State-space Estimation Research Articles

A State Space and Density Estimation Framework for Sleep Staging in Obstructive Sleep Apnea.

Although the importance of sleep is increasingly recognized, the lack of robust and efficient algorithms hinders scalable sleep assessment in healthy persons and those with sleep disorders. Polysomnography (PSG) and visual/manual scoring remain the gold standard in sleep evaluation, but more efficient/automated systems are needed. Most previous works have demonstrated algorithms in high agreement with the gold standard in healthy/normal (HN) individuals-not those with sleep disorders. This paper presents a statistical framework that automatically estimates whole-night sleep architecture in patients with obstructive sleep apnea (OSA)-the most common sleep disorder. Single-channel frontal electroencephalography was extracted from 65 HN/OSA sleep studies, and decomposed into 11 spectral features in 60903 30s sleep epochs. The algorithm leveraged kernel density estimation to generate stage-specific likelihoods, and a 5-state hidden Markov model to estimate per-night sleep architecture. Comparisons to full PSG expert scoring revealed the algorithm was in fair agreement with the gold standard (median Cohen's kappa = 0.53). Further, analysis revealed modest decreases in median scoring agreement as OSA severity increased from HN (kappa = 0.63) to severe (kappa = 0.47). A separate implementation on HN data from the Physionet Sleep-EDF Database resulted in a median kappa = 0.65, further indicating the algorithm's broad applicability. Results of this work indicate the proposed single-channel framework can emulate expert-level scoring of sleep architecture in OSA. Algorithms constructed to more accurately model physiological variability during sleep may help advance automated sleep assessment, for practical and general use in sleep medicine.

An adaptive sliding mode control of delta operator systems with input nonlinearity containing unknown slope parameters

The problem of observer-based adaptive sliding mode control of delta operator systems with time-varying delays subject to input nonlinearity is investigated. The slope parameters of this nonlinearity are unmeasured. A novel adaptive control law is established such that the sliding surface in the state-estimation space can be reached in a finite time. A delay-dependent sufficient condition for the asymptotic stability of both the error system and the sliding mode dynamics is derived via linear matrix inequality (LMI). Finally, a simulation example is presented to show the validity and advantage of the proposed method.

Stateless model checking with data-race preemption points

Stateless model checking is a powerful technique for testing concurrent programs, but suffers from exponential state space explosion when the test input parameters are too large. Several reduction techniques can mitigate this explosion, but even after pruning equivalent interleavings, the state space size is often intractable. Most prior tools are limited to preempting only on synchronization APIs, which reduces the space further, but can miss unsynchronized thread communication bugs. Data race detection, another concurrency testing approach, focuses on suspicious memory access pairs during a single test execution. It avoids concerns of state space size, but may report races that do not lead to observable failures, which jeopardizes a user’s willingness to use the analysis. We present Quicksand, a new stateless model checking framework which manages the exploration of many state spaces using different preemption points. It uses state space estimation to prioritize jobs most likely to complete in a fixed CPU budget, and it incorporates data-race analysis to add new preemption points on the fly. Preempting threads during a data race’s instructions can automatically classify the race as buggy or benign, and uncovers new bugs not reachable by prior model checkers. It also enables full verification of all possible schedules when every data race is verified as benign within the CPU budget. In our evaluation, Quicksand found 1.25x as many bugs and verified 4.3x as many tests compared to prior model checking approaches.

Dealing with financial instability under a DSGE modeling approach with banking intermediation: A predictability analysis versus TVP-VARs

In the dynamic stochastic general equilibrium (DSGE) literature there has been an increasing awareness on the role that the banking sector can play in macroeconomic activity. We present a DSGE model with financial intermediation as in Gertler and Karadi (2011). The estimation of shocks and of the structural parameters shows that time-variation should be crucial in any attempted empirical analysis. Since DSGE modelling usually fails to take into account inherent nonlinearities of the economy, we propose a novel time-varying parameter (TVP) state-space estimation method for VAR processes both for homoskedastic and heteroskedastic error structures. We conduct an exhaustive empirical exercise to compare the out-of-sample predictive performance of the estimated DSGE model with that of standard ARs, VARs, Bayesian VARs and TVP-VARs. We find that the TVP-VAR provides the best forecasting performance for the series of GDP and net worth of financial intermediaries for all steps-ahead, while the DSGE model outperforms the other specifications in forecasting inflation and the federal funds rate at shorter horizons.

