Noise Matrices Research Articles

Observer-based IM stator fault diagnosis: Experimental validation

In this paper, an experimental validation of an efficient approach to the Fault Detection and Isolation (FDI) of Induction Motor (IM) is proposed. The problem of Inter-turn short circuits (ITSC) in the stator windings is addressed. By introducing fault factors in the IM model an observer-based residual generator is designed, allowing the detection of ITSC in stator windings. The residual generator is built around an extended Kalman Filter (EKF) in order to estimate state variables and fault factors, which permits the evaluation of the severity of the fault. To overcome the problem of tuning the EKF a PSO algorithm is developed. It carries out a heuristic search of the noise matrices by optimizing a cost function. The proposed solution is validated by computer simulations and by real-time implementation on dSPACE 1104 Digital Signal Processor (DSP) test-bench under the healthy and the faulty conditions of IM. To perform tests under faulty conditions, an IM with customized design is built and the stator is rewound permitting to create ITSC. The results reveal the quick detection of the faults, the quantification of its severity and confirm the efficacy of this observer-based FDI algorithm.

A novel demodulation structure for quadrate modulation signals using the segmentary neural network modelling

In digital communication, the baseband information signal is modulated by the high-frequency carrier to produce a passband signal and applied to the transmission line. QASK (quadrature amplitude-shift keying), QFSK (quadrature frequency-shift keying), and QPSK (quadrature phase-shift keying) modulations from Quadrate type digital modulations are used for high-speed communication in passband digital modulations. They are a widespread modulation for fast and easy data transmission, especially in wireless communication and modem devices. In these modulations, four separate carriers are used, and since each carrier represents 2 bits, the transmission rate doubles compared to conventional digital modulation. This study aims to obtain the baseband signal from quadrate type modulation signals. For this purpose, all 8-bit data between Decimal 0–255 were obtained in QASK, QFSK, and QPSK modulations and signal matrices were formed. The various SNR (signal to noise ratio) values of 5 dB-10 dB-15 dB-20 dB noise were added to these signals to examine the system performance during the modulated signal transmission. The generated signals were given to the demodulation system developed using different methods and tested. The best results were obtained in developed a segmentary NN (Neural Network). In this study, it was observed that modulation signal matrices were given directly to an ANN (Artificial Neural Network) and that the results could not be predicted with the application of noise matrices for testing. Then the modulation signals with the proposed method are divided into four parts. Each segment represents a two-bit piece of data. In the case of a column matrix, four parts were applied as input to the neural network model. In the output of ANN, the result matrix to be predicted is created. Each modulation signal applied to the network input was classified between 0 and 3 at the output. Modulation data-carrying 8 bits are applied to the network in 4 steps and classified. 4 separate classification data from the ANN output is converted back to 2-bit logic. Therefore, signals carrying 8 bits of data are obtained in 4 steps. After the formation of the ANN network, baseband digital signal estimation was performed quickly in 4 steps across each byte modulation signals under different noises coming into the network, and demodulation data was successfully achieved.

Adaptive Robust Unscented Kalman Filter for AUV Acoustic Navigation.

Autonomous underwater vehicle (AUV) acoustic navigation is challenged by unknown system noise and gross errors in the acoustic observations caused by the complex marine environment. Since the classical unscented Kalman filter (UKF) algorithm cannot control the dynamic model biases and resist the influence of gross errors, an adaptive robust UKF based on the Sage-Husa filter and the robust estimation technique is proposed for AUV acoustic navigation. The proposed algorithm compensates the system noise by adopting the Sage-Husa noise estimation technique in an online manner under the condition that the system noise matrices are kept as positive or semi positive. In order to control the influence of gross errors in the acoustic observations, the equivalent gain matrix is constructed to improve the robustness of the adaptive UKF for AUV acoustic navigation based on Huber’s equivalent weight function. The effectiveness of the algorithm is verified by the simulated long baseline positioning experiment of the AUV, as well as the real marine experimental data of the ultrashort baseline positioning of an underwater towed body. The results demonstrate that the adaptive UKF can estimate the system noise through the time-varying noise estimator and avoid the problem of negative definite of the system noise variance matrix. The proposed adaptive robust UKF based on the Sage-Husa filter can further reduce the influence of gross errors while adjusting the system noise, and significantly improve the accuracy and stability of AUV acoustic navigation.

