Presence Of Additive Noise Research Articles

Asymptotic normality and finite-sample robustness of the Fourier spot volatility estimator in the presence of microstructure noise

We study the efficiency and robustness of the Fourier spot volatility estimator by Malliavin and Mancino [2002] when high-frequency prices are contaminated by microstructure noise. Firstly, we show that the estimator is consistent and asymptotically efficient in the presence of additive noise, establishing a Central Limit Theorem (CLT) with the optimal rate of convergence n 1 / 8 . Additionally, we complete the asymptotic theory proved by Mancino and Recchioni [2015] in the absence of noise, obtaining a CLT with the optimal rate of convergence n 1 / 4 . Feasible CLTs with the optimal convergence rate are also obtained, by proving the consistency of the Fourier estimators of the spot volatility of volatility and the quarticity in the presence of noise. Secondly, we introduce a feasible method for selecting the cutting frequencies of the estimator in the presence of noise, based on the optimization of the integrated asymptotic variance. Finally, we provide support to the accuracy and robustness of the method by means of a numerical study and an empirical exercise, which is conducted using tick-by-tick prices of three US stocks with different liquidity.

Fokker-Planck modeling of the stochastic dynamics of a Rijke tube.

We derive and numerically validate a low-order oscillator model to capture the stochastic dynamics of a prototypical thermoacoustic system (a Rijke tube) undergoing a subcritical Hopf bifurcation in the presence of additive noise. We find that on the fixed-point branch before the bifurcation, the system is dominated by the first duct mode, and the Fokker-Planck solution for the first Galerkin mode can adequately predict the stochastic dynamics of the overall system. We also find that this analytical framework predicts well the dominant mode on the limit-cycle branch, but underperforms in the hysteretic bistable zone where the role of nonlinearities is more pronounced. Besides offering new insights into stochastic thermoacoustic behavior, this study shows that an analytical framework based on the Fokker-Planck equation can facilitate the early detection of thermoacoustic instabilities in a Rijke-tube model subjected to noise.

Quantum advantage of time-reversed ancilla-based metrology of absorption parameters

Quantum estimation of parameters defining open-system dynamics may be enhanced by using ancillas that are entangled with the probe but are not submitted to the dynamics. Here we consider the important problem of estimation of transmission of light by a sample, with losses due to absorption and scattering. We show, through the determination of the quantum Fisher information, that the ancilla strategy leads to the best possible precision in single-mode estimation—the one obtained for a Fock-state input—through joint photon counting of probe and ancilla, which are modes of a bimodal squeezed state produced by an optical parametric amplifier. This proposal overcomes the challenge of producing and detecting high-photon-number Fock states, and it is quite robust in the presence of additional noise: We show that it is immune to phase noise and the precision does not change if the incoming state gets disentangled. Furthermore, the quantum gain is still present under moderate photon losses of the input beams. We also discuss an alternative to joint photon counting, which is readily implementable with present technology and approaches the quantum Fisher information result for weak absorption, even with moderate photon losses of the input beams before the sample is probed: a time-reversal procedure, placing the sample between two optical parametric amplifiers, with the second undoing the squeezing produced by the first one. The precision of estimation of the loss parameter is obtained from the average outgoing total photon number and its variance. In both procedures, the state of the probe and the detection procedure are independent of the value of the parameter. Published by the American Physical Society 2024

Phase estimation using sine fitting with low number of samples is biased in the presence of additive noise

It is demonstrated here that the initial phase estimation of a sine wave corrupted by additive noise using the least squares sine fitting algorithm is not biased, even for low number of samples, contrary to what happens in the case of the amplitude estimation. Monte Carlo simulations are presented which corroborate the conclusion reached. This result is of particular importance when studying the uncertainty of measurement methods based on phase estimation like ultrasonic non‑destructive testing.

Estimation of parameters of autoregressive models with fractional differences in the presence of additive noise

Estimation of parameters of autoregressive models with fractional differences in the presence of additive noise

Precision of sinewave amplitude estimation in the presence of additive noise and quantization error

Abstract This research paper delves into a comprehensive investigation concerning the impact of additive noise and quantization error on the precision of amplitude, offset, and phase estimates of a sine wave fitted to a set of data points acquired by a waveform digitizer. Simulation results are used to validate the expressions presented.

