Stochastic Measurement Noise Research Articles

Adaptive consensus for uncertain multi-agent systems with stochastic measurement noises

This paper addresses asymptotic consensus for multi-agent systems with the measurement of neighbor information interfered by stochastic noises. Notably, intractable parametric uncertainties are allowed in the agent dynamics, which, coupling with inherent nonlinearities, firmly ask for distributed adaptive compensation. To limit the influence scope of measurement noises on adaptive mechanism, the distributed protocol design is separated into two aspects: (i)Reference consensus based on relative information. Local dynamic generators, providing certain reference signals, are constructed by exploiting the relative information multiplying a subtle time-varying gain. With the measurement noises attenuated via the time-varying gain, all the generators are guaranteed to evolve for all time and reach consensus in the almost sure sense. (ii)Agent tracking based on individual estimate. Utilizing individual information, local adaptive estimates are proposed for the agent uncertainties while not involving the noise measurements. In this way, a distributed adaptive protocol is designed to make each agent state track the corresponding reference signal while preventing the inherent nonlinearities from incurring finite-time explosion, and furthermore, to enable all the agents to reach average consensus in the almost sure sense.

Experimental Case Study of Stochastic Surrogate-Assisted Engine Calibration

Reducing experimental calibration cost to achieve optimal system performance is challenging, especially for highly nonlinear engine systems. With the advancement and widespread adoption of machine learning methods for control applications, it is now possible to use an intelligent black-box model to efficiently optimize nonlinear control systems without the detailed knowledge of system dynamics. The surrogate-assisted optimization approach has been recently proven to work effectively to reduce the overall experimental budget (cost). However, its application to calibrate and optimize a practical control system experimentally is a challenge due to stochastic system and measurement noises. This article experimentally calibrates and optimizes the control parameters of a 6.7L Ford diesel engine using the stochastic surrogate-assisted optimization automatically based on a stochastic Kriging model, which is the first step toward automating the engine calibration process. Two engine control variables, namely, exhaust gas recirculation valve and variable geometry turbocharger vane positions, are calibrated to obtain a tradeoff between engine efficiency, in terms of brake-specific fuel consumption, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{NO}_{x}$</tex-math></inline-formula> emissions, utilizing both the deterministic and stochastic surrogate-assisted learning algorithms. Experimental results show a much better representation of the output response surfaces with the stochastic surrogate-assisted optimization than that from the deterministic approach. Note that the stochastic approach helps direct the search toward the global optimal region without wasting the evaluation budget in exploring the local optima, and the deterministic approach cannot effectively handle stochastic system and measurement noises, resulting in overfitting the data. Therefore, to solve a practical optimization problem with noises, stochastic surrogate-assisted optimization is recommended.

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.

A novel switching Gaussian-heavy-tailed distribution based robust fixed-interval smoother

In nonlinear systems, the stochastic process and measurement noises may be non-stationary heavy-tailed distribution due to the dynamic outliers induced by unreliable sensors and complicated environments. The main purpose of this paper is to address the problem by establishing a new switching Gaussian-heavy-tailed (SGHT) distribution. We model the noise with the help of switching between the Gaussian and the newly designed 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 fixed-interval smoother is derived. The experiment results of the synthetic data and real vehicle localization dataset demonstrate the superior performance of the proposed smoother as compared with cutting-edge smoother.

Estimation and Error Analysis for Optomechanical Inertial Sensors.

A sensor model and methodology to estimate the forcing accelerations measured using a novel optomechanical inertial sensor with the inclusion of stochastic bias and measurement noise processes is presented. A Kalman filter for the estimation of instantaneous sensor bias is developed; the outputs from this calibration step are then employed in two different approaches for the estimation of external accelerations applied to the sensor. The performance of the system is demonstrated using simulated measurements and representative values corresponding to a bench-tested 3.76 Hz oscillator. It is shown that the developed methods produce accurate estimates of the bias over a short calibration step. This information enables precise estimates of acceleration over an extended operation period. These results establish the feasibility of reliably precise acceleration estimates using the presented methods in conjunction with state of the art optomechanical sensing technology.