Analysis and Design of Robust Max Consensus for Wireless Sensor Networks

A novel distributed algorithm for estimating the maximum of the node initial state values in a network, in the presence of additive communication noise is proposed. Conventionally, the maximum is estimated locally at each node by updating the node state value with the largest received measurements in every iteration. However, due to the additive channel noise, the estimate of the maximum at each node drifts at each iteration and this results in nodes diverging from the true max value. Max-plus algebra is used as a tool to study this ergodic process. The subadditive ergodic theorem is invoked to establish a constant growth rate for the state values due to noise, which is studied by analyzing the max-plus Lyapunov exponent of the product of noise matrices in a max-plus semiring. The growth rate of the state values is upper bounded by a constant which depends on the spectral radius of the network and the noise variance. Upper and lower bounds are derived for both fixed and random graphs. Finally, a two-run algorithm robust to additive noise in the network is proposed and its variance is analyzed using concentration inequalities. Simulation results supporting the theory are also presented.

Optimizing a Kalman filter with an evolutionary algorithm for nonlinear quadrotor attitude dynamics

Kalman filter is a linear minimum – mean square error estimator. However, process and measurement noise matrices of the Kalman filter must be known a priori to achieve this optimality condition. But in most cases, these parameters are guessed or tuned by trial and error approach both of which do not guarantee optimality and convergence. So in this work, an evolutionary algorithm is proposed to estimate the process and measurement noise covariance matrices of the Kalman filter to improve the performance of the sub – optimal filter. A fitness function is also proposed to achieve multi – dimensional optimization. Results are validated for both linear and nonlinear quadrotor attitude dynamics. Proposed method compared with optimization algorithms such as optimal Kalman filter, covariance – matrix adaptation evolution strategy and simulated annealing. Monte Carlo analysis showed that proposed algorithm is capable of tuning the state estimator better than the other algorithms. Thus, proposed algorithm reduces sensor errors and ensures efficient estimation of the quadrotor.

A note on the Pennington-Worah distribution

This paper is concerned with a new expression of the so-called Pennington-Worah distribution, characterizing the asymptotic empirical eigenvalue distribution of some non linear random matrix ensembles. More precisely consider $M= \frac{1} {m} YY^{*}$ with $Y=f(WX)$ where $W$ and $X$ are random rectangular matrices with i.i.d. centered entries. The function $f$ is applied pointwise and can be seen as an activation function in (random) neural networks. The asymptotic empirical distribution of this ensemble has been computed in [16] and [3]. Here it is related to the Marcenko-Pastur distribution and information plus noise matrices.

Generalized Least Squares Based Channel Estimation for FBMC-OQAM

The presence of intrinsic inter-carrier interference (ICI) and inter-symbol interference (ISI) at the output of the matched filter receiver in filter bank multi-carrier with offset quadrature amplitude modulation (FBMC-OQAM) systems complicates the task of channel estimation (CE). The conventional approach is to use a pilot symbol preamble structure, such as in the interference approximation/cancellation methods (IAM/ICM), together with a simple virtual symbol (VS) based CE scheme. However, this virtual symbol approach ignores the residual interference from the data portion of the FMBC burst as well as the correlation of the noise across the sub-carriers; both of these factors ultimately limit the performance. In this paper, we propose a generalized least squares (GLS) based CE scheme which, when applied to the IAM/ICM pilot structures, takes into account both the correlated noise and data interference effects. Closed-form expressions are derived for the channel estimation mean-squared error (CE-MSE) of the proposed GLS method and for the conventional VS method, and it is shown that the proposed method leads to a significant reduction of the CE-MSE by up to 6 dB when compared with the VS based method. This is demonstrated to result in improved bit error rate (BER) performance, especially when higher-order modulation is employed, making it an attractive channel estimation method for many modern deployment scenarios. The proposed GLS-based channel estimation scheme is parameterized allowing a flexible trade-off between channel frequency selectivity, estimation complexity and CE-MSE gain. Finally, symmetry properties of the intrinsic interference coefficients for a general FBMC-OQAM system are also proved, which facilitate the computation of the noise and interference autocorrelation matrices required by the proposed algorithm.

