Steady-state Variance Research Articles

Intrawell stochastic resonance of bistable system

In this paper, we describe application of a single-well approximation to a bistable system. Based on this approximation, the relationship between system response speed and steady state variance is obtained. It becomes possible to determine the performance of stochastic resonance (SR) systems by a single measure, the signal-to-noise ratio (SNR) gain. The peaking phenomenon of SNR gain can be found in the single-well-approximated bistable system with the excitation of Gaussian white noise via changing system response speed or sampling period. The mechanisms of some SR phenomena are then discussed, including intrawell SR, parameter-induced SR.

Variance-constrained filtering for uncertain stochastic systems with missing measurements

In this note, we consider a new filtering problem for linear uncertain discrete-time stochastic systems with missing measurements. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The system measurements may be unavailable (i.e., missing data) at any sample time, and the probability of the occurrence of missing data is assumed to be known. The purpose of this problem is to design a linear filter such that, for all admissible parameter uncertainties and all possible incomplete observations, the error state of the filtering process is mean square bounded, and the steady-state variance of the estimation error of each state is not more than the individual prescribed upper bound. It is shown that, the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic Riccati-like inequalities or linear matrix inequalities. The explicit expression of the desired robust filters is parameterized, and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach.

On designing /sub ∞ filters with circular pole and error variance constraints

In this paper, we deal with the problem of designing a H/sub /spl infin// filter for discrete-time systems subject to error variance and circular pole constraints. Specifically, we aim to design a filter such that the H/sub /spl infin// norm of the filtering error-transfer function is not less than a given upper bound, while the poles of the filtering matrix are assigned within a prespecified circular region, and the steady-state error variance for each state is not more than the individual prespecified value. The filter design problem is formulated as an auxiliary matrix assignment problem. Both the existence condition and the explicit expression of the desired filters are then derived by using an algebraic matrix inequality approach. The proposed design algorithm is illustrated by a numerical example.

Block adaptive filters with deterministic reference inputs for event-related signals: BLMS and BRLS

Adaptive estimation of the linear coefficient vector in truncated expansions is considered for the purpose of modeling noisy, recurrent signals. Two different criteria are studied for block-wise processing of the signal: the mean square error (MSE) and the least squares (LS) error. The block LMS (BLMS) algorithm, being the solution of the steepest descent strategy for minimizing the MSE, is shown to be steady-state unbiased and with a lower variance than the LMS algorithm. It is demonstrated that BLMS is equivalent to an exponential averager in the subspace spanned by the truncated set of basis functions. The block recursive least squares (BRLS) solution is shown to be equivalent to the BLMS algorithm with a decreasing step size. The BRLS is unbiased at any occurrence number of the signal and has the same steady-state variance as the BLMS but with a lower variance at the transient stage. The estimation methods can be interpreted in terms of linear, time-variant filtering. The performance of the methods is studied on an ECG signal, and the results show that the performance of the block algorithms is superior to that of the LMS algorithm. In addition, measurements with clinical interest are found to be more robustly estimated in noisy signals.

Robust filtering for bilinear uncertain stochastic discrete-time systems

This paper deals with the robust filtering problem for uncertain bilinear stochastic discrete-time systems with estimation error variance constraints. The uncertainties are allowed to be norm-bounded and enter into both the state and measurement matrices. We focus on the design of linear filters, such that for all admissible parameter uncertainties, the error state of the bilinear stochastic system is mean square bounded, and the steady-state variance of the estimation error of each state is not more than the individual prespecified value. It is shown that the design of the robust filters can be carried out by solving some algebraic quadratic matrix inequalities. In particular, we establish both the existence conditions and the explicit expression of desired robust filters. A numerical example is included to show the applicability of the present method.

Steady‐state analysis of complex adaptive IIR notch filters for the detection of single sinusoid

AbstractIn this paper, we present a new structure for a complex adaptive infinite impulse response (IIR) notch filter which is useful for the detection of complex sinusoids in communication and radar systems. The proposed structure is based on the gradient algorithm. The adaptive detection of a complex sinusoid with additive complex white noise has been investigated. A quantitative analysis for the steady‐state coefficient fluctuation has been developed. Analytical expressions for the steady‐state variance of complex variable coefficient fluctuation have been obtained. It has been shown that the variance of the complex coefficient fluctuation does not depend on the angular frequency of the input sinusoid. Finally, the results of computer simulations which confirm the theoretical predictions are presented. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 85(1): 32–40, 2002

Nonlocal thermodynamic equilibrium self-consistent average-atom model for plasma physics.

A time-dependent collisional-radiative average-atom model is presented to study statistical properties of highly charged ion plasmas in off-equilibrium conditions. The time evolution of electron populations and the electron covariance matrix is obtained as approximate solutions of a master equation. Atomic structure is described either with a screened-hydrogenic model including l splitting, or by calculating one-electron states in a self-consistent average-atom potential. Collisional and radiative excitation/deexcitation and ionization/recombination rates, as well as autoionization and dielectronic recombination rates, are formulated within the average-configuration framework. Local thermodynamic equilibrium is obtained as a specific steady-state solution. The influence of atomic structure and the role of autoionization and dielectronic recombination processes are studied by calculating steady-state average ionization and ionization variance of hot plasmas with or without radiation field.