A top-down measure of gene-to-gene coordination for analyzing cell-to-cell variability

Recent technological advances, such as single-cell RNA sequencing (scRNA-seq), allow the measurement of gene expression profiles of individual cells. These expression profiles typically exhibit substantial variations even across seemingly homogeneous populations of cells. Two main different sources contribute to this measured variability: actual differences between the biological activity of the cells and technical measurement errors. Analysis of the biological variability may provide information about the underlying gene regulation of the cells, yet distinguishing it from the technical variability is a challenge. Here, we apply a recently developed computational method for measuring the global gene coordination level (GCL) to systematically study the cell-to-cell variability in numerical models of gene regulation. We simulate ‘biological variability’ by introducing heterogeneity in the underlying regulatory dynamic of different cells, while ‘technical variability’ is represented by stochastic measurement noise. We show that the GCL decreases for cohorts of cells with increased ‘biological variability’ only when it is originated from the interactions between the genes. Moreover, we find that the GCL can evaluate and compare—for cohorts with the same cell-to-cell variability—the ratio between the introduced biological and technical variability. Finally, we show that the GCL is robust against spurious correlations that originate from a small sample size or from the compositionality of the data. The presented methodology can be useful for future analysis of high-dimensional ecological and biochemical dynamics.

Fault tolerance in non‐linear systems: A model‐based approach with a robust soft sensor design

A novel multiple Kalman filtre (KF)-based scheme is proposed, as a generalisation of conventional gain-scheduling techniques, for fault diagnosis and tolerance in a large class of multiple-input and multiple-output non-linear systems. The outputs are corrupted by unknown stochastic disturbance and measurement noise. A reliable and computationally efficient, two-stage identification of a piecewise linear parameter-varying Box–Jenkins dynamic model that better approximates the non-linear system, at each operating point, and the design of the associated KFs are proposed. Novel emulators, whose induced parameter changes mimic likely and predictive operating scenarios, are used to provide an accurate model identification and robustness to noise, disturbance, non-linearity errors and model perturbations. These crucial emulators generate missing representative data, aid predictive analytics, and improve the reliability and accuracy of the identified KF model. A novel formulation of the KF is used for fault isolation, and the Bayes strategy is used to isolate difficult-to-detect incipient faults in noisy environments. The proposed scheme leads to the design of a novel robust soft sensor aimed at replacing the maintenance-prone hardware sensor in practical applications including product quality assessment, performance monitoring, condition-based maintenance, fault diagnosis and fault-tolerant control. The proposed soft sensor was successfully evaluated on simulated and laboratory-scale physical control systems.

Adaptive iterative learning control for switched discrete-time systems with stochastic measurement noise

This paper investigates an adaptive iterative learning control (AILC) scheme for a class of switched discrete-time linear systems with stochastic measurement noise. For the case when the subsystems dynamics are unknown and the switching rule is arbitrarily fixed, the iteration-wise input-output data-based system lower triangular matrix estimation is derived by means of minimizing an objective function with a gradient-type technique. Then, the AILC is constructed in an interactive form with system matrix estimation for the switched linear systems to track the desired trajectory. Based on the derivation of the boundedness of the estimation error of system matrix, by virtue of norm theory and statistics technique, the tracking error and the covariance matrix of the tracking error are derived to be bounded, respectively. Finally, the AILC concept is extended to nonlinear systems by utilizing linearization techniques. Simulation results illustrate the validity and effectiveness of the proposed AILC schemes.

Data-Driven Output-Feedback Fault-Tolerant Tracking Control Method and Its Application to a DC Servo System

The paper is concerned with the problem of data-driven output-feedback fault-tolerant tracking control design for unknown discrete-time linear systems with stochastic measurement and process noise. With the aid of a proposed input-output data-based online iterative identification algorithm, this study presents a fault detection strategy, an approximate dynamic programming approach to performance optimization, and a method for the achievement of tracking control via a pre-filter. The resulting fault-tolerant control (FTC) scheme is applied to a practical DC servo motor system with load fluctuations and nonlinearity. Finally, the experimental test demonstrates that the proposed FTC strategy (including a methodology for compensating load variations and nonlinearity) has better applicability and practicability than the one given by the previous work, where a load needs to be held constant and it is required that the motor run in a nearly linear small working region.

Adaptive Iterative Learning Control of Switched Nonlinear Discrete-Time Systems With Unmodeled Dynamics

This paper is concerned with the issue of adaptive iterative learning control (AILC) for single-input, single-output (SISO), switched nonlinear discrete-time systems with unmodeled dynamics and stochastic measurement noise. Under the random switching rule, the nonlinear subsystem is estimated by a linear model which is constructed by minimizing the discrepancy between the real system output and the estimated system output with gradient-type technique. Meanwhile, the adaptive switched control law is designed by the updated subsystem matrix estimation. By taking advantages of norm theory, the boundedness of the estimation error is derived. Further, by the manner of the statistical technique, the results are conducted that the expectation of the tracking error is monotonically convergent to zero and the covariance matrix of the tracking error is bounded. Finally, simulation results are given to validate the proposed scheme is effective.

