, animal movement occurs in continuous time but we tend to observe it at fixed time intervals. To account for the temporal mismatch between observations and movement decisions, we used a state-space model where movement decisions (steps and turns) are made in continuous time. That is, at any time there is a non-zero probability of making a change in movement direction. The movement process is then observed at regular time intervals. As the likelihood function of this state-space model turned out to be intractable yet simulating data is straightforward, we conduct inference using different variations of Approximate Bayesian Computation (ABC). We explore the applicability of this approach as a function of the discrepancy between the temporal scale of the observations and that of the movement process in a simulation study. Simulation results suggest that the model parameters can be recovered if the observation time scale is moderately close to the average time between changes in movement direction. Good estimates were obtained when the scale of observation was up to five times that of the scale of changes in direction. We demonstrate the application of this model to a trajectory of a sheep that was reconstructed in high resolution using information from magnetometer and GPS devices. The state-space model used here allowed us to connect the scales of the observations and movement decisions in an intuitive and easy to interpret way. Our findings underscore the idea that the time scale at which animal movement decisions are made needs to be considered when designing data collection protocols. In principle, ABC methods allow to make inferences about movement processes defined in continuous time but in terms of easily interpreted steps and turns.

scholarly journals A continuous-time state-space model for rapid quality control of argos locations from animal-borne tags

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Ian D. Jonsen ◽  
Toby A. Patterson ◽  
Daniel P. Costa ◽  
Philip D. Doherty ◽  
Brendan J. Godley ◽  
...  
Keyword(s):  
Quality Control ◽  
State Space ◽  
Continuous Time ◽  
State Space Model ◽  
Space Model

Improved State-Space Model Identification Using Input and Output Data with Steady State Values

2004 ◽  
Vol 37 (11) ◽  
pp. 215-220
Author(s):  
Manabu Kosaka ◽  
Hiroshi Uda ◽  
Eiichi Bamba ◽  
Hiroshi Shibata
Keyword(s):  
Steady State ◽  
State Space ◽  
State Space Model ◽  
Model Identification ◽  
Output Data ◽  
Space Model ◽  
Input And Output

State-space Model Identification Using Input and Output Data With Steady State Values Zeroing Multiple Integrals of Output Error

2005 ◽  
Vol 128 (3) ◽  
pp. 746-749
Author(s):  
Manabu Kosaka ◽  
Hiroshi Uda ◽  
Eiichi Bamba ◽  
Hiroshi Shibata
Keyword(s):  
Steady State ◽  
System Identification ◽  
State Space ◽  
State Space Model ◽  
Hankel Matrix ◽  
Output Data ◽  
Single Input Single Output ◽  
Space Model ◽  
Output Error ◽  
Input And Output

This study proposes a new deterministic off-line identification method that obtains a state-space model using input and output data with steady state values. This method comprises of two methods: Zeroing the 0∼N-tuple integral values of the output error of single-input single-output transfer function model (Kosaka et al., 2004) and Ho-Kalman’s method (Zeiger and McEwen, 1974). Herein, we present a new method to derive a matrix similar to the Hankel matrix using multi-input and multi-output data with steady state values. State space matrices A, B, C, and D are derived from the matrix by the method shown in Zeiger and McEwen, 1974 and Longman and Juang, 1989. This method’s utility is that the derived state-space model is emphasized in the low frequency range under certain conditions. Its salient feature is that this method can identify use of step responses; consequently, it is suitable for linear mechanical system identification in which noise and vibration are unacceptable. Numerical simulations of multi-input multi-output system identification are illustrated.

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