Distributed and Localized Model Predictive Control—Part II: Theoretical Guarantees

Engineered cyberphysical systems are growing increasingly large and complex. These systems require scalable controllers that robustly satisfy state and input constraints in the presence of additive noise – such controllers should also be accompanied by theoretical guarantees on feasibility and stability. In our companion paper, we introduced Distributed and Localized Model Predictive Control (DLMPC) for large-scale linear systems; DLMPC is a scalable <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">closed-loop</i> MPC scheme in which subsystems need only exchange local information in order to synthesize and implement local controllers. In this paper, we provide recursive feasibility and asymptotic stability guarantees for DLMPC. We leverage the System Level Synthesis framework to express the maximal positive robust invariant set for the closed-loop system and its corresponding Lyapunov function in terms of the closed-loop system responses. We use the invariant set as the terminal set for DLMPC, and show that this guarantees feasibility with minimal conservatism. We use the Lyapunov function as the terminal cost, and show that this guarantees stability. We provide fully distributed and localized algorithms to compute the terminal set offline, and also provide necessary additions to the online DLMPC algorithm to accommodate coupled terminal constraint and cost. In all algorithms, only local information exchange is necessary, and computational complexity is independent of the global system size – we demonstrate this analytically and experimentally. This is the first distributed MPC approach that provides minimally conservative yet fully distributed guarantees for recursive feasibility and asymptotic stability in the nominal and robust settings.

Robust estimators of two dimensional sinusoidal model parameters

In this paper we consider the two dimensional (2-D) sinusoidal model. This particular model has several applications in the statistical signal processing and in texture analysis. Extensive work has been done in developing several efficient procedures and establishing their properties. The least squares estimators (LSEs) are known to be the most efficient estimators in presence of additive noise. But it is observed that the LSEs are quite sensitive in presence of outliers. In this paper we propose to use the weighted least squares estimators (WLSEs) of the unknown parameters in presence of additive white noise. It is observed that in presence of outliers, the WLSEs are more robust than the least squares estimators (LSEs) and they behave very similarly to some of the other well known robust estimators, for example the least absolute deviation estimators (LADEs). It is observed that developing the properties of the LADEs is not immediate. We derive the consistency and asymptotic normality properties of the WLSEs. Extensive simulations have been performed to show the effectiveness of the proposed method. One synthetic data set has been analyzed to illustrate how the proposed method can be used in practice.

A novel adaptive time delay identification technique

In this work, a novel online adaptive time delay identification method is proposed for a class of signal processing and communication applications, where the received signal is a combination of the transmitted signal and its delayed forms with the delay values being uncertain and required to be estimated. The design relies on a filtered form of a prediction error-like term which is then used in the design of the novel nonlinear adaptive update law. The stability of the identification algorithm is then investigated via novel Lyapunov based tools and the time delay identification is proven to be globally uniformly ultimately bounded. Several numerical simulations are conducted to evaluate the performance of the proposed identifier where constant, slowly varying and suddenly changing delays are successfully identified even in the presence of additive noise.

Overview of Identification Methods of Autoregressive Model in Presence of Additive Noise

This paper presents an overview of the main methods used to identify autoregressive models with additive noises. The classification of identification methods is given. For each group of methods, advantages and disadvantages are indicated. The article presents the simulation results of a large number of the described methods and gives recommendations on choosing the best methods.

Estimation of delay times from time series of ring self-oscillatory time-delay systems

Introduction: The problem of delay time estimation in ring self-oscillatory time-delay systems arises in various fields of science and is of great importance in the study of real systems generating chaotic time series. Purpose: To conduct a comparative analysis of the operation of methods for the reconstruction of time-delay systems from chaotic time series in the absence and presence of additive noise. Methods: Methods for estimating the delay time according to the statistics of extrema, using the autocorrelation function and the method of order time asymmetry are used. Based on the latter method, a method is proposed that is focused on estimating the delay times in systems with two delays. Results: We carry out a comparative analysis of the operation of four methods for reconstructing the delay times in self-oscillating time-delay systems from chaotic time series using the example of Ikeda systems with one and two delay times. We demonstrate that in the absence of additive noise, the delay time estimation method based on statistics of extrema is the most accurate one for the case of time series analysis of systems with both one and two delays. In the presence of additive noise, the modified method of order time asymmetry proposed in the work in the case of the analysis of systems with one delay time works no worse than the method of the autocorrelation function and order time asymmetry. In the case of two delay times, the modified order time asymmetry method works better than others. Practical relevance: The described methods can have a practical application in estimating the delay time of self-oscillating systems, yet the level of additive noise can affect the accuracy of the estimate.