Joint Detection and DOA Tracking with a Bernoulli Filter Based on Information Theoretic Criteria

In this paper, we study the problem of the joint detection and direction-of-arrival (DOA) tracking of a single moving source which can randomly appear or disappear from the surveillance volume. Firstly, the Bernoulli random finite set (RFS) is employed to characterize the randomness of the state process, i.e., the dynamics of the source motion and the source appearance. To increase the performance of the detection and DOA tracking in low signal-to-noise ratio (SNR) scenarios, the measurements are obtained directly from an array of sensors and allow multiple snapshots. A track-before-detect (TBD) Bernoulli filter is proposed for tracking a randomly on/off switching single dynamic system. Secondly, since the variances of the stochastic signal and measurement noise are unknown in practical applications, these nuisance parameters are marginalized by defining an uninformative prior, and the likelihood function is compensated by using the information theoretic criteria. The simulation results demonstrate the performance of the filter.

Switching and Data Injection Attacks on Stochastic Cyber-Physical Systems

In this article, we consider the problem of attack-resilient state estimation, that is, to reliably estimate the true system states despite two classes of attacks: (i) attacks on the switching mechanisms and (ii) false data injection attacks on actuator and sensor signals, in the presence of stochastic process and measurement noise signals. We model the systems under attack as hidden mode stochastic switched linear systems with unknown inputs and propose the use of a multiple-model inference algorithm to tackle these security issues. Moreover, we characterize fundamental limitations to resilient estimation (e.g., upper bound on the number of tolerable signal attacks) and discuss the topics of attack detection, identification, and mitigation under this framework. Simulation examples of switching and false data injection attacks on a benchmark system and an IEEE 68-bus test system show the efficacy of our approach to recover resilient (i.e., asymptotically unbiased) state estimates as well as to identify and mitigate the attacks.

Ensuring Stability and Fidelity of Recursively Identified Control-Relevant Models

In this work, a recursive system identification algorithm is extended to improve reliability and better handle stochastic disturbances, measurement noise, and other adverse phenomena. The proposed approach involves the modification of the recursive predictor-based subspace identification (PBSID) algorithm to incorporate constraints on the fidelity and accuracy of the identified models, correctness of the sign of the input-to-output gains, and the integration of heuristics to ensure stability of the recursively identified models. The efficacy of the proposed approach is demonstrated using case studies involving the modeling of time-varying glucose–insulin dynamics.

Active vibration control for seismic excited building structures under actuator saturation, measurement stochastic noise and quantisation

This paper investigates the active vibration control for seismic excited building structures in presenting of actuator saturation, stochastic measurement noise and quantisation. The active vibration controllers are placed in some storeys, meanwhile, some active tuned mass dampers (ATMDs) are also installed at the top floor and oscillating under their control forces. All of the control forces are generated by actuators which are only capable of providing limited outputs. Since the system states are difficult or barely impossible to be accurately measured, an observer based control law is proposed to guarantee system stability, meanwhile, an H2/H∞ index is employed for further improving the control performance. By the proposed control strategy, the mean square exponentially stability of close-looped system can be guaranteed almost surely while the desired H2/H∞ performance can be achieved simultaneously. In addition, the convergence rate of system state can be pre-scheduled. By regulating the different locations of sensors and controllers, the vibration response can be mitigated in different level. Numerical examples are provided to demonstrate the effectiveness of the proposed method.

Fault‐tolerant formation control of non‐linear multi‐vehicle systems with application to quadrotors

This study is concerned with the fault-tolerant (FT) formation control problem with a guaranteed H ∞ performance for non-linear multi-vehicle systems subject to actuator faults. The authors consider a practical situation: the information transferred between adjacent vehicles is disturbed and each vehicle is interfered by stochastic disturbance and measurement noise. For each vehicle, a decentralised state observer and an adaptive fault estimator are designed based on which a novel cooperative FT control (FTC) protocol is proposed to drive all the vehicles to the desired formation configuration. Taking the system noise into consideration, the error dynamics are modelled by I t o ^ stochastic differential equations, whose properties are used for designing and analysing the Lyapunov function in the framework of I t o ^ calculus. It is proved that the formation error system is mean-square asymptotically stable with a prescribed attenuation level in an H ∞ sense by the proposed FTC scheme. The observer, estimator and controller gains can be obtained by solving algebraic Riccati inequalities. Finally, the theoretical results are illustrated by simulations and real experiments.

