An extended state observer with adjustable bandwidth for measurement noise

In this paper,a bandwidth-adjustable extended state observer(ABESO)is proposed for the systems with measurement noise.It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates noise,which conflicts with observation accuracy.Therefore,we introduce a bandwidth scaling factor such that ABESO is formulated to a 2-degree-of-freedom system.The observer gain is determined and the bandwidth scaling factor adjusts the bandwidth according to the tracking error.When the tracking error decreases,the bandwidth decreases to suppress the noise,otherwise the bandwidth does not change.It is proven that the error dynamics are bounded and converge in finite time.The relationship between the upper bound of the estimation error and the scaling factor is given.When the scaling factor is less than 1,the ABESO has higher estimation accuracy than the linear extended state observer(LESO).Simulations of an uncertain nonlinear system with compound disturbances show that the proposed ABESO can successfully estimate the total disturbance in noisy environments.The mean error of total disturbance of ABESO is 15.28% lower than that of LESO.

Adaptive adjustment of iterative learning control gain matrix in harsh noise environment

For the robustness problem of open-loop P-type iterative learning control under the influence of measurement noise which is inevitable in actual systems, an adaptive adjustment algorithm of iterative learning nonlinear gain matrix based on error amplitude is proposed and two nonlinear gain functions are given. Then with the help of Bellman-Gronwall lemma, the robustness proof is derived. At last, an example is simulated and analyzed. The results show that when there exists measurement noise, the proposed learning law adjusts the learning gain matrix on line based on error amplitude, thus can make a compromise between learning convergence rate and convergence accuracy to some extent： the fast convergence rate is achieved with high gain in initial learning stage, the strong robustness and high convergence accuracy are achieved at the same time with small gain in the end learning stage, thus better learning results are obtained.

Selection of noise parameters for Kalman filter

The Bayesian probabilistic approach is proposed to estimate the process noise and measurement noise parameters for a Kalman filter. With state vectors and covariance matrices estimated by the Kalman filter, the likehood of the measurements can be constructed as a function of the process noise and measurement noise parameters. By maximizing the likelihood function with respect to these noise parameters, the optimal values can be obtained. Furthermore, the Bayesian probabilistic approach allows the associated uncertainty to be quantified. Examples using a single-degree-of-freedom system and a ten-story building illustrate the proposed method. The effect on the performance of the Kalman filter due to the selection of the process noise and measurement noise parameters was demonstrated. The optimal values of the noise parameters were found to be close to the actual values in the sense that the actual parameters were in the region with significant probability density. Through these examples, the Bayesian approach was shown to have the capability to provide accurate estimates of the noise parameters of the Kalman filter, and hence for state estimation.

Noise analysis and measurement of time delay and integration charge coupled device

Time delay and integration （TDI） charge coupled device （CCD） noise sets a fundamental limit on image sensor performance, especially under low illumination in remote sensing applications. After introducing the complete sources of CCD noise, we study the effects of TDI operation mode on noise, and the relationship between different types of noise and number of the TDI stage. Then we propose a new technique to identify and measure sources of TDI CCD noise employing mathematical statistics theory, where theoretical analysis shows that noise estimated formulation converges well. Finally, we establish a testing platform to carry out experiments, and a standard TDI CCD is calibrated by using the proposed method. The experimental results show that the noise analysis and measurement methods presented in this paper are useful for modeling TDI CCDs.

Skew t Distribution-Based Nonlinear Filter with Asymmetric Measurement Noise Using Variational Bayesian Inference

This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise.Based on the cubature Kalman filter,we propose a new nonlinear filtering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise.The system states and the statistics of skew t noise distribution,including the shape matrix,the scale matrix,and the degree of freedom(DOF)are estimated jointly by employing variational Bayesian(VB)inference.The proposed method is validated in a target tracking example.Results of the simulation indicate that the proposed nonlinear filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.

Stochastic bounded consensus tracking of leader-follower multi-agent systems with measurement noises and sampled-data

This paper is concerned with the stochastic bounded consensus tracking problems of leader-follower multi-agent systems, where the control input of an agent can only use the information measured at the sampling instants from its neighbours or the virtual leader with a time-varying reference state, and the measurements are corrupted by random noises. The probability limit theory and the algebra graph theory are employed to derive the necessary and sufficient conditions guaranteeing the mean square bounded consensus tracking. It is shown that the maximum allowable upper boundary of the sampling period simultaneously depends on the constant feedback gains and the network topology. Furthermore, the effects of the sampling period on the tracking performance are analysed. It turns out that from the view point of the sampling period, there is a trade-off between the tracking speed and the static tracking error. Simulations are provided to demonstrate the effectiveness of the theoretical results.