Controlling chimera and solitary states by additive noise in networks of chaotic maps

We study numerically the spatio-temporal dynamics of ring networks of coupled discrete-time systems in the presence of additive noise. The robustness of chimera states with respect to noise perturbations is explored for two ensembles in which the individual elements are described by either logistic maps or Henon maps in the chaotic regime. The influence of noise on the behavior of solitary states is investigated for a ring of nonlocally coupled Lozi maps. Numerical simulations are performed for a set of different noise realizations and random initial conditions to provide reliable statistical data. The type of dynamics of the considered networks is quantified by using a cross-correlation coefficient. We find that there is a finite and sufficiently wide region with respect to the coupling strength and the noise intensity where the probability of observing the chimeras and solitary states is high.

A Model-Agnostic Method for PMU Data Recovery Using Optimal Singular Value Thresholding

This paper presents a fast model-agnosticmethod for recovering noisy Phasor Measurement Unit (PMU) data streams with missing entries. The measurements are first transformed into a Page matrix, and the original signals are reconstructed using low-rank matrix estimation based on optimal singular value thresholding. Two variations of the recovery algorithm are shown- a) an offline block-processing method for imputing past measurements, and b) an online method for predicting future measurements. Information within a PMU channel (temporal correlation) as well as from different PMU channels in a network (spatial correlation) are utilized to recover degraded data. The proposed method is fast and needs no explicit knowledge of the underlying system model or measurement noise distribution. The performance of the recovery algorithms is illustrated using simulated measurements from the IEEE 39-bus test system as well as real measurements from an anonymized U.S. electric utility. Extensive numeric tests show that the original signals can be accurately recovered in the presence of additive noise, consecutive data drop, as well as simultaneous data erasures across multiple PMU channels.

Corrupted bifractal features in finite uncorrelated power-law distributed data

Multifractal Detrended Fluctuation Analysis stands out as one of the most reliable methods for unveiling multifractal properties, specially when real-world time series are under analysis. However, little is known about how several aspects, like artefacts during the data acquisition process, affect its results. In this work we have numerically investigated the performance of Multifractal Detrended Fluctuation Analysis applied to synthetic finite uncorrelated data following a power-law distribution in the presence of additive noise, and periodic and randomly-placed outliers. We have found that, on one hand, spurious multifractality is observed as a result of data finiteness, while additive noise leads to an underestimation of the exponents hq for q<0 even for low noise levels. On the other hand, additive periodic and randomly-located outliers result in a corrupted inverse multifractality around q=0. Moreover, the presence of randomly-placed outliers corrupts the entire multifractal spectrum, in a way proportional to their density. As an application, the multifractal properties of the time intervals between successive aircraft landings at three major European airports are investigated.

A gradient-type noise-tolerant finite-time neural network for convex optimization

As one of powerful methods for solving optimization problems, the gradient-type neural network has attracted the attention of many scholars. Up to now, there are few studies on finite-time convergence and the ability of noise tolerance of gradient-type networks. Motivated by the superior performance of various activation functions and advantages of gradient-type networks for solving constrained optimization, this paper aims to introduce a suitable activation function in a gradient-type neural network to solve convex optimization. It is shown that the state solution of the network converges to an optimal solution of the original convex optimization and the convergence time is finite under mild conditions. The capability of the network to suppress bounded noises is also analyzed theoretically. Superior to existing models for constrained optimization, the resulting network model not only has fast convergence but also can tolerate additive noises. Some numerical results are reported, including the results for smooth and nonsmooth problems, to show that the presented network is effective for convex constrained problems in the absence and presence of additive noises.