H $$\infty $$ ∞ observer-based sliding mode control for singularly perturbed systems with input nonlinearity

This paper considers the problem of \(H \infty \) observer-based sliding mode control for singularly perturbed systems with input nonlinearities. First, a proper observer is designed such that the observer error system with disturbance attenuation level is asymptotically stable. Then, an observer-based sliding surface is constructed under which a criterion for the input-to-state stability (ISS) of the sliding mode dynamics with respect to the observer error is obtained via linear matrix inequality. The criterion presented is independent of the small parameter, and the upper bound for ISS can be obtained efficiently. In addition, a sliding mode control law is synthesized to guarantee the reachability of the sliding surface in the state estimation space. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed theoretical results.

Algebraic Systems Biology: A Case Study for the Wnt Pathway.

Steady-state analysis of dynamical systems for biological networks gives rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here, the variety is described by a polynomial system in 19 unknowns and 36 parameters. It has degree 9 over the parameter space. This case study explores multistationarity, model comparison, dynamics within regions of the state space, identifiability, and parameter estimation, from a geometric point of view. We employ current methods from computational algebraic geometry, polyhedral geometry, and combinatorics.

Robust H-infinity control for a class of neutral-type systems via sliding mode observer

In this paper, the problem of observer-based H-infinity integral sliding mode control (ISMC) is investigated for a class of uncertain neutral-type systems with time delay (NTSTD). An ISMC strategy is put forward based on the sliding mode observer. A new sufficient condition of robust asymptotic stability for the overall systems composed of the error system and sliding mode dynamics with disturbance attenuation level is derived via linear matrix inequality (LMI). Then, a SMC law is designed such that the reachability of the sliding surface defined in the state-estimate space can be guaranteed. Finally, a simulation example is presented to demonstrate the feasibility of the obtained result.

Quantized Observer-Based Sliding Mode Control for Networked Control Systems Via the Time-Delay Approach

This paper investigates the sliding mode control problem for networked control systems, which are influenced by the non-ideal network environment, such as network-induced delays, packet dropouts and quantization errors. The states of the system are assumed to be unavailable, and an observer is designed to estimate the state of the system, based on which a sliding mode controller is given to guarantee the closed-loop system to be stable. Furthermore, it is shown that the proposed control scheme ensures the reachability of the sliding surfaces in both the state estimate space and the estimation error space. Finally, a numerical example is given to illustrated the effectiveness of the proposed methodology.

Predictive Model Reference Adaptive Controller to Compensate Heart Motion in Minimally Invasive CABG Surgery.

Heart beating is a major challenge in minimally invasive coronary artery surgery. A promising solution is to develop a motion compensation robotic system that gives the surgeon an impression of operating on motionless tissue by synchronizing the surgical tool automatically with the heart tissue motion. To achieve higher control accuracy, an intelligent controller called Predictive Model Reference Adaptive Controller is presented herein, which is adapted not only by observed reference signals but, also by unknown reference signals that are not observed by a camera but could be predicted by a state space estimator. To develop such a system, first the heart surface motion is tracked by the Lucas-Kanade tracking algorithm and validated by human observation. The results of implementing this control algorithm on a real human heart data set show capability of achieving a motion compensation system with high control accuracy.

Adaptive resampling-based particle filtering for tool life prediction

Trending analysis has been widely investigated for prediction of tool wear, which impacts not only tool life but also the quality of machined products. This paper presents a Bayesian approach to predicting the flank wear rate, linking vibration data measured during machining with the state of tool wear. Variations in the measured data are aggregated based on the Kullback–Leibler divergence, which provides a measure for the distance between the current and initial probability distributions of measurement, when no wear is present. Subsequently, state space estimation of the tool wear is realized by particle filtering (PF), a non-linear and non-Gaussian system estimation technique. To overcome the sample impoverishment problem in sequential importance resampling (SIR), a new resampling scheme is proposed, which has shown to more reliably quantify the confidence interval and improve the prediction accuracy of the remaining useful life (RUL) prediction of the tool as compared to standard SIR method. The developed method is experimentally evaluated using a set of benchmark data measured from a high speed CNC machine that performed milling operations. Good results are confirmed by the comparison between the predicted tool wear state and off-line tool wear measurement.