Consensus for High-Order Linear Multi-Agent Systems with Unknown but Bounded Measurement Noises

The staticε-consensus problem for a high-order linear multi-agent system is studied over a connected undirected communication topology,in which the state measurements of neighbors are affected by unknown but bounded(UBB)noises.Using the dead-zone function and binomial coefficients,we propose a distributed consensus protocol.Under this protocol,all agents achieve staticε-consensus,i.e.,the first components of the states for each agent reachε-consensus,and the remaining components reach agreement at zero.Numerical examples illustrate the validity of the theoretical results.

Stochastic bounded consensus tracking of leader-follower multi-agent systems with measurement noises based on sampled data with general sampling delay

In this paper we provide a unified framework for consensus tracking of leader-follower multi-agent systems with measurement noises based on sampled data with a general sampling delay. First, a stochastic bounded consensus tracking protocol based on sampled data with a general sampling delay is presented by employing the delay decomposition technique. Then, necessary and sufficient conditions are derived for guaranteeing leader-follower multi-agent systems with measurement noises and a time-varying reference state to achieve mean square bounded consensus tracking. The obtained results cover no sampling delay, a small sampling delay and a large sampling delay as three special cases. Last, simulations are provided to demonstrate the effectiveness of the theoretical results.

Stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise

The current paper is devoted to the study of the stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise. First, the dynamics of stochastic FitzHugh-Nagumo systems are studied. Then, the existence and uniqueness of their invariant measures, which mix exponentially are proved. Finally, the asymptotic behaviors of invariant measures when size of noise gets to zero are investigated.

Self-tuning measurement fusion white noise deconvolution estimator with correlated noises

For the multisensor linear discrete time-invariant stochastic systems with correlated noises and unknown noise statistics,an on-line noise statistics estimator is presented by using the correlation method.Substituting it into the steady-state Riccati equation,the self-tuning Riccati equation is obtained.Using the Kalman filtering method,based on the self-tuning Riccati equation,a self-tuning weighted measurement fusion white noise deconvolution estimator is presented.By the dynamic error system analysis（DESA） method,it is proved that the self-tuning fusion white noise deconvolution estimator converges to the optimal fusion steadystate white noise deconvolution estimator in a realization,so that it has the asymptotic global optimality.A simulation example for Bernoulli-Gaussian input white noise shows its effectiveness.

CALIBRATION OF A 6-DOF SPACE ROBOT USING GENETIC ALGORITHM

The kinematic error model of a 6-DOF space robot is deduced, and the cost function of kinematic parameter identification is built. With the aid of the genetic algorithm （GA） that has the powerful global adaptive probabilistic search ability, 24 parameters of the robot are identified through simulation, which makes the pose （position and orientation） accuracy of the robot a great improvement. In the process of the calibration, stochastic measurement noises are considered. Lastly, generalization of the identified kinematic parameters in the whole workspace of the robot is discussed. The simulation results show that calibrating the robot with GA is very stable and not sensitive to measurement noise. Moreover, even if the robot＇s kinematic parameters are relative, GA still has strong search ability to find the optimum solution.

Synchronization of chaos using radial basis functions neural networks

The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.

ADAPTIVE FUSION ALGORITHMS BASED ON WEIGHTED LEAST SQUARE METHOD

Weighted fusion algorithms, which can be applied in the area of multi-sensor data fusion, are advanced based on weighted least square method. A weighted fusion algorithm, in which the relationship between weight coefficients and measurement noise is established, is proposed by giving attention to the correlation of measurement noise. Then a simplified weighted fusion algorithm is deduced on the assumption that measurement noise is uncorrelated. In addition, an algorithm, which can adjust the weight coefficients in the simplified algorithm by making estimations of measurement noise from measurements, is presented. It is proved by emulation and experiment that the precision performance of the multi-sensor system based on these algorithms is better than that of the multi-sensor system based on other algorithms.

A scheme for Sagnac-effect quantum enhancement with Fock state light input

Sagnac effect enhancement can improve optical gyro precision. For a certain input intensity, we suggest that the other input port of beam splitter（BS） should be fed with some quantum light to break through shot noise limit（SNL） to improve Sagnac effect without increasing radiation-pressure noise（NRP）. We design a Sagnac effect quantum enhancement criterion（SQEC） to judge whether some quantum light can enhance Sagnac effect and present a Sagnac effect enhancement scheme that utilizing Fock state light and parity measurement technique to extract the output phase. The results of the theoretical analysis show that the maximum sensitivity can be reached at θ = 0, and the phase precision can break through SNL and even achieve Heisenberg limit（HL）. When the Fock state average photon number n is far less than coherent state, the minimum measurable angular rate is improved with √2n＋1 times, which can deduce shot noise and increase NRP little.