Parameter Estimation in Switching Markov Systems and Unsupervised Smoothing

Stationary jump Markov linear systems (JMLSs) model linear systems whose parameters evolve with time according to a hidden finite state Markov chain. We propose an algorithm for parameter estimation of a recent class of JMLS s called conditionally Gaussian pairwise Markov switching models (CGPMSMs). Our algorithm, named Double-EM (DEM), is based on the expectation–maximization (EM) principle applied twice sequentially. The first EM is applied to the couple (switches, observations) temporarily assumed to be a pairwise Markov chain. The second one is used to estimate the remaining conditional transitions and conditional noise matrices of the CGPMSM. The efficiency of the proposed algorithm is studied via unsupervised smoothing on simulated data. In particular, smoothing results, produced with CGPMSM in an unsupervised manner using DEM, can be more efficient than the ones obtained with the nearest classic conditionally Gaussian linear state-space model based on true parameters and true switches.

Using Joint Generalized Eigenvectors of a Set of Covariance Matrix Pencils for Deflationary Blind Source Extraction

In this paper, we develop a new deflationary blind source extraction (BSE) algorithm that extracts source signals in a sequential fashion via the joint generalized eigenvectors of a set of covariance matrix pencils. The new concept of joint generalized eigenvector is defined. We prove that these vectors can be made unique and identical to the source extraction vectors with properly selected matrix pencils. To resolve the open problem of estimating joint generalized eigenvectors, we develop an approach based on the deflation operation and the proportional property of the joint generalized eigenvectors. Specifically, with the proportional property, we show that the estimation problem can be formulated as an optimization involving a quadratic cost function and a unit-rank matrix constraint. An efficient iterative algorithm is then developed by applying the gradient search, matrix shrinkage, deflation, and symmetry-preserving vectorization techniques. This algorithm estimates the joint generalized eigenvectors and conducts BSE sequentially. Its computational complexity and convergence are analyzed. Simulations demonstrate that this algorithm outperforms many typical BSE or blind source separation algorithms. In particular, the new algorithm is more robust to both heavy noise and ill-conditioned mixing matrices.

Hybrid Genetic Algorithm and Kalman Filter Approach to Estimate the Clamping Force of Electro-Mechanical Brake

In thispaper, a hybrid genetic algorithm (GA) and Kalman filter approach to combining motor encoder and current sensor models is presented to accurate estimate the clamping force of an electro-mechanical brake (EMB). Elimination of the clamping force sensor and measurement cables results in lower cost and increased reliability of an EMB system, including its electric motor.A Kalman filter is a special kind of observer that provides optimal filtering of the measurement noise and inside the system if the covariances of these noises are known. The proposed combined estimator is based on Kalman filter optimized by GA in which the motor encoder is used in a dynamic stiffness model and the motor current sensor is used to give measurement updates in a torque balance model. A real-coded GA is used to optimize the noise matrices and improve the performance of the Kalman filter. Experimental results show that, by using the proposed estimator, the virtual clamping force sensor can handle highly dynamic situations, making it suitable for possible use in sensorless fault-tolerant control. It is shown that the proposed combined estimator improves the root mean square error (RMSE) performance. The developed estimator can be used in real vehicle environments because it can adapt to parameter variations.

Relativistic and noise effects on multiplayer Prisoners’ dilemma with entangling initial states

Three-players Prisoners’ dilemma (Alice, Bob and Colin) is studied in the presence of a single collective environment effect as a noise. The environmental effect is coupled with final states by a particular form of Kraus operators $$K_0$$ and $$K_1$$ through amplitude damping channel. We introduce the decoherence parameter $$0\le p\le 1$$ to the corresponding noise matrices, in order to controling the rate of environment influence on payoff of each players. Also, we consider the Unruh effect on the payoff of player, who is located at a noninertial frame. We suppose that two players (Bob and Colin) are in Rindler region I from Minkowski space-time, and move with same uniform acceleration ( $$r_b=r_c$$ ) and frequency mode. The game is begun with the classical strategies cooperation (C) and defection (D) accessible to each player. Furthermore, the players are allowed to access the quantum strategic space (Q and M). The quantum entanglement is coupled with initial classical states by the parameter $$\gamma \in [0,\pi /2]$$ . Using entangled initial states by exerting an unitary operator $$\hat{J}$$ as entangling gate, the quantum game (competition between Prisoners, as a three-qubit system) is started by choosing the strategies from classical or quantum strategic space. Arbitrarily chosen strategy by each player can lead to achieving profiles, which can be considered as Nash equilibrium or Pareto optimal. It is shown that in the presence of noise effect, choosing quantum strategy Q results in a winning payoff against the classical strategy D and, for example, the strategy profile (Q, D, C) is Pareto optimal. We find that the unfair miracle move of Eisert from quantum strategic space is an effective strategy for accelerated players in decoherence mode ( $$p=1$$ ) of the game.