State Space Estimation for an Electromechanical Actuator Valve Using Extended Kalman Filter

This paper presents a state space estimation for an Electromechanical Actuator Valve using Extended Kalman Filter (EKF). A proposed actuator model includes a Tustin’s friction model with strong nonlinearities, hence it represents an accurate model for describing the friction phenomenon in an Electromechanical Actuator valve. In my work the EKF is used for estimation of three states, namely the motor current, valve angular velocity - and position. Both the actuator model and the EKF algorithm were implemented in MATLAB®. The measurements to input data in the EKF are performed in National Instruments CompactRIO system. Outline of our examination should be to take a conclusion, how much EKF is capable for accurate estimation of the desired states. Furthermore we will use this method for further developing the fault detection in the Electromechanical Actuator Valve.

Observer-Based Robust Passive Control for a Class of Uncertain Neutral Systems: An Integral Sliding Mode Approach

The problem of integral sliding mode control (ISMC) with passivity is investigated for a class of uncertain neutral systems with time-varying delay (NTSTD) and external disturbance. The system states are unavailable. An ISMC strategy is proposed based on the state estimate. By employing a novel sliding functional, a new sufficient criterion of robust asymptotic stability and passivity for both the error system and the sliding mode (SM) dynamic system is derived via linear matrix inequality (LMI) technique. Then, a SM controller is synthesized to guarantee the reachability of the sliding surface predefined in the state estimate space. Finally, a numerical example shows the feasibility and superiority of the obtained result.

Modelling Gestural Know-how in Pottery Based on State-space Estimation and System Dynamic Simulation

This paper presents a methodology for modelling expert gestural performances in wheel-throwing pottery. The approach is based on building an operational model that describes how expert gestures are performed, taking also into consideration relationships between different parts of the body. This model is estimated using state-space estimation methodology and its predictive performance is evaluated using system dynamic simulation. Moreover, the confidence bounds derived of the expert gesture performance in wheel-throw pottery are computed. They could be used as benchmarks in real-time experiments in order to generate the appropriate feedback for sensorimotor learning of gestures.

Ensemble Kalman Filtering with a Divided State-Space Strategy for Coupled Data Assimilation Problems*

Abstract This study considers the data assimilation problem in coupled systems, which consists of two components (subsystems) interacting with each other through certain coupling terms. A straightforward way to tackle the assimilation problem in such systems is to concatenate the states of the subsystems into one augmented state vector, so that a standard ensemble Kalman filter (EnKF) can be directly applied. This work presents a divided state-space estimation strategy, in which data assimilation is carried out with respect to each individual subsystem, involving quantities from the subsystem itself and correlated quantities from other coupled subsystems. On top of the divided state-space estimation strategy, the authors also consider the possibility of running the subsystems separately. Combining these two ideas, a few variants of the EnKF are derived. The introduction of these variants is mainly inspired by the current status and challenges in coupled data assimilation problems and thus might be of interest from a practical point of view. Numerical experiments with a multiscale Lorenz 96 model are conducted to evaluate the performance of these variants against that of the conventional EnKF. In addition, specific for coupled data assimilation problems, two prototypes of extensions of the presented methods are also developed in order to achieve a trade-off between efficiency and accuracy.

Assessment and Dynamic Modeling of the Size of Technology Transfer

The size of technology imports and exports as well as the share of technology-based industries in the labor force are important means that can be utilized to assess the level of technology transfer in an economy. This paper reviews and discusses, within the United Arab Emirates (UAE) context, factors of technology transfer, exports and imports of technology products, outlining strengths and weaknesses. The annual size of imports, exports, and trade balance of technology products is further used to describe trend and make predictions and forecasts of the level of technology transfer. Using official trade data spanning the period from 1981 to 2013, the state-space methodology is utilized to handle the dynamic time series models and to study the developments of the state over time. Employing the Kalman filter, within the state-space framework, necessary estimation and forecasts are made. UAE strengths and weaknesses in terms of factors influencing technology transfer are discussed. Evidence suggests increasing domestic demand for technology products, insufficient domestic production, and increasing dependency on technology imports. Despite recent growth in UAE technology industries, the huge deficit in technology products trade balance indicates a negative trend in technology transfer. Policy implications are highlighted including the need for quality education, effective diffusion and internal transfer and generation of technology.

