Statistical Signal Research Articles

Stability of Compressed Recursive Least Squares with Forgetting Factor Algorithm

To identify the unknown sparse time-varying parameters of the stochastic dynamic system, we integrate compressive sensing theory with the traditional recursive least squares with forgetting factor (FFLS) algorithm, and propose a compressed adaptive filtering algorithm. Our algorithm is designed to first compress the original high-dimensional sparse regression vector by using the sensing matrix, and then apply the FFLS algorithm to estimate the compressed parameters. Subsequently, the original high-dimensional sparse parameters can be well recovered by a reconstruction technique. We introduce an excitation condition on the compressed stochastic regressors, under which the stability of the proposed algorithm (i.e., the upper bound of the estimation error) is established without assuming independence, stationarity or ergodicity of the system signals. The effectiveness of our theoretical results is demonstrated by a numerical example, which also shows that our proposed algorithm has better performance than both the compressed least mean squares algorithm and the uncompressed FFLS algorithm for tracking high-dimensional sparse parameters.

Quaternion Extreme Learning Machine Based on Real Augmented Representation

Widely linear modeling is an important quaternion signal processing technique for capturing the complete secondorder statistics of quaternion signals. However, the algorithms based on widely linear modeling are computationally expensive due to the augmented variables and statistics. In this letter, a fast estimation technique based on a real augmented representation of widely linear modeling is proposed in the context of quaternion extreme learning machine with augmented hidden layer (QELMAH), resulting in a reduction of almost 93% of multiplications and 75% of additions. An equivalence between the proposed algorithm and the original QELMAH is theoretically established by proving that the trained networks with the proposed algorithm and the original one mathematically implement identical mapping. Such a technique is also applicable to the widely linear quaternion recursive least squares algorithm. The theoretical analysis and the effectiveness of the proposed algorithms are validated by simulations on two benchmark problems.

ANALYSIS OF ACCURACY OF NONLINEAR CONTROL SYSTEMS OF MULTI-ROTOR UAVS UNDER STATIONARY RANDOM SIGNALS

A large number of articles and monographs are devoted to the development of line-ar control systems for multi-rotor UAVs, in which, based on the methods of the modern theory of automatic regulation and control, the problems of choosing the regulators that provide the required performance indices and stability margins of UAVs’ control systems are considered, taking into account structural and parametric uncertainties , nonlinearities of separate channels, various external control and disturbing signals, including determinis-tic and random signals, etc. At the same time, there are practically no works that study the issues of analyzing the dynamic accuracy of nonlinear control systems for multi-rotor UAVs under random external signals, for example, wind gusts, etc. In the article, based on the approximate method of statistic linearization, an engi-neering technique for analyzing the accuracy of nonlinear UAVs’ control systems with PID controllers in separate channels under stationary random signals with a Gaussian probabil-ity distribution and non-zero mathematical expectations are considered. It is shown that the use of the statistic linearization method allows reducing the accuracy analysis of the of independent nonlinear control channels of UAVs to a joint analysis of the accuracy of two different linear systems with respect to the mathematical expectation and the centered random component of the input signal. Analysis of the accuracy of each of these linear systems is carried out by known methods of classical control theory. A numerical example of the analysis of statistical accuracy of the control system of a quadcopter with satura-tion-type nonlinearities in the measuring devices of the system is given.

Learning Product Graphs From Spectral Templates

Graph Learning (GL) is at the core of leveraging connections in machine learning (ML). By observing a dataset of graph signals and considering specific assumptions, Graph Signal Processing (GSP) provides practical constraints in GL. Inferring a graph with desired frequency signatures, i.e., spectral templates, from stationary graph signals has gained great attention. However, a severe computational burden is a challenging barrier, especially for inference from high-dimensional product graph signals, i.e., graph signals live on the product of smaller factor graphs. Few product GL methods have been proposed for mostly inference with smoothness assumption, while they are limited to learning only two factor graphs, handle only the Cartesian products, and have not addressed GL with desired spectral templates. To bridge the mentioned gaps, we propose a method for learning product graphs from product graph signals in which the product GL problem can be broken into separated optimizations associated with each (significantly smaller) factor graph. Besides, unlike the current approaches, our method can learn from any type of product graph (possibly with more than two factor graphs) without needing to know the type of graph products beforehand, and with significantly reduced complexity than learning directly from product graph signals. In addition to devising theoretical sufficient recovery conditions and validating them numerically, experimental results on synthetic and real-world data, i.e., multi-view image and brain signal analysis, illustrate meaningful factor graphs supported by expert-related research and also superiority over the current methods for learning from spectral templates. The implementation codes are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/ArefEinizade2/ProdSpecTemp</uri> .

