Non-parametric adaptive locally asymptotically optimum detection in additive noise

In this paper, a new approach to non-parametric signal detection with independent noise sampling is presented. The present approach is based on the locally asymptotically optimum (LAO) methodology, which is valid for vanishingly small signals and very large sample sizes, and on semi-parametric statistics. Its unique feature and essential difference from other techniques is that LAO non-parametric detectors are optimum according to the Neyman-Pearson criterion by being asymptotically uniformly most powerful at false alarm level α (AUMP (α)) and adaptive in the sense that no loss in Fisher's information number is incurred when the underlying noise process is no longer parametrically defined. Accordingly, they are robust against deviations from the postulated noise model and, unlike other non-parametric detectors, are distribution-free under both hypotheses H₀ (“noise only present”) and H₁ (“signal and noise present”). Non-parametric LAO detectors are derived from an asymptotic stochastic expansion of the log-likelihood ratio for coherent and narrowband incoherent “on-off” signals. Moreover, under the present framework it is shown that, in direct contrast to already known results, the non-parametric sign detector is AUMP (α) and adaptive even for non-constant signal samples.     

Discrete time robust detection of stochastic signals in non-Gaussian contaminated noise

For many applications in signal detection, imprecise knowledge of the underlying noise process often makes desirable the employment of a robust detector. In this paper we consider the discrete time detection of stochastic signals in white noise, where the univariate noise density is known perfectly only on an interval about the origin. We present a method to enhance the asymptotic performance of the detector by exploiting this knowledge, and at the same time preserve robustness properties of the detector to the remaining inexact knowledge of the univariate noise density via a saddlepoint condition. We then provide examples to show that improved performance is indeed obtained.     

Improved non-parametric coincidence detectors

Simple extensions of the polarity–coincidence correlator (PCC) for non-parametric detection of a common random signal in two-input systems are considered. The new detectors are based on conditional tests and are shown to be capable of a better performance than the PCC. For the case of Gaussian noise, substantial improvement in performance over that of the PCC is established.     

Two-Sample Non-parametric Detectors Using Dependent Samples

The performance of two-sample non-parametric detectors using dependent samples is considered. It is shown that in the situation in which square-law envelope detection is employed, the signals to be detected fluctuate in accordance with a chi-square distribution and the background interference is additive Gaussian noise; the two-sample Generalized Sign (GS), Mann-Whitney (MW), Modified Savage (MS) and Modified Rank Square (MRS) detectors have superior asymptotic processing times to those that are obtained when independent samples are used. Also, it is shown that in addition to the advantage of improved performance, detection using dependent samples can have implementation advantages as compared with detection based on the use of independent samples.     

Fault detection in finite frequency domain for constrained networked systems under multi-packet transmission

In this paper, the fault detection problem is studied in finite frequency domain for constrained networked systems under multi-packet transmission. The considered transmission mechanism is that only one packet including parts of the measured information can be transmitted through the communication channel and their accessing is scheduled by a designed stochastic protocol. Then by virtues of the introduced performance indices in finite frequency domain, a novel effective fault detection scheme is presented, in which the fault detection filters completing the task with partially available measurements are designed to make sure that the residual is sensitive to the reference input and the fault in faulty cases and robust to the reference input in fault-free case. Further, convex conditions in terms of time-domain inequalities are developed to handle the proposed fault detection scheme. The theoretical results are validated by the simulation to detect the sensor fault on a lateral-directional aerodynamic model.     

Robust stabilization of power systems subject to a series of lightning strokes modeled by Markov jumps: Attracting ellipsoids approach

Power systems are subject to stochastic faults and process random noise. The faults (due to e.g. lightning strokes) can be temporary or permanent. When a lightning stroke hits a transmission line, the circuit breakers open to clear the fault and reclose. The resulting parameters changes are modelled as a discrete-time Markov jumps in this paper using the practical statistical failure rates. System parameters are also subject to random noise e.g. line reactance’s depend on the conductors spacing which in turn depends on stochastic wind speeds. This paper presents a novel power system excitation control robust against such stochastic uncertainties. The design is based on a derived sufficient condition in the framework of linear matrix inequalities (LMI), and the attracting ellipsoid approach. The effectiveness of the proposed control is tested on a multi-machine power system.     