ROBUST Hinfinity CONTROL FOR SYSTEMS WITH TIME-VARYING PARAMETER UNCERTAINTY AND VARIANCE CONSTRAINTS

In this paper, the problem of designing robust Hinfinity controllers for linear continuous-time systems subjected to time-varying parameter uncertainty and steady-state variance constraints is considered. The goal of this problem is to design the state feedback controller, such that for all admissible time-varying parameter perturbations, the steady-state variance of each state is not more than the individual prespecified upper bound and the Hinfinity norm of the transfer function from disturbance inputs to system outputs meets the prespecified upper bound constraint, simultaneously. The parameter uncertainties are allowed to be time-varying and norm-bounded. A purely algebraic matrix equation approach is effectively utilized to solve the problem addressed. The existence conditions as well as the explicit expression of desired controllers are presented, and two illustrative examples are used to demonstrate the applicability of the proposed design procedure.

Variance-constrained multiobjective filtering for uncertain continuous-time stochastic systems

In this paper, we consider stochastic linear continuous-time systems subject to parameter uncertainties affecting both system dynamics and noise statistics. A linear filter is used to estimate a linear combination of the states of the system. The problem addressed is the design of a perturbation-independent filter such that, for all admissible parameter perturbations, the following three objectives are simultaneously achieved. Firstly the filtering process is D-stable, that is, the eigenvalues of the filtering matrix are located inside a prespecified disc. Secondly the steady-state variance of the estimation error of each state is not more than the individual prespecified value. Thirdly the transfer function from exogenous noise inputs to error state outputs meets the prespecified H norm upper bound constraint. Therefore, the resulting filtering process will be provided with the expected transient property, steady-state error variance constraint and disturbance rejection behaviour, irrespective of the parameter uncertainties. An effective algebraic matrix inequality approach is developed to solve such a multiobjective H2

Robust H/sub 2//H/sub ∞/ filtering for linear systems with error variance constraints

In this correspondence, we consider the robust H/sub 2//H/sub /spl infin// filtering problem for linear perturbed systems with steady-state error variance constraints. The purpose of this multiobjective problem is to design a linear filter that does not depend on the parameter perturbations such that the following three performance requirements are simultaneously satisfied. (1) The filtering process is asymptotically stable. (2) The steady-state variance of the estimation error of each state is not more than the individual prespecified value. (3) The transfer function from exogenous noise inputs to error state outputs meets the prespecified H/sub /spl infin// norm upper bound constraint. We show that in both continuous and discrete-time cases, the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic Riccati-like equations/inequalities. We present both the existence conditions and the explicit expression of desired robust filters. An illustrative numerical example is provided to demonstrate the flexibility of the proposed design approach.

Low-dimensional representation of error covariance

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensionalapproximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause thesteady-state analysis error covariance to admit a low-dimensional representation. A usefulmeasure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-stateanalysis error covariance matrix eigenvalues are derived from the bound matrix. The estimatesgeneralize to time-dependent systems. If much of the steady-state analysis error variance is dueto a few dominant modes, the leading eigenvectors of the bound matrix approximate those ofthe steady-state analysis error covariance matrix. The analytical results are illustrated in twonumerical examples where the Kalman filter is carried to steady state. The first example usesthe dynamics of a generalized advection equation exhibiting non-modal transient growth.Failure to observe growing modes leads to increased steady-state analysis error variances.Leading eigenvectors of the steady-state analysis error covariance matrix are well approximatedby leading eigenvectors of the bound matrix. The second example uses the dynamics of adamped baroclinic wave model. The leading eigenvectors of a lowest-order approximation ofthe bound matrix are shown to approximate well the leading eigenvectors of the steady-stateanalysis error covariance matrix.

Robust state estimation for perturbed systems with error variance and circular pole constraints: The discrete-time case

This paper is concerned with the problem of robust state estimation for linear perturbed discrete-time systems with error variance and circular pole constraints. The goal of this problem addressed is the design of a linear state estimator such that, for all admissible uncertainties in both state and output equations, the following two performance requirements are simultaneously satisfied: (1) the poles of the filtering matrix are all constrained to lie inside a prespecified circular region; and (2) the steady-state variance of the estimation error for each state is not more than the individual prespecified value. It is shown that this problem can be converted to an auxiliary matrix assignment problem and solved by using an algebraic matrix equation/inequality approach. Specifically, the conditions for the existence of desired estimators are obtained and the explicit expression of these estimators is also derived. The main results are then extended to the case when an H performance requirement is added. Finally, a numerical example is presented to demonstrate the significance of the proposed technique.

Robust control of linear uncertain systems with regional pole and variance constraints

This paper concerns the design problem of state feedback controllers which guarantee the closed-loop poles within a specified disc and steady-state variances to be less than a set of given upper bounds for linear systems with norm-bounded parameter uncertainties. Using the linear matrix inequality approach, the existence conditions of such controllers are derived. A parametrized representation of the desired controllers is presented in terms of the feasible solutions to a certain linear matrix inequality system. Based on this, a solution to the minimum-effect guaranteed-performance design problem is presented in the sense that the required control effort is minimized subject to performance constraints.