Decentralized damage diagnostic technique for tall buildings using VARMAX model

Civil infrastructure,especially buildings,are becoming more slender,tall,and multipurpose,creating a need to continuously monitor their health to ensure the safety and security of human lives and assets.While the majority of structural health monitoring techniques use measurements from the entire structure,in this study,an output-only damage diagnostic technique using a decentralized concept(subdomain-based)for tall buildings and employing a vector form of the autoregressive moving average with exogenous input(VARMAX)model is proposed,which offers reduced instrumentation and data handling requirements.Unlike other decentralized approaches,this technique predicts more than one DOF at a time so the number of subdomains required for the diagnosis of the complete structure is minimized.The proposed subdomain-based damage diagnostic algorithm works with ambient loads and does not require any correlated numerical models since it is solely based on measured data.The proposed algorithm can identify the time instant of damage,spatial location(s)and characterize the damage intensity.Efforts have been made to account for confounding factors such as environmental and operational variabilities separate from measurement noise to avoid false positive alarms.The effectiveness of the proposed technique is illustrated using synthetic time history responses from a twenty-story framed structure under ambient loading and an experimental study on a ten-story framed structure.Both numerical and experimental investigations confirm the effectiveness of the method and its robustness to environmental/operational variabilities and measurement noise.

一种改进的指令调节自适应控制器在无人水下航行器深度控制中的实验研究

Command governor–based adaptive control(CGAC)is a recent control strategy that has been explored as a possible candidate for the challenging task of precise maneuvering of unmanned underwater vehicles(UUVs)with parameter variations.CGAC is derived from standard model reference adaptive control(MRAC)by adding a command governor that guarantees acceptable transient performance without compromising stability and a command filter that improves the robustness against noise and time delay.Although simulation and experimental studies have shown substantial overall performance improvements of CGAC over MRAC for UUVs,it has also shown that the command filter leads to a marked reduction in initial tracking performance of CGAC.As a solution,this paper proposes the replacement of the command filter by a weight filter to improve the initial tracking performance without compromising robustness and the addition of a closed-loop state predictor to further improve the overall tracking performance.The new modified CGAC(M-CGAC)has been experimentally validated and the results indicate that it successfully mitigates the initial tracking performance reduction,significantly improves the overall tracking performance,uses less control force,and increases the robustness to noise and time delay.Thus,M-CGAC is a viable adaptive control algorithm for current and future UUV applications.

Data-driven discovery of linear dynamical systems from noisy data

In modern science and engineering disciplines,data-driven discovery methods play a fundamental role in system modeling,as data serve as the external representations of the intrinsic mechanisms within systems.However,empirical data contaminated by process and measurement noise remain a significant obstacle for this type of modeling.In this study,we have developed a data-driven method capable of directly uncovering linear dynamical systems from noisy data.This method combines the Kalman smoothing and sparse Bayesian learning to decouple process and measurement noise under the expectation-maximization framework,presenting an analytical method for alternate state estimation and system identification.Furthermore,the discovered model explicitly characterizes the probability distribution of process and measurement noise,as they are essential for filtering,smoothing,and stochastic control.We have successfully applied the proposed algorithm to several simulation systems.Experimental results demonstrate its potential to enable linear dynamical system discovery in practical applications where noise-free data are intractable to capture.

Photonic-assisted single system for microwave frequency and phase noise measurement

We propose a photonic-assisted single system for measuring the frequency and phase noise of microwave signals in a large spectral range. Both the frequency and phase noise to be measured are extracted from the phase difference between the signal under testing and its replica delayed by a span of fiber and a variable optical delay line(VODL). The system calibration, frequency measurement, and phase noise measurement are performed by adjusting the VODL at different working modes. Accurate frequency and phase noise measurement for microwave signals in a large frequency range from 5 to 50 GHz is experimentally demonstrated.

Distributed Kalman filter for UWB/INS integrated pedestrian localization under colored measurement noise

Colored Measurement Noise(CMN)has a great impact on the accuracy of human localization in indoor environments with Inertial Navigation System(INS)integrated with Ultra Wide Band(UWB).To mitigate its influence,a distributed Kalman Filter(dKF)is developed for Gauss-Markov CMN with switching Colouredness Factor Matrix(CFM).In the proposed scheme,a data fusion filter employs the difference between the INS-and UWB-based distance measurements.The main filter produces a final optimal estimate of the human position by fusing the estimates from local filters.The effect of CMN is overcome by using measurement differencing of noisy observations.The tests show that the proposed dKF developed for CMN with CFM can reduce the localization error compared to the original dKF,and thus effectively improve the localization accuracy.

Output feedback control with disturbancecompensation in nonlinear MIMO systems undermeasurement noises

A novel output feedback control law with disturbance compensation for nonlinear multiinputmulti-output (MIMO) time-invariant systems under measurement noises is proposed. Thedesigned control law, based on the noise and disturbance estimations, ensures the accuracy insteady state depending on the disturbance, only one component of noise vector and its firstderivatives. Therefore, the proposed algorithm is efficient under noises with large magnitudes.Sufficient conditions in terms of linear matrix inequalities (LMIs) provide a practical exponentialstability of the closed-loop system. The simulations illustrate an efficiency of the proposedmethod compared with some existing ones.