Output-error state-space identification of vibrating structures using evolution strategies: a benchmark study

In this study, four widely accepted and used variants of Evolution Strategies (ES) are adapted and applied to the output-error state-space identification problem. The selection of ES is justified by prior strong indication of superior performance to similar problems, over alternatives like Genetic Algorithms (GA) or Evolutionary Programming (EP). The ES variants that are being tested are (i) the (1+1)-ES, (ii) the <TEX>$({\mu}/{\rho}+{\lambda})-{\sigma}$</TEX>-SA-ES, (iii) the <TEX>$({\mu}_I,{\lambda})-{\sigma}$</TEX>-SA-ES, and (iv) the (<TEX>${\mu}_w,{\lambda}$</TEX>)-CMA-ES. The study is based on a six-degree-of-freedom (DOF) structural model of a shear building that is characterized by light damping (up to 5%). The envisaged analysis is taking place through Monte Carlo experiments under two different excitation types (stationary / non-stationary) and the applied ES are assessed in terms of (i) accurate modal parameters extraction, (ii) statistical consistency, (iii) performance under noise-corrupted data, and (iv) performance under non-stationary data. The results of this suggest that ES are indeed competitive alternatives in the non-linear state-space estimation problem and deserve further attention.

State-space estimation with a Bayesian filter in a coupled PDE system for transient gas flows

The accuracy of the first-principle models describing the evolution of gas dynamics in pipelines is sometimes limited by the lack of understanding of the gas transport phenomena. In this paper, a stochastic filtering approach is proposed based on a sequential Monte Carlo method to provide real-time estimates of the state in gas pipelines. After constructing a state-space model of the compressible single-phase flow based on the laws of conservation of mass and momentum, the optimal sequential importance resampling filter (SIR) is implemented. The state variables are updated with simulated measurements. The two-step Lax–Wendroff method is used for the discretization of the partial differential equations describing the gas model in both space and time to obtain finite-dimensional discrete-time state-space representations. The system states are then combined into an augmented state vector. The resulting nonlinear state-space model is used for the design of the particle filter that provides real-time estimations of the system states. Simulation results for a coupled PDE system describing an unsteady isothermal gas flow demonstrate the effectiveness of the proposed method. A sensitivity analysis is conducted to examine the performance of the filter for different model and observation error covariances and observation intervals.

A state-space approach to mathematical modeling and parameters identification of vehicle frontal crash

In this paper a state-space estimation procedure that relies on the time-domain analysis of input and output signals is used for mathematical modeling of vehicle frontal crash. The model is a double-spring–mass–damper system, whereby the front mass and real mass represent the chassis and the passenger compartment, respectively. It is observed that the dynamic crash of the model is closer to the dynamic crash from experimental when the mass of the chassis is greater than the mass of the passenger compartment. The dynamic crash depends on pole placement and the estimated parameters. It is noted that when the poles of the model are closer to zero, the dynamic crash of the model is far from the dynamic crash from the experimental data. The stiffness and damping coefficients play an important role in the dynamic crash.

A Bayesian approach to identifying and compensating for model misspecification in population models

State-space estimation methods are increasingly used in ecology to estimate productivity and abundance of natural populations while accounting for variability in both population dynamics and measurement processes. However, functional forms for population dynamics and density dependence often will not match the true biological process, and this may degrade the performance of state-space methods. We therefore developed a Bayesian semiparametric state-space model, which uses a Gaussian process (GP) to approximate the population growth function. This offers two benefits for population modeling. First, it allows data to update a specified "prior" on the population growth function, while reverting to this prior when data are uninformative. Second, it allows variability in population dynamics to be decomposed into random errors around the population growth function ("process error") and errors due to the mismatch between the specified prior and estimated growth function ("model error"). We used simulation modeling to illustrate the utility of GP methods in state-space population dynamics models. Results confirmed that the GP model performs similarly to a conventional state-space model when either (1) the prior matches the true process or (2) data are relatively uninformative. However, GP methods improve estimates of the population growth function when the function is misspecified. Results also demonstrated that the estimated magnitude of "model error" can be used to distinguish cases of model misspecification. We conclude with a discussion of the prospects for GP methods in other state-space models, including age and length-structured, meta-analytic, and individual-movement models.

Non-fragile observer-based sliding mode control for Markovian jump systems with mixed mode-dependent time delays and input nonlinearity

This paper is concerned with the state estimation and the sliding mode control (SMC) for a class of Markovian jump systems with mixed mode-dependent time delays and input nonlinearity. A non-fragile observer is designed to estimate the system states, and an observer-based SMC is synthesized to ensure the reachability of the sliding surfaces in the state-estimation space. By constructing a novel mode-dependent Lyapunov–Krasovskii functional, some new criteria are established for the existence and the solvability of the desired observer-based sliding mode controller. Finally, numerical examples are presented to illustrate the effectiveness and less conservativeness of the proposed theoretical results.