Robust Kalman filtering for discrete‐time systems with stochastic uncertain time‐varying parameters

A robust Kalman filter is proposed for time-varying discrete-time linear systems with uncertainties in state, input noise, and measurement matrices. The filter is obtained by solving an optimisation problem such that the upper bound on the variance of estimation error to be minimised for all admissible uncertainties. A numerical example is presented to show the performance of the proposed robust filter.

Non-Stationary Rician Noise Estimation in Parallel MRI Using a Single Image: AVariance-Stabilizing Approach.

Parallel magnetic resonance imaging (pMRI) techniques have gained a great importance both in research and clinical communities recently since they considerably accelerate the image acquisition process. However, the image reconstruction algorithms needed to correct the subsampling artifacts affect the nature of noise, i.e., it becomes non-stationary. Some methods have been proposed in the literature dealing with the non-stationary noise in pMRI. However, their performance depends on information not usually available such as multiple acquisitions, receiver noise matrices, sensitivity coil profiles, reconstruction coefficients, or even biophysical models of the data. Besides, some methods show an undesirable granular pattern on the estimates as a side effect of local estimation. Finally, some methods make strong assumptions that just hold in the case of high signal-to-noise ratio (SNR), which limits their usability in real scenarios. We propose a new automatic noise estimation technique for non-stationary Rician noise that overcomes the aforementioned drawbacks. Its effectiveness is due to the derivation of a variance-stabilizing transformation designed to deal with any SNR. The method was compared to the main state-of-the-art methods in synthetic and real scenarios. Numerical results confirm the robustness of the method and its better performance for the whole range of SNRs.

GPU-Based Parallel Design of the Hyperspectral Signal Subspace Identification by Minimum Error (HySime)

Signal subspace identification provides a performance improvement in hyperspectral applications, such as target detection, spectral unmixing, and classification. The HySime method is a well-known unsupervised approach for hyperspectral signal subspace identification. It computes the estimated noise and signal correlation matrices from which a subset of eigenvectors is selected to best represent the signal subspace in the least square sense. Depending on the complexity and dimensionality of the hyperspectral scene, the HySime algorithm may be computationally expensive. In this paper, we propose a massively parallel design of the HySime method for acceleration on NVIDIA's graphics processing units (GPUs). Our pure GPU-based implementation includes the optimal use of the page-locked host memory, block size, and the number of registers per thread. The proposed implementation was validated in terms of accuracy and performance using the NASA AVIRIS hyperspectral data. The benchmark with the NVIDIA GeForce GTX 580 and Tesla K20 GPUs shows significant speedups with regards to the optimized CPU-based serial counterpart. This new fast implementation of the HySime method demonstrates good potential for real-time hyperspectral applications.

Real-Time Orbit Determination for Future Korean Regional Navigation Satellite System

This paper presents an algorithm for Real-Time Orbit Determination (RTOD) of navigation satellites for the Korean Regional Navigation Satellite System (KRNSS), when the navigation satellites generate ephemeris by themselves in abnormal situations. The KRNSS is an independent Regional Navigation Satellite System (RNSS) that is currently within the basic/ preliminary research phase, which is intended to provide a satellite navigation service for South Korea and neighboring countries. Its candidate constellation comprises three geostationary and four elliptical inclined geosynchronous orbit satellites. Relative distance ranging between the KRNSS satellites based on Inter-Satellite Ranging (ISR) is adopted as the observation model. The extended Kalman filter is used for real-time estimation, which includes fine-tuning the covariance, measurement noise, and process noise matrices. Simulation results show that ISR precision of 0.3–0.7 m, ranging capability of 65,000 km, and observation intervals of less than 20 min are required to accomplish RTOD accuracy to within 1 m. Furthermore, close correlation is confirmed between the dilution of precision and RTOD accuracy.

Adaptive detection method of infrared small target based on target-background separation via robust principal component analysis

Motivated by the robust principal component analysis, infrared small target image is regarded as low-rank background matrix corrupted by sparse target and noise matrices, thus a new target-background separation model is designed, subsequently, an adaptive detection method of infrared small target is presented. Firstly, multi-scale transform and patch transform are used to generate an image patch set for infrared small target detection; secondly, target-background separation of each patch is achieved by recovering the low-rank and sparse matrices using adaptive weighting parameter; thirdly, the image reconstruction and fusion are carried out to obtain the entire separated background and target images; finally, the infrared small target detection is realized by threshold segmentation of template matching similarity measurement. In order to validate the performance of the proposed method, three experiments: target-background separation, background clutter suppression and infrared small target detection, are performed over different clutter background with real infrared small targets in single-frame or sequence images. A series of experiment results demonstrate that the proposed method can not only suppress background clutter effectively even if with strong noise interference but also detect targets accurately with low false alarm rate.