Switching Gaussian-heavy-tailed distribution based robust Gaussian approximate filter for INS/GNSS integration

In inertial navigation system and global navigation satellite system (INS/GNSS) integration, the practical stochastic measurement noise may be non-stationary heavy-tailed distribution due to outlier measurements induced by multipath and/or non-line-of-sight receptions of the original GNSS signals. To address the problem, a new switching Gaussian-heavy-tailed (SGHT) distribution is presented, which models the measurement noise with the help of switching between the Gaussian and the an existing heavy-tailed distribution. Then, utilizing two auxiliary parameters satisfying categorical and Bernoulli distributions respectively, we construct the SGHT distribution as a hierarchical Gaussian presentation. Furthermore, applying variational Bayesian inference, a novel SGHT distribution based robust Gaussian approximate filter is derived. Meanwhile, to reduce the computational complexity of the filtering process, an improved fixed-point iteration method is designed. Finally, the simulation of integrated navigation for an aircraft illustrates effectiveness and superiority of the proposed filter as compared the existing robust filters.     

Enhancing performance of generalized minimum variance control via dynamic data reconciliation

The design, tuning, and implementation of controllers are crucial for the solutions to control problems. Generalized minimum variance control (GMVC) has attractive properties and it is widely used for controller performance enhancement. The measured signals of process output variables, which are used as feedback signals, are generally subject to measurement noise. However, the GMVC theory assumes the feedback signals are the process outputs, which rarely consider the unavoidable measurement noise. By additionally considering the measurement noise, the control performance of GMVC with the measurement noise is analyzed in this paper. The dynamic data reconciliation (DDR) method, which uses the information of both the process model and the measurement data to reconcile the measured signals, is introduced. It is combined with GMVC to reduce the effect of the measurement noise on the results of GMVC. The effectiveness of GMVC combined with DDR is illustrated in two case studies, where the proposed method is compared with the original GMVC and the GMVC with the conventional digital filter. The results in both SISO and MIMO control systems show that the proposed GMVC combined with DDR can reduce the effect of the measurement noise and achieve better control performance.     

Adaptive neural control for nonlinear switched systems with improved MDADT and its applications

In this paper, a new framework of the robust adaptive neural control for nonlinear switched stochastic systems is established in the presence of external disturbances and system uncertainties. In the existing works, the design of robust adaptive control laws for nonlinear switched systems mainly relies on the average dwell time method, while the design and analysis based on the model-dependent average dwell time (MDADT) method remains a challenge. An improved MDADT method is developed for the first time, which greatly relaxes the requirements of Lyapunov functions of any two subsystems. Benefiting from the improved MDADT, a switched disturbance observer for discontinuous disturbances is proposed, which realizes the real-time gain adjustment. For known and unknown piecewise continuous nonlinear functions, a processing method based on the tracking differentiator and the neural network is proposed, which skillfully guarantees the continuity of the control law. The theoretical proof shows that the semiglobal uniform ultimate boundedness of all closed-loop signals can be guaranteed under switching signals with MDADT property, and simulation results of the longitudinal maneuvering control at high angle of attack are given to further illustrate the effectiveness of the proposed framework.     

Analyzing noise-induced tracking errors in control systems with saturation: A stochastic linearization approach

Noise Induced Tracking Error (NITE) refers to the tracking error of the mean of the output in feedback control systems with nonlinear instrumentation subject to zero-mean measurement noise. Most of the previous work rely on the stochastic averaging for NITE analysis, the validity of which requires that the bandwidth of the zero mean measurement noise is much higher than that of the system. This is because the results obtained by stochastic averaging are asymptotic with respect to the noise bandwidth. Due to the asymptotic nature of the analysis tool, it is not straightforward to provide a quantitative argument for high bandwidth. An alternative method in the literature that can analyze NITE is stochastic linearization for random input, which is analogous to the well known describing function approach for sinusoidal input. Unlike stochastic averaging, stochastic linearization is not an asymptotic approximation. Therefore, analysis can be carried out for any given noise bandwidth. We carry out NITE analysis using stochastic linearization for a class of LPNI systems that are prone to NITE; identify the system conditions under which the averaging analysis of NITE may yield inaccurate results for a finite noise bandwidth; and prove that the results from the two methods agree as the noise bandwidth approaches infinity. In addition, an existing NITE mitigation strategy is extended based on the proposed method. Numerical examples are given to illustrate the results.     