A Rapid Learning Model based on Selected Frequency Range Spectral Subtraction for the Data-Driven Fault Diagnosis of Manufacturing Systems

Limited amount of training dataset is often a critical problem in developing a diagnosis model or computational intelligence of mechanical failures. In this paper, we propose a Selected Frequency Range Critical Information Map (SFCIM)-based data-driven diagnosis method for detecting mechanical system failure with a relatively small amount of available dataset. The algorithm determines whether there is a failure with reference to normal condition signals using the spectral subtraction method. In this process, time-domain synchronization and time-frequency representation are applied. In addition, the dominant frequency range is selected based on Fisher’s scores for the more efficient calculation. We designed this algorithm to provide users with time-frequency domain information about system failure through SFCIM instead of the only simple decision of diagnosis. The usefulness of our method has been checked with the following problems of the small amount of available dataset: diagnoses of (1) the IMS bearing faults, (2) input gear faults of a manipulator driving system, and (3) a driving system of an industrial robot by load current signals. From these case studies, we also confirmed that the proposed method was practical and useful for fault diagnosis regardless of signal types, such as stationary, non-stationary, accelerometer-based vibration, or current signal.

Nonstationary feature extraction based on stochastic resonance and its application in rolling bearing fault diagnosis under strong noise background.

When the load and speed of rotating machinery change, the vibration signal of rolling bearing presents an obvious nonstationary characteristic. Stochastic resonance (SR) mainly is convenient to analyze the stationary feature of vibration signals with high signal-to-noise ratio. However, it is difficult for SR to extract the nonstationary feature of rolling bearings under strong noise background. For one thing, the frequency change of nonstationary signals makes the occurrence of SR very difficult. For another, the features of rolling bearings are large parameters and further prevent the SR method from performing well. Therefore, combined with order analysis (OA), adaptive frequency-shift SR is presented in this paper. To solve the problem of frequency change, OA is used to convert the nonstationary feature into stationary feature, which resamples the nonstationary signal in the time domain to stationary signal in the angular domain. To solve the other problem, the frequency-shift method based on Fourier transform is adopted to move the fault feature frequency to low frequency, and thus SR is more likely to occur under small parameter conditions. The simulated and experimental results indicate that not only the amplitude of fault feature but also the signal-to-noise ratio is significantly improved. These demonstrate that the fault features of rolling bearing in variable speed conditions are extracted successfully.

Asynchronous x-ray multiprobe data acquisition for x-ray transient absorption spectroscopy.

Laser pump X-ray Transient Absorption (XTA) spectroscopy offers unique insights into photochemical and photophysical phenomena. X-ray Multiprobe data acquisition (XMP DAQ) is a technique that acquires XTA spectra at thousands of pump-probe time delays in a single measurement, producing highly self-consistent XTA spectral dynamics. In this work, we report two new XTA data acquisition techniques that leverage the high performance of XMP DAQ in combination with High Repetition Rate (HRR) laser excitation: HRR-XMP and Asynchronous X-ray Multiprobe (AXMP). HRR-XMP uses a laser repetition rate up to 200 times higher than previous implementations of XMP DAQ and proportionally increases the data collection efficiency at each time delay. This allows HRR-XMP to acquire more high-quality XTA data in less time. AXMP uses a frequency mismatch between the laser and x-ray pulses to acquire XTA data at a flexibly defined set of pump-probe time delays with a spacing down to a few picoseconds. AXMP introduces a novel pump-probe synchronization concept that acquires data in clusters of time delays. The temporally inhomogeneous distribution of acquired data improves the attainable signal statistics at early times, making the AXMP synchronization concept useful for measuring sub-nanosecond dynamics with photon-starved techniques like XTA. In this paper, we demonstrate HRR-XMP and AXMP by measuring the laser-induced spectral dynamics of dilute aqueous solutions of Fe(CN)6 4- and [FeII(bpy)3]2+ (bpy: 2,2'-bipyridine), respectively.

