The Identification and Parameterization of Armax and State Space Forms

Econometrica ◽  
1976 ◽  
Vol 44 (4) ◽  
pp. 713 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
State Space ◽  
Space Forms

State-space forms for higher-order discrete-time models

1998 ◽  
Vol 34 (1-2) ◽  
pp. 23-31 ◽  
Author(s):  
A.Raymond Comeau ◽  
Noriyuki Hori
Keyword(s):  
State Space ◽  
Discrete Time ◽  
Higher Order ◽  
Space Forms ◽  
Discrete Time Models

scholarly journals The validation of new phase-dependent gait stability measures: a modelling approach

2021 ◽  
Vol 8 (2) ◽  
pp. 201122
Author(s):  
Jian Jin ◽  
Dinant Kistemaker ◽  
Jaap H. van Dieën ◽  
Andreas Daffertshofer ◽  
Sjoerd M. Bruijn
Keyword(s):  
State Space ◽  
Strong Correlations ◽  
Risk Of Falling ◽  
Predictive Capacity ◽  
Space Forms ◽  
Gait Stability ◽  
Finite Time Lyapunov Exponent ◽  
Foot Strike ◽  
Falls In Older Adults ◽  
Prevention Methods

Identification of individuals at risk of falling is important when designing fall prevention methods. Current measures that estimate gait stability and robustness appear limited in predicting falls in older adults. Inspired by recent findings on changes in phase-dependent local stability within a gait cycle, we devised several phase-dependent stability measures and tested for their usefulness to predict gait robustness in compass walker models. These measures are closely related to the often-employed maximum finite-time Lyapunov exponent and maximum Floquet multiplier that both assess a system's response to infinitesimal perturbations. As such, they entail linearizing the system, but this is realized in a rotating hypersurface orthogonal to the period-one solution followed by estimating the trajectory-normal divergence rate of the swing phases and the foot strikes. We correlated the measures with gait robustness, i.e. the largest perturbation a walker can handle, in two compass walker models with either point or circular feet to estimate their prediction accuracy. To also test for the dependence of the measures under state space transform, we represented the point feet walker in both Euler–Lagrange and Hamiltonian canonical form. Our simulations revealed that for most of the measures their correlation with gait robustness differs between models and between different state space forms. In particular, the latter may jeopardize many stability measures' predictive capacity for gait robustness. The only exception that consistently displayed strong correlations is the divergence of foot strike. Our results admit challenges of using phase-dependent stability measures as objective means to estimate the risk of falling.

Detection of Shocks in Structural Time Series Model Using State Space Forms

2018 ◽  
Vol 12 (1) ◽  
pp. 143-163
Author(s):  
Reza Zabihi Moghadam ◽  
Rahim Chinipardaz ◽  
Gholamali Parham ◽  
◽  
◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Time Series Model ◽  
Space Forms ◽  
Structural Time Series ◽  
Structural Time

Hybrid state-space self-tuning control using dual-rate sampling

1991 ◽  
Vol 138 (1) ◽  
pp. 50 ◽  
Author(s):  
Leang S. Shieh ◽  
Xiao M. Zhao ◽  
John W. Sunkel
Keyword(s):  
State Space ◽  
Hybrid State ◽  
Self Tuning

Extended State Space of the Rational sl(2) Gaudin Model in Terms of Laguerre Polynomials

2013 ◽  
Vol 58 (11) ◽  
pp. 1084-1091
Author(s):  
Yu.V. Bezvershenko ◽  
◽  
P.I. Holod ◽  
Keyword(s):  
State Space ◽  
Laguerre Polynomials ◽  
Gaudin Model ◽  
Extended State
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