Spectral noise correlations of an ultrafast frequency comb.

Cavity-based noise detection schemes are combined with ultrafast pulse shaping as a means to diagnose the spectral correlations of both the amplitude and phase noise of an ultrafast frequency comb. The comb is divided into ten spectral regions, and the distribution of noise as well as the correlations between all pairs of spectral regions are measured against the quantum limit. These correlations are then represented in the form of classical noise matrices, which furnish a complete description of the underlying comb dynamics. Their eigendecomposition reveals a set of theoretically predicted, decoupled noise modes that govern the dynamics of the comb. These matrices also contain the information necessary to deduce macroscopic noise properties of the comb.

Preserving Global Exponential Stability of Hybrid BAM Neural Networks with Reaction Diffusion Terms in the Presence of Stochastic Noise and Connection Weight Matrices Uncertainty

We study the impact of stochastic noise and connection weight matrices uncertainty on global exponential stability of hybrid BAM neural networks with reaction diffusion terms. Given globally exponentially stable hybrid BAM neural networks with reaction diffusion terms, the question to be addressed here is how much stochastic noise and connection weights matrices uncertainty the neural networks can tolerate while maintaining global exponential stability. The upper threshold of stochastic noise and connection weights matrices uncertainty is defined by using the transcendental equations. We find that the perturbed hybrid BAM neural networks with reaction diffusion terms preserve global exponential stability if the intensity of both stochastic noise and connection weights matrices uncertainty is smaller than the defined upper threshold. A numerical example is also provided to illustrate the theoretical conclusion.

Modified Bryson-Frazier Smoother Cross-Covariance

The Expectation Maximization algorithm can be used to estimate Kalman filter parameter matrices. This requires smoother results and typically the Rauch-Tung-Striebel smoother is used for this purpose. If either of the state transition or plant noise matrices require estimation, a sequence of single time-step smoother cross-covariance matrices, based on the Rauch-Tung-Striebel smoother formulation, are also required. The modified Bryson-Frazier smoother could be used as the smoother for the Expectation Maximization algorithm, but to estimate the state transition or plant noise matrix, this smoother would first need a method to generate the sequence of single time-step smoother cross-covariance matrices based on the modified Bryson-Frazier formulation. This paper develops an expression for these modified Bryson-Frazier cross-covariance matrices, thus allowing the modified Bryson-Frazier smoother to be substituted for the Rauch-Tung-Striebel smoother in the Expectation Maximization algorithm. The modified Bryson-Frazier smoother formulation requires inversion only of filter innovation matrices, which are generally much smaller than state error covariance matrices, which allows both greater computational speed and better numerical accuracy due to smaller matrix size. This formulation can be used even when covariance and transition matrices are singular.

Estimating the effect of temporally autocorrelated environments on the demography of density‐independent age‐structured populations

Summary In age‐structured populations, environmental autocorrelations influence the long‐run population growth rate as well as the variance in future population size. We used the concept of individual reproductive value to examine how autocorrelated environments affect the dynamics of age‐structured populations, leading to transparent interpretations and estimation of these effects. Environmental autocorrelation is expressed by the covariances between mean individual reproductive values for each age class and size of the same age class with stochastic components depending only on noise matrices from previous years. Thus, if an age class that is large in a given year also tends to perform better than the temporal average of that class in the contribution per individual to future population sizes, then the environmental autocorrelation will be positive. We use a simple model with temporal autocorrelation in recruitment rate to illustrate the theory through analytical results as well as stochastic simulations. We show how the effect of environmental autocorrelation, the term included in the long‐run growth rate, as well as influencing the variance of future population size, can be estimated using a combination of individual‐based demographic data and time series of fluctuations in age composition without estimating autocorrelations and cross‐correlations of large numbers of age‐specific vital rates. The method was applied to data from four mammal species. These analyses revealed that the influence of autocorrelations in the environmental noise on the dynamics of these species was small and in two populations almost negligible. The theoretical explorations as well as the empirical estimates indicate that the temporal scaling of the environmental autocorrelation must be long to substantially affect the long‐term population growth rate. The white noise approximation is therefore often very accurate.