Global convergence towards statistical independence for noisy mixtures of stationary and non-stationary signals

Global convergence towards statistical independence for noisy mixtures of stationary and non-stationary signals

A Carrier Synchronization Lock Detector Based on Weighted Detection Statistics for APSK Signals

To solve the application limitations of conventional detectors caused by discrete phase distribution of high-order APSK signals, and the problem that the detection performance will degrade when the automatic control gain is unideal, a carrier synchronization lock detector based on weighted detection statistics is proposed for APSK signals. Based on the detection statistics of the Linn detector, the proposed detector calculates a weighted factor according to the amplitude difference of the signal on the APSK constellation to adjust the weight of detection statistics for different rings. The proposed detector solves the detection performance degradation problem of the Linn detector caused by uneven phase distribution. In order to further improve detection performance, the detection threshold and statistical signal length are reasonably designed. The expectation and variance properties are derived, and the lock detection probability is analyzed. The performance of the proposed detector is verified through simulations. Simulation results show that the proposed carrier synchronization lock detector has better performance than the Linn detector.

Covariance recovery for one-bit sampled stationary signals with time-varying sampling thresholds

One-bit quantization, which relies on comparing the signals of interest with given threshold levels, has attracted considerable attention in signal processing for communications and sensing. A useful tool for covariance recovery in such settings is the arcsine law, that estimates the normalized covariance matrix of zero-mean stationary input signals. This relation, however, only considers a zero sampling threshold, which can cause a remarkable information loss. In this paper, the idea of the arcsine law is extended to the case where one-bit analog-to-digital converters (ADCs) apply time-varying thresholds. Specifically, three distinct approaches are proposed, investigated, and compared, to recover the autocorrelation sequence of the stationary signals of interest. Additionally, we will study a modification of the Bussgang law, a famous relation facilitating the recovery of the cross-correlation between the one-bit sampled data and the zero-mean stationary input signal. Similar to the case of the arcsine law, the Bussgang law only considers a zero sampling threshold. This relation is also extended to accommodate the more general case of time-varying thresholds for the stationary input signals.

PHY-layer authentication exploiting CFO for smart healthcare systems with mmWave communication technology

In this paper we study the problem of validating the legitimacy of devices collecting health data from patients for a smart healthcare system with millimeter wave (mmWave) communication technique, and propose a cost-effective physical layer (PHY-layer) scheme, which utilizes the intrinsic hardware fingerprinting features in terms of carrier frequency offset (CFO). In particular, we first extract the CFO feature caused by the oscillator mismatch in mmWave hardware architecture supporting ultra-high data rates by using the maximum likelihood estimation and parabolic interpolation method, and then formulate the problem of authenticating devices as a binary hypothesis test based on the resulting feature. With the help of statistical signal processing, the analytical expressions for false alarm and detection probabilities are further derived statistically. Finally, extensive simulations are conducted to verify the theoretical results for modeling of the two probabilities. In addition, we also examine the impact of various system parameters on the efficiency of the proposed authentication scheme.

Predictive Quantization and Symbolic Dynamics

Capturing long-term statistics of signals and time series is important for modeling recurrent phenomena, especially when such recurrences are a-periodic and can be characterized by the approximate repetition of variable length motifs, such as patterns in human gestures and trends in financial time series or musical melodies. Regressive and auto-regressive models that are common in such problems, both analytically derived and neural network-based, often suffer from limited memory or tend to accumulate errors, making them sensitive during training. Moreover, such models often assume stationary signal statistics, which makes it difficult to deal with switching regimes or conditional signal dynamics. In this paper, we describe a method for time series modeling that is based on adaptive symbolization that maximizes the predictive information of the resulting sequence. Using approximate string-matching methods, the initial vectorized sequence is quantized into a discrete representation with a variable quantization threshold. Finding an optimal signal embedding is formulated in terms of a predictive bottleneck problem that takes into account the trade-off between representation and prediction accuracy. Several downstream applications based on discrete representation are described in this paper, which includes an analysis of the symbolic dynamics of recurrence statistics, motif extraction, segmentation, query matching, and the estimation of transfer entropy between parallel signals.

A new class of composite objective multistep estimating sequence techniques

A plethora of problems arising in signal processing, machine learning and statistics can be cast as large-scale optimization problems with a composite objective structure. Such problems are typically solved by utilizing iterative first-order algorithms. In this work, we devise a new accelerated gradient-based estimating sequence technique for solving large-scale optimization problems with composite objective structure. Specifically, we introduce a new class of estimating functions, which are obtained by utilizing both a tight lower bound on the objective function, as well as the gradient mapping technique. Then, using the proposed estimating functions, we construct a class of Composite Objective Multi-step Estimating-sequence Techniques (COMET), which are endowed with an efficient line-search procedure. We prove that our proposed COMET enjoys the accelerated convergence rate, and our newly established convergence results allow for step-size adaptation. Our theoretical findings are supported by extensive computational experiments on various problem types and real-world datasets. Moreover, our numerical results show evidence of the robustness of the proposed method to the imperfect knowledge of the smoothness and strong convexity parameters.