Output-Feedback Control of Unknown Linear Discrete-Time Systems With Stochastic Measurement and Process Noise via Approximate Dynamic Programming.

This paper studies the optimal output-feedback control problem for unknown linear discrete-time systems with stochastic measurement and process noise. A dithered Bellman equation with the innovation covariance matrix is constructed via the expectation operator given in the form of a finite summation. On this basis, an output-feedback-based approximate dynamic programming method is developed, where the terms depending on the innovation covariance matrix are available with the aid of the innovation covariance matrix identified beforehand. Therefore, by iterating the Bellman equation, the resulting value function can converge to the optimal one in the presence of the aforementioned noise, and the nearly optimal control laws are delivered. To show the effectiveness and the advantages of the proposed approach, a simulation example and a velocity control experiment on a dc machine are employed.

Active suspension control with state estimation using finite Markov chains

State estimation and optimal control of a nonlinear stochastic MacPherson suspension system using finite state and action Markov chains is considered. A system model and optimal controller are iteratively constructed based on k-means clustering of closed loop data and re-discretisation of the continuous system state space. Bayesian estimation of measured and unmeasured states using a cell filter is considered, and the unscented Kalman filter is considered as an alternative implementation. The main contribution is the introduction of the finite state and action Markov chains to the optimal control design and state estimation in active suspension systems. The application for active suspension control is illustrated and discussed via simulations using a simplified nonlinear model of a MacPherson system including stochastic road and measurement noise.

Fast and Robust Vanishing Point Detection for Unstructured Road Following

Vision-based unstructured road following is a challenging task due to the nature of the scene. This paper describes a novel algorithm to improve the accuracy and robustness of vanishing point estimation with very low computational cost. The novelties of this paper are three aspects: 1) We use joint activities of four Gabor filters and confidence measure for speeding up the process of texture orientation estimation. 2) Misidentification chances and computational complexity of the algorithm are reduced by using a particle filter. It limits vanishing point search range and reduces the number of pixels to be voted. The algorithm combines the peakedness measure of vote accumulator space with the displacements of moving average of observations to regulate the distribution of vanishing point candidates. 3) Attributed to the design of a noise-insensitive observation model, the proposed system still has high detection accuracy even when less than 60 sparsely distributed vanishing point candidates are used for voting as the influence introduced by the stochastic measurement noise of vote function and the sparsity of the vanishing point candidates is reduced. The method has been implemented and tested over 20 000 video frames. Experimental results demonstrate that the algorithm achieves better performance than some state-of-the-art texture-based vanishing point detection methods in terms of detection accuracy and speed.

Integral-based event triggering controller design for stochastic LTI systems via convex optimisation

ABSTRACTThe presence of measurement noise in the event-based systems can lower system efficiency both in terms of data exchange rate and performance. In this paper, an integral-based event triggering control system is proposed for LTI systems with stochastic measurement noise. We show that the new mechanism is robust against noise and effectively reduces the flow of communication between plant and controller, and also improves output performance. Using a Lyapunov approach, stability in the mean square sense is proved. A simulated example illustrates the properties of our approach.

A maximum-likelihood method for estimating parameters, stochastic disturbance intensities and measurement noise variances in nonlinear dynamic models with process disturbances

An improved approximate maximum likelihood algorithm is developed for estimating measurement noise variances along with model parameters and disturbance intensities in nonlinear stochastic differential equation (SDE) models. This algorithm uses a Laplace approximation and B-spline basis functions for approximating the likelihood function of the parameters given the measurements. The resulting Laplace approximation maximum likelihood estimation (LAMLE) algorithm is tested using a nonlinear continuous stirred tank reactor (CSTR) model. Estimation results for four model parameters, two process disturbance intensities and two measurement noise variances are obtained using LAMLE and are compared with results from two other maximum-likelihood-based methods, the continuous-time stochastic method (CTSM) of Kristensen and Madsen (2003) and the Fully Laplace Approximation Estimation Method (FLAEM) (Karimi and McAuley, 2014). Parameter estimations using 100 simulated data sets reveal that the LAMLE estimation results tend to be more precise and less biased than corresponding estimates obtained using CTSM and FLAEM.