RFDOA-Net: An Efficient ConvNet for RF-Based DOA Estimation in UAV Surveillance Systems

This paper presents a convolution neural network (CNN)-based direction of arrival (DOA) estimation method for radio frequency (RF) signals acquired by a nonuniform linear antenna array (NULA) in unmanned aerial vehicle (UAV) localization systems. The proposed deep CNN, namely RFDOA-Net, is designed with three primary processing modules, such as collective feature extraction, multi-scaling feature processing, and complexity-accuracy trade-off, to learn the multi-scale intrinsic characteristics for multi-class angle classification. In several specific modules, the regular convolutional and grouped convolutional layers are leveraged with different filter sizes to enrich diversified features and reduce network complexity besides adopting residual connection to prevent vanishing gradient. For performance evaluation, we generate a synthetic signal dataset for DOA estimation under the multipath propagation channel with the presence of additive noise, propagation attenuation and delay. In simulations, the effectiveness of RFDOA-Net is investigated comprehensively with various processing modules and antenna configurations. Compared with several state-of-the-art deep learning-based models, RFDOA-Net shows the superiority in terms of accuracy with over 94% accuracy at 5 dB signal-to-noise ratio (SNR) with cost-efficiency.

Early Detection of Defects through the Identification of Distortion Characteristics in Ultrasonic Responses

Ultrasonic techniques are widely used for the detection of defects in solid structures. They are mainly based on estimating the impulse response of the system and most often refer to linear models. High-stress conditions of the structures may reveal non-linear aspects of their behavior caused by even small defects due to ageing or previous severe loading: consequently, models suitable to identify the existence of a non-linear input-output characteristic of the system allow to improve the sensitivity of the detection procedure, making it possible to observe the onset of fatigue-induced cracks and/or defects by highlighting the early stages of their formation. This paper starts from an analysis of the characteristics of a damage index that has proved effective for the early detection of defects based on their non-linear behavior: it is based on the Hammerstein model of the non-linear physical system. The availability of this mathematical model makes it possible to derive from it a number of different global parameters, all of which are suitable for highlighting the onset of defects in the structure under examination, but whose characteristics can be very different from each other. In this work, an original damage index based on the same Hammerstein model is proposed. We report the results of several experiments showing that our proposed damage index has a much higher sensitivity even for small defects. Moreover, extensive tests conducted in the presence of different levels of additive noise show that the new proposed estimator adds to this sensitivity feature a better estimation stability in the presence of additive noise.

Wireless Chaos-Based Communication System: Literature Review

Since the early 1990s, a slew of chaotic-based communication systems have been proposed, all of which take advantage of chaotic waveform properties. The inspiration stems from the substantial benefits that this form of nonlinear signal offers. Many communication schemes and applications have been specifically designed for chaos-based communication systems to achieve this goal, with energy, data rate, and synchronization awareness being taken into account in most designs. However, non-coherent chaos-based systems have recently received a lot of attention in order to take advantage of the benefits of chaotic signals and non-coherent detection while avoiding the use of chaotic synchronization, which has poor performance in the presence of additive noise. This paper provides a thorough examination of all wireless radio frequency chaos-based communication systems. It begins by describing the difficulties of chaos implementations and synchronization processes, then moves on to a thorough literature review and study of chaos-based coherent techniques and their applications.

Stochastic sensitivity of bull and bear states

We study the price dynamics generated by a stochastic version of a Day–Huang type asset market model with heterogenous, interacting market participants. To facilitate the analysis, we introduce a methodology that allows us to assess the consequences of changes in uncertainty on the dynamics of an asset price process close to stable equilibria. In particular, we focus on noise-induced transitions between bull and bear states of the market under additive as well as parametric noise. Our results are obtained by combining the stochastic sensitivity function (SSF) approach, a mixture of analytical and numerical techniques, due to Mil’shtein and Ryashko (1995) with concepts and techniques from the study of non-smooth 1D maps. We find that the stochastic sensitivity of the respective bull and bear equilibria in the presence of additive noise is higher than under parametric noise. Thus, recurrent transitions are likely to be observed already for relatively low intensities of additive noise.

Hadamard-transform spectral acquisition with an acousto-optic tunable filter in a broadband stimulated Raman scattering microscope.

We present a novel configuration for high spectral resolution multiplexing acquisition based on the Hadamard transform in stimulated Raman scattering (SRS) microscopy. The broadband tunable output of a dual-beam femtosecond laser is filtered by a fast, narrowband, and multi-channel acousto-optic tunable filter (AOTF). By turning on and off different subsets of its 8 independent channels, the AOTF generates the spectral masks given by the Hadamard matrix. We demonstrate a seamless and automated operation in the Raman fingerprint and CH-stretch regions. In the presence of additive noise, the spectral measurements using the multiplexed method show the same signal-to-noise ratio of conventional single-wavenumber acquisitions performed with 4 times longer integration time.