Algorithms for Weld Depth Measurement in Laser Welding of Copper with Scanning Optical Coherence Tomography.

In-process monitoring of weld penetration depth is possible with optical coherence tomography (OCT). The weld depth can be identified with OCT by statistical signal processing of the raw OCT signal and keyhole mapping. This approach is only applicable to stable welding processes and requires a time-consuming keyhole mapping to identify the optimal placement of a singular OCT measuring beam. In this work, we use an OCT measurement line for the identification of the weld depth. This approach shows the advantage that the calibration effort can be reduced as the measurement line requires only calibration in one dimension. As current literature focuses on weld depth measurement with a singular measurement point in the keyhole, no optimal algorithm exists for weld depth measurement with an OCT measurement line. We developed seven different weld depth processing pipelines and tested these algorithms under different weld conditions, such as stable deep penetration welding, unstable deep penetration welding, and heat conduction welding. We analyzed the accuracy of the weld depth processing algorithms by comparing the measured weld depth with metallographic weld depths. The intensity accumulation approach is identified as the most accurate algorithm for successful weld depth measurement with a scanning OCT measurement line.

Investigation of Vibration Signal Processing using Short Time Fourier Transform for Internal Combustion Engine

The methods of short-time Fourier transform (STFT) signal processing have been used to enhance the condition monitoring of machines. It can be better to use in reciprocating machines such as internal combustion engines, as the signal is non-stationary. The FFT usage wouldn’t be beneficial in this case as it treats stationary signals such as those captured from rotating machines. The vibration of machines became challenging, as for the engine, pack up, faults in such complex systems can lead to frequency alternation and amplitude. In the present study, the vibration signal was acquired from the engine at the vicinity of the piston 2 and 3 to get acceptable signal intensity. The normal state is measured at idle speed condition and two other speeds 2000 and 3000 rpm. Three faults are investigated namely; misfire of one cylinder, two cylinder misfire and ignition timing. Then, the signal processed using STFT was used to distinguish and detect fault using vibration signal. The output signals were exported to MATLAB for further analysis. The experimental results revealed that the normal condition had more vibration than one cylinder misfire than two cylinder misfire due to the damping effect. In addition, the vibration levels at ignition timing (3 BTDC), (3 ATDC), (6 BTDC) and (6 ATDC) were recorded as maximum when compared to normal condition at 5 BTDC.

Orthogonality constrained analytic CMA for blind signal extraction improvement

The well-known Analytic Constant Modulus Algorithm (ACMA) is a classic algebraic method for signal separation and equalization, which can achieve blind signal recovery and fast convergence. In this paper, we explore new means for incorporating the inherent statistical signal orthogonality in ACMA for improved signal separation and recovery. This statistical orthogonality constraint adds new restrictions to ACMA, leading to a novel approach we denote as Orthogonality Constrained Analytic Constant Modulus Algorithm (OC-ACMA). We further generalize OC-ACMA for applications in blind equalization. Results show that OC-ACMA can successfully separate and recover constant modulus signals at higher accuracy.

A Novel Blind Image Source Separation Using Hybrid Firefly Particle Swarm Optimization Algorithm

Signal and image separation are extensively used in numerous imaging applications and communication systems. In this paper, a novel Blind Source Separation (BSS) approach, based on the Hybrid Firefly Particle Swarm Optimization (HFPSO), is proposed for separating mixed images. This approach processes the observed source without any prior knowledge about the model and the statistics of the source signal. The proposed method presents high robustness against local minima and converges quickly to the global minimum. Via numerical simulations, the proposed approach is tested and validated in comparison with standard Particle Swarm Optimization (PSO), Robust Independent Component Analysis (RobustICA), and Artificial Bee Colony (ABC) algorithms. The obtained results show that the presented technique outperforms the existing ones in terms of quality of image separation, the Signal-to-Noise Ratio (PSNR), and Structural Similarity Index Measure (SSIM). Moreover, the obtained results demonstrate that our approach provides also promising results in image separation from noisy mixtures.

