Time-correlated Noise Research Articles

Globally Optimal Distributed Fusion Filter for Descriptor Systems with Time-Correlated Measurement Noises.

This paper concerns the distributed fusion filtering problem for descriptor systems with time-correlated measurement noises. The original descriptor is transformed into two reduced-order subsystems (ROSs) based on singular value decomposition. For the first ROS, a new measurement is obtained using measurement difference technology. Each sensor produces a local filter based on the fusion predictor from the fusion center and its own new measurement and then sends it to the fusion center. In the fusion center, based on local filters, a distributed fusion filter with feedback (DFFWF) in the linear minimum variance (LMV) sense is proposed by applying an innovative approach. The DFFWF for the second ROS is also obtained based on the DFFWF for the first ROS. Then, the DFFWF for the original descriptor is obtained. The proposed DFFWF can achieve the same estimation accuracy as the centralized fusion filter (CFF) under the condition that all local filter gain matrices are of full column rank. Its optimality is strictly proved. Moreover, it has robustness and reliability due to the parallel processing of local filters. Two simulation examples demonstrate the effectiveness of the developed fusion algorithm.

Distributed State Estimation for Continuous-Time Linear Systems With Correlated Measurement Noise

In this article, the problem of distributed state estimation for a continuous-time linear system with a sensor network is investigated, where each sensor can only communicate with its neighbors and contains time-correlated measurement noise. To solve this problem, a novel augmented leader-following information fusion strategy is first proposed to collect measurements and system matrices. Then, a class of distributed state estimators is developed with bounded estimation error covariances. Further, a closed-form relation between the designed distributed estimator and the centralized estimator is established. It is found that the estimation performance of the former converges to that of the latter when the consensus gain tends to infinity. The proposed estimator is further extended to the fully distributed case by introducing an adaptive law for the consensus gain without using any global information. Moreover, it is shown that the designed estimator is applicable for systems with deterministic noise. Finally, several comparative numerical simulations are provided to demonstrate the effectiveness and superiority of the theoretical results.

Memory effects on energy loss and diffusion of heavy quarks in the quark-gluon plasma

We study the dynamics of heavy quarks in a thermalized quark-gluon plasma with a time-correlated thermal noise, $\ensuremath{\eta}$. In this case, it is said that $\ensuremath{\eta}$ has memory. We use an integro-differential Langevin equation in which the memory enters via the thermal noise and the dissipative force. We assume that the time correlations of the noise decay exponentially on a timescale, $\ensuremath{\tau}$, which we treat as a free parameter. We compute the effects of $\ensuremath{\tau}\ensuremath{\ne}0$ on the thermalization time of the heavy quarks, on their momentum broadening, and on the nuclear modification factor. We find that overall memory slows down the momentum evolution of heavy quarks: In fact, transverse momentum broadening and the formation of ${R}_{AA}$ are slowed down by memory and the thermalization time of the heavy quarks become larger. The potential impact on other observables is discussed briefly.

Navigation Algorithm-Agnostic Integrity Monitoring based on Solution Separation with Constrained Computation Time and Sensor Noise Overbounding

Integrity monitoring (IM) in autonomous navigation has been extensively researched, but currently available solutions are mainly applicable to specific algorithms and sensors, or limited by linearity or 'Gaussianity' assumptions. This study investigates a Solution Separation (SS) based framework for universal IM, scalable to multi-sensor fusion as each hypothesis assumes a whole sensor measurement set as faulty. Architecturally we consider that: 1) multi sensor systems must account for various sensor noise models which lead to inconsistent estimates of uncertainties, 2) a module must be able to detect sensor failure or sensor noise mismodeling and suggest better bounds for the error, without being constantly conservative, 3) some algorithms are computationally heavy to monitor in the SS setting or the provided covariances cannot be interpreted in IM. A hybrid SS architecture can be practical, where some solutions are evaluated with a navigation algorithm with known characteristics, although the all-sensor-in solution is evaluated with the monitored algorithm. Experiments are run on filter and smoothing-based navigation algorithms. In addition, we experiment with hybrid SS monitoring and time-correlated noise to evaluate the appropriability of our framework in the context of the above-mentioned requirements. This is a novel framework in the IM domain, directly integrable in existing navigation solutions and, in our opinion, it will facilitate the quantification of the effect of different sensors in navigation safety.

Critical slowing down in dynamical systems driven by nonstationary correlated noise

Precursor signals for bifurcation-induced critical transitions have recently gained interest across many research fields. Common indicators, including variance and autocorrelation increases, rely on the dynamical system being driven by white noise. Here, we show that these metrics raise false alarms for systems driven by time-correlated noise, if the autocorrelation of the noise process increases with time. We introduce an indicator for systems driven by nonstationary short-term memory noise, and show that this indicator performs well in situations where the classical methods fail.

A Detection of Red Noise in PSR J1824–2452A and Projections for PSR B1937+21 Using NICER X-Ray Timing Data

Abstract We have used X-ray data from the Neutron Star Interior Composition Explorer (NICER) to search for long-timescale temporal correlations (“red noise”) in the pulse times of arrival (TOAs) from the millisecond pulsars PSR J1824−2452A and PSR B1937+21. These data more closely track intrinsic noise because X-rays are unaffected by the radio-frequency-dependent propagation effects of the interstellar medium. Our search yields strong evidence (natural log Bayes factor of 9.634 ± 0.016) for red noise in PSR J1824−2452A, but the search is inconclusive for PSR B1937+21. In the interest of future X-ray missions, we devise and implement a method to simulate longer and higher-precision X-ray data sets to determine the timing baseline necessary to detect red noise. We find that the red noise in PSR B1937+21 can be reliably detected in a 5 yr mission with a TOA error of 2 μs and an observing cadence of 20 observations per month compared to the 5 μs TOA error and 11 observations per month that NICER currently achieves in PSR B1937+21. We investigate detecting red noise in PSR B1937+21 with other combinations of observing cadences and TOA errors. We also find that time-correlated red noise commensurate with an injected stochastic gravitational-wave background having an amplitude of A GWB = 2 × 10−15 and spectral index of timing residuals of γ GWB = 13/3 can be detected in a pulsar with similar TOA precision to PSR B1937+21. This is with no additional red noise in a 10 yr mission that observes the pulsar 15 times per month and has an average TOA error of 1 μs.

Gaussian estimation for non‐linear stochastic uncertain systems with time‐correlated additive noises and packet dropout compensations

This paper discusses the problem of state estimation for non-linear stochastic uncertain systems with time-correlated