Deconvolution of 40 Hz steady-state fields reveals two overlapping source activities of the human auditory cortex

Steady-state auditory evoked fields were recorded from 15 subjects using a whole head MEG system. Stimuli were 800 ms trains of binaural clicks with constant stimulus onset asynchrony (SOA). Seven different SOA settings (19, 21, 23, 25, 27, 29 and 31 ms) were used to give click rates near 40 Hz. Transient responses to each click were reconstructed using a new algorithm that deconvoluted the averaged responses to the different trains. Spatio-temporal multiple dipole modelling in relation to 3D MRI scans revealed two overlapping source components in both the left and right auditory cortex. The primary sources in the medial part of Heschl's gyrus exhibited a N19-P30-N40 m pattern. The secondary, weaker sources at more lateral sites on Heschl's gyrus showed a N24-P36-N46 m pattern. When applied to transient middle latency auditory evoked fields (MAEFs) recorded at SOAs of 95-135 ms, the primary sources imaged activities similar to the deconvoluted steady-state responses, but the secondary source activities were inconsistent. Linear summation of the deconvoluted source waveforms accounted for more than 96% of the steady-state variance. This indicates that the primary activity of the auditory cortex remains constant up to high stimulation rates and is not specifically enhanced around 40 Hz.

Propagation of stochastic temperature fluctuations in refrigerated fruits: Propagation des fluctuations de température stochastiques dans des fruits réfrigérés

A steady state variance propagation algorithm is derived to investigate the effect of stochastic air temperature disturbances on the variability of the temperature field inside refrigerated fruits during cold storage conditions. The disturbances are modelled by continuous-time autoregressive processes of variable order. The algorithm is based on the finite element formulation of the heat conduction equation and involves the numerical solution of matrix equations of the Lyapunov and Sylvester type. As an example, the cold storage of pineapple has been considered. It is shown that disturbances of different order but with the same scale of fluctuation result in comparable centre temperature variances.

A new memoryless nonlinear gradient algorithm for a second-order adaptive IIR notch filter and its performance analysis

Adaptive infinite impulse-response (IIR) notch filters have been widely studied for many years. However, further efforts are still to be made to pursue new algorithms which work better than the conventional plain gradient algorithm but have little increase in complexity. In this paper, we employ the gradient linearization, Taylor series expansion, and calculus of variations to derive a novel memoryless nonlinear gradient algorithm for a second-order adaptive IIR notch filter, which improves the estimation performance considerably. Approximate closed-form expressions for the stability bounds on the step size parameter and the steady-state coefficient variance are also derived. Extensive simulations indicate the significant improvement that may be achieved using the new algorithm, and verify the validity of the analytical results.

L/sub 2/ optimal filter reduction: a closed-loop approach

This paper is concerned with the problem of order reduction of a full-order Kalman filter for a stable linear signal model so that the steady-state filtering error variance associated with the reduced order filter is minimized. By an orthogonal parameterization, the above problem is formulated to minimize the filtering error variance over a set of orthogonal matrices. Both continuous and iterative algorithms are derived to compute an optimal reduced-order filter. The algorithms are shown to possess good properties, including the desirable convergence property. The proposed algorithms are simple and effective. Numerical examples are presented to demonstrate the effectiveness and the significant advantages of the proposed algorithms over the existing open-loop methods such as the well-known balanced truncation method.

Robust variance-constrained design for uncertain continuous stochastic systems via output feedback

This paper studies the problem of robust controller design for linear perturbed continuous stochastic systems with variance constraints via output feedback. The goal is to design static output feedback controllers such that the uncertain system has the desired stability margin and the steady-state variance constraints. The existence conditions for the desired controllers are discussed, and the analytical expression of these controllers is also characterized. A numerical example is provided to demonstrate the directness and effectiveness of the proposed method.

Steady-state variance analysis of adaptive, digital, coherent MPSK receiver

The phase estimation error variance of an adaptive, digital, coherent PSK receiver is analysed in the steady-state at high SNR. It is shown that, because of the risk function chosen in the gain adaptation algorithm of the phase estimator, the phase error variance is minimised.

Performance analysis of GPS carrier phase observable

The accuracy analysis of Global Positioning System (GPS) carrier phase observable measured by a digital GPS receiver is presented. A digital phase-locked loop (DPLL) is modeled to extract the carrier phase of the received signal after a pseudorandom noise (PRN) code synchronization system despreads the received PRN coded signal. Based on phase noise characteristics of the input signal, the following performance of the first, second, and third-order DPLLs is analyzed mathematically: (1) loop stability and transient process; (2) steady-state probability density function (pdf), mean and variance of phase tracking error; (3) carrier phase acquisition performance; and (4) mean time to the first cycle-slipping. The theoretical analysis is verified by Monte Carlo computer simulations. The analysis of the dependency of the phase input noise and receiver design parameters provides with an important reference in designing the carrier phase synchronization system for high accuracy GPS positioning.