Permutation Lempel-Ziv 복잡성 척도를 적용한 근 피로도 추정

A new approach for quantifying muscle fatigue is presented by analyzing the deterministic complexity in the surface electromyogram(SEMG) using Permutation Lempel-Ziv(PLZ) complexity measure. The PLZ complexity measure provide a metric for the number of distinct deterministic patterns in signals by combining permutation patterns and Lempel-Ziv complexity analysis. For muscle fatigue experiment by using PLZ complexity measure, surface EMG signals from eleven subjects were recorded in biceps brachii muscle with constant isometric 20, 50, and 80%MVC contractions. The PLZ complexity measure is evaluated with the performance of muscle fatigue estimation for the SEMG signals compared to the performance of previous reported LZ complexity measure. This PLZ complexity measure has advantages that is computationally easy to compute and does not require any assumptions about the stationarity of the SEMG signal.

Estimation of Harvested RF Energy Based on Survey of Ambient RF Power for Optimized Rectifier Design

This paper presents estimation of harvested RF energy by means of measurement survey and rectifier circuit simulation. The survey was done in an indoor environment in Bangkok, Thailand using a low-cost in-house developed measurement system. From the survey, channel power distribution of a signal with 950 MHz center frequency and 20 MHz bandwidth was created. The maximum time averaged channel power is -7.6 dBm whereas the mean value with maximum signal statistic is -11.1 dBm. A single stage rectifier is simulated with 5 different nominal values of RF input power which is used to optimize the rectifier for maximum RF-to-DC power conversion efficiency. The rectifier composes a Schottky diode, a matching network and a simple load consisting of a resistor and a storage capacitor. Parameters of the simplified LC matching network have been varied to match the rectifier’s input impedance to 50 Ω for various nominal values of the RF input power. In addition, the load resistance was varied according to the nominal RF input power for an optimal power conversion efficiency of the rectifier. The rectifier delivers the highest harvested RF energy with a nominal RF input power of -9 dBm which is a value between the maximum and the mean values from the survey. The DC energy converted from ambient RF energy by the rectifier can be estimated. With this information, it can be assessed what type of applications based on available RF energy can be applied for the test area. This rectifier optimization strategy can be applied to any kind of RF signal since it is based on actual measurement results. Moreover, the proposed rectifier can be designed for reconfigurability regarding nominal RF input power at the location of interest by varying the matching network parameters and the load resistance. In practical applications, the reconfigurable rectifier can maintain a high level of power conversion efficiency over a wide range of RF input power. This can be done by optimizing the rectifier’s input matching network and the load resistance for the highest possible power harvested from the environment where the rectifier is located.

Synthesis of the loading system for the conduct of in-kind transmission tests of vehicles and special equipment

Abstract. Problem. The paper solves an important scientific and practical problem, which allows to improve the quality of testing units and aggregates of the transmission of vehicles and special equipment on test stands with a balancing load. Conducting experimental tests on specialized stands allows you to maintain high stability of the factors that are set and maintained, the accuracy of their regulation, and the possibility of in-depth observations of executive devices. The accuracy of measurement and registration of parameters of automated measurements is increased due to the use of microprocessor systems with a digital network structure of data transmission between the control module and peripheral units and measurement modules. The application of the proposed laboratory experimental equipment to the balancing load allows to determine and improve the competitive advantages of energy-efficient tractors with electric transmission. Methodology. The methods of theoretical basic electrical engineering have been developed in the production and calculation of circuits using circuits. Also classical methods of statistics of signals from ADC were used. Results. The technique of processing information from the current, voltage and temperature sensors using a mathematical apparatus without using harmonic analysis is presented. The hardware implementation of the proposed method allows the use of simplified computing tools. Originality. Complex analysis of the data obtained from the current, voltage and temperature sensors is carried out. During the analysis, the range of velocities with stable operation of the measurement system was determined. Practical value. As a result of the work, an important scientific and practical problem was solved, which allows to increase the energy efficiency of tractors. To maintain the maximum energy efficiency of the traction electric drive of the tractor in the modes of various loads, its control system must include means of displaying the current state of the energy parameters of the power plant. The electrical equipment must include an on-board computer, which helps the driver to make the optimal tasks of work, according to preliminary calculations, as well as display the information needed on the route, the state of the vehicle, means of communication. communication of the car with the external environment, with the navigation system, etc. The on-board computer provides information to the touch screen with programmable virtual controls, and communicates with the driver's mobile systems.