Order Statistical Filtering: a Robust Method of Noise Estimation

The detection of a narrowband signal in a sonar environment with spatially uncorrelated white noise depends very much on the accuracy in estimating the noise power so that a threshold can be correctly fixed. The conventional MA method presents a large bias when operated in an environment where interfering signals exist in the neighborhood. Various types of nonlinear methods based on the use of order statistics are introduced and analyzed and are found to be much more robust.     

Asymptotic memoryless detection of random signals in dependent noise

Design of detectors for strong mixing signals in strong mixing noise is considered, where a large degree of dependency may occur between the signal and noise. Under the criterion of asymptotic relative efficiency, it is shown that this design reduces to determining the solution of an integral equation, where only knowledge of the second order statistics of the randon processes involved is required. In particular, if the signal is independent of the noise and has nonzero mean, the optimal detector is the same as in the known constant signal case. It is also shown that it is possible to delete several regularity conditions which may be difficult to check in practice in the slightly more restrictive case where the maximal correlation coefficients of the signal and noise tend to zero.     

Stochastic bipartite consensus with measurement noises and antagonistic information

This paper is dedicated to the stochastic bipartite consensus issue of discrete-time multi-agent systems subject to additive/multiplicative noise over antagonistic network, where a stochastic approximation time-varying gain is utilized for noise attenuation. The antagonistic information is characterized by a signed graph. We first show that the semi-decomposition approach, combining with Martingale convergence theorem, suffices to assure the bipartite consensus of the agents that are disturbed by additive noise. For multiplicative noise, we turn to the tool from Lyapunov-based technique to guarantee the boundedness of agents’ states. Based on it, the bipartite consensus with multiplicative noise can be achieved. It is found that the constant stochastic approximation control gain is inapplicable for the bipartite consensus with multiplicative noise. Moreover, the convergence rate of stochastic MASs with communication noise and antagonistic exchange is explicitly characterized, which has a close relationship with the stochastic approximation gain. Finally, we verify the obtained theoretical results via a numerical example.     

Output regulation control for stochastic systems with additive noise

This paper investigates the robust output regulation problem for stochastic systems with additive noises. As is known, for the output regulation control problem, a general method is to regard that the system is disturbed by an autonomous exosystem (which is consisted by external disturbances and reference signals), and for the system disturbed by the white noise, the stochastic differential equations (SDEs) should be utilized in modeling, accordingly, a controller with a feedforward regulator is constructed for the stochastic system with an exosystem, which can not only cancel the external disturbance, but also transform the trajectory tracking problem into the stabilization problem; In consideration of the state variables in stochastic systems cannot be measured completely, we embed an observer to the controller, such that the random interference can be suppressed, and the trajectory tracking can be achieved. Based on the stochastic control theory, the criteria of the exponential practical stability in the mean square is presented for the closed-loop system, finally, through tuning the controller parameters, the mean square of the tracking error can converge to an arbitrarily small neighborhood of the origin.     

Implicit and explicit discrete-time realizations of the robust exact filtering differentiator

This paper presents explicit and implicit discrete-time realizations for the robust exact filtering differentiator, aiming to facilitate an adequate posterior implementation structure in digital devices. This paper firstly presents an analysis of an explicit discrete-time realization of the filtering differentiator based on linear systems’ exact discretization with a zero-order holder. For this case, however, high-order terms in the filter dynamics may cause instability of the estimation error for signals with unbounded derivatives. Hence, two other new discrete-time realizations of the filtering differentiator are derived by removing some high-order terms in the filter dynamics. The first one is an explicit discrete-time realization, while the second one is implicit. After a finite time, both preserve the accuracy of the continuous-time robust exact filtering differentiator in the presence of measurement noise. For each proposed discrete-time scheme, a stability analysis based on homogeneity is provided. Finally, the simulation results include comparisons between the proposed implicit and explicit discrete-time realizations with other existing schemes. These numerical studies highlight that the implicit scheme supersedes the explicit one, consistent with the implicit and explicit realizations of other continuous-time algorithms.     

Global mean square exponential stability and stabilization of uncertain switched delay systems with Lévy noise and flexible switching signals

This paper focuses on the stability analysis and stabilization problem for a class of uncertain switched delay systems with Lévy noise and flexible switching signals which unify the high-frequency switching and low-frequency switching. By employing the theory of switched systems, mathematical induction and stochastic analysis technique, some sufficient conditions in form of algebraic inequalities are derived to guarantee the stability and stabilization of such systems. Different from dwell time and average dwell time, the proposed switching rule constrained the partial dwell-time shows that the switching number in the same time interval can be more elastic. Finally, numerical examples are implemented to illustrate the effectiveness of the theoretical results.     

Intermittent fault detection for delayed stochastic systems over sensor networks

This paper is concerned with the intermittent fault (IF) detection problem for a class of linear discrete-time stochastic systems over sensor networks with constant time delay. By utilizing the lifting method, the distributed decoupled observers are proposed based on the output information of neighbor nodes and the node itself. In order to detect the appearing time and disappearing time of the IF, the truncated residuals are designed by introducing a sliding-time window. Furthermore, the IF detection and location thresholds are determined based on the hypothesis testing technique and the detectability of the IF is analyzed in the framework of stochastic analysis. Finally, a simulation example is presented to illustrate the effectiveness of the derived results.     

Bias-compensated affine-projection-like algorithm based on maximum correntropy criterion for robust filtering

This article proposes an affine-projection-like maximum correntropy (APLMC) algorithm for robust adaptive filtering. The proposed APLMC algorithm is derived by using the objective function based on the maximum correntropy criterion (MCC), which can availably suppress the bad effects of impulsive noise on filter weight updates. But the overall performance of the APLMC algorithm may be decreased when the input signal is polluted by noise. To compensate for the deviation of the APLMC algorithm in the input noise interference environment, the bias compensation (BC) method is introduced. Therefore, the bias-compensated APLMC (BC-APLMC) algorithm is presented. Besides, the convergence of the BC-APLMC algorithm in the mean and the mean square sense is studied, which provides a constraint range for the step-size. Computer simulation results show that the APLMC, and BC-APLMC algorithms are valid in acoustic echo cancellation and system identification applications. It also shows that the proposed algorithms are robust in the presence of input noise and impulse noise.     

Robust augmented complex-valued normalized M-estimate subband adaptive filtering algorithm against colored non-circular inputs and impulsive noise

Recently, the augmented complex-valued normalized subband adaptive filtering (ACNSAF) algorithm has been proposed to process colored non-circular signals. However, its performance will deteriorate severely under impulsive noise interference. To overcome this issue, a robust augmented complex-valued normalized M-estimate subband adaptive filtering (ACNMSAF) algorithm is proposed, which is obtained by modifying the subband constraints of the ACNSAF algorithm using the complex-valued modified Huber (MH) function and is derived based on CR calculus and Lagrange multipliers. In order to improve both the convergence speed and steady-state accuracy of the fixed step size ACNMSAF algorithm, a variable step size (VSS) strategy based on the minimum mean squared deviation (MSD) criterion is devised, which allocates individual adaptive step size to each subband, fully exploiting the structural advantages of SAF and significantly improving the convergence performance of the ACNMSAF algorithm as well as its tracking capability in non-stationary environment. Then, the stability, transient and steady-state MSD performance of the ACNMSAF algorithm in the presence of colored non-circular inputs and impulsive noise are analyzed, and the stability conditions, transient and steady-state MSD formulas are also derived. Computer simulations in impulsive noise environments verify the accuracy of theoretical analysis results and the effectiveness of the proposed algorithms compared to other existing complex-valued adaptive algorithms.