Observer Design for Non-Uniform Sampled Systems Using Gain-Scheduling

2014 ◽  
Author(s):  
Omid Bagherieh ◽  
Behrooz Shahsavari ◽  
Ehsan Keikha ◽  
Roberto Horowitz
Keyword(s):  
Kalman Filter ◽  
Hard Disk Drives ◽  
Gain Scheduling ◽  
Observer Design ◽  
Time Varying ◽  
Time Intervals ◽  
Varying Coefficients ◽  
Regular Time ◽  
Time Varying Coefficients ◽  
Sampled Systems

In non-uniform sampled systems, the measurements are arriving at irregular time intervals. However, the control is updated at regular time intervals. An observer is required to obtain the estimate of the states during the control update times. We evaluate two observer designs: A Kalman filter and a gain-scheduling observer. The Kalman filter has the optimal performance. However, it is computationally expensive. In contrast, a recent gain-scheduling synthesis technique [1] can be used to design a time varying observer, whose time varying coefficients are a function of the measured sampling time variations. This observer is suboptimal, but it has significantly less computational complexity as compared to the Kalman filter, which makes it feasible to implement. Simulations are conducted for a self servo writing process in hard disk drives, in order to evaluate performance of H2 gain-scheduling observer design.

scholarly journals Time-Varying Coefficient Models And The Kalman Filter : Applications To Hedge Funds

2021 ◽  
Author(s):  
Ana G.S. Punales
Keyword(s):  
Kalman Filter ◽  
Hedge Funds ◽  
Hedge Fund ◽  
Varying Coefficient Models ◽  
Time Varying ◽  
Likelihood Estimator ◽  
Varying Coefficients ◽  
Industry Performance ◽  
Non Linear ◽  
Time Varying Coefficients

There are various studies concerned with the estimation of stochastically varying coefficients for the hedge fund series but just [sic] few are available in the literature that study the model with time-varying coefficients and non-linear factor, or make a comparison of the series before and during the financial crisis. This work studies a model with linear and non-linear factors with stochastically varying coefficients to obtain better estimation of the exposure of the hedge fund and accuracy in the results. Better exposure estimates implies better hedging against negative changes in the market hence a reduction in the risk taken by the hedge fund manager. Besides, different techniques have been studied, implemented and applied in this thesis to estimate and analyze time varying exposures of different HFRX Index (an index that describes the hedge fund industry performance). The study shows that option-like models with time-varying coefficients perform the best for most of the HFRX indexes analyzed. It also shows that the Kalman Filter technique combined with the Maximum Likelihood Estimator is the best approach to estimate time-varying coefficients. In addition, we provide evidence that Kalman Filter is in a better position to capture changes in the exposure to the market conditions.

scholarly journals Time-Varying Coefficient Models And The Kalman Filter : Applications To Hedge Funds

2021 ◽  
Author(s):  
Ana G.S. Punales
Keyword(s):  
Kalman Filter ◽  
Hedge Funds ◽  
Hedge Fund ◽  
Varying Coefficient Models ◽  
Time Varying ◽  
Likelihood Estimator ◽  
Varying Coefficients ◽  
Industry Performance ◽  
Non Linear ◽  
Time Varying Coefficients

There are various studies concerned with the estimation of stochastically varying coefficients for the hedge fund series but just [sic] few are available in the literature that study the model with time-varying coefficients and non-linear factor, or make a comparison of the series before and during the financial crisis. This work studies a model with linear and non-linear factors with stochastically varying coefficients to obtain better estimation of the exposure of the hedge fund and accuracy in the results. Better exposure estimates implies better hedging against negative changes in the market hence a reduction in the risk taken by the hedge fund manager. Besides, different techniques have been studied, implemented and applied in this thesis to estimate and analyze time varying exposures of different HFRX Index (an index that describes the hedge fund industry performance). The study shows that option-like models with time-varying coefficients perform the best for most of the HFRX indexes analyzed. It also shows that the Kalman Filter technique combined with the Maximum Likelihood Estimator is the best approach to estimate time-varying coefficients. In addition, we provide evidence that Kalman Filter is in a better position to capture changes in the exposure to the market conditions.

scholarly journals The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

scholarly journals Estimating latent group structure in time-varying coefficient panel data models

2019 ◽  
Author(s):  
Jia Chen
Keyword(s):  
Panel Data ◽  
Data Models ◽  
Panel Data Models ◽  
Time Varying ◽  
Clustering Method ◽  
Varying Coefficient ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Latent Group ◽  
Group Structures

Summary This paper studies the estimation of latent group structures in heterogeneous time-varying coefficient panel data models. While allowing the coefficient functions to vary over cross-sections provides a good way to model cross-sectional heterogeneity, it reduces the degree of freedom and leads to poor estimation accuracy when the time-series length is short. On the other hand, in a lot of empirical studies, it is not uncommon to find that heterogeneous coefficients exhibit group structures where coefficients belonging to the same group are similar or identical. This paper aims to provide an easy and straightforward approach for estimating the underlying latent groups. This approach is based on the hierarchical agglomerative clustering (HAC) of kernel estimates of the heterogeneous time-varying coefficients when the number of groups is known. We establish the consistency of this clustering method and also propose a generalised information criterion for estimating the number of groups when it is unknown. Simulation studies are carried out to examine the finite-sample properties of the proposed clustering method as well as the post-clustering estimation of the group-specific time-varying coefficients. The simulation results show that our methods give comparable performance to the penalised-sieve-estimation-based classifier-LASSO approach by Su et al. (2018), but are computationally easier. An application to a panel study of economic growth is also provided.

scholarly journals Gray’s Time-Varying Coefficients Model for Posttransplant Survival of Pediatric Liver Transplant Recipients with a Diagnosis of Cancer

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yi Ren ◽  
Chung-Chou H. Chang ◽  
Gabriel L. Zenarosa ◽  
Heather E. Tomko ◽  
Drew Michael S. Donnell ◽  
...  
Keyword(s):  
Liver Transplant ◽  
Failure Time ◽  
Penalized Splines ◽  
Time Varying ◽  
Piecewise Constant ◽  
Varying Coefficients ◽  
Covariate Effects ◽  
Pediatric Liver ◽  
Time Varying Coefficients ◽  
Pediatric Liver Transplant

Transplantation is often the only viable treatment for pediatric patients with end-stage liver disease. Making well-informed decisions on when to proceed with transplantation requires accurate predictors of transplant survival. The standard Cox proportional hazards (PH) model assumes that covariate effects are time-invariant on right-censored failure time; however, this assumption may not always hold. Gray’s piecewise constant time-varying coefficients (PC-TVC) model offers greater flexibility to capture the temporal changes of covariate effects without losing the mathematical simplicity of Cox PH model. In the present work, we examined the Cox PH and Gray PC-TVC models on the posttransplant survival analysis of 288 pediatric liver transplant patients diagnosed with cancer. We obtained potential predictors through univariable(P<0.15)and multivariable models with forward selection(P<0.05)for the Cox PH and Gray PC-TVC models, which coincide. While the Cox PH model provided reasonable average results in estimating covariate effects on posttransplant survival, the Gray model using piecewise constant penalized splines showed more details of how those effects change over time.

Sign in / Sign up

Export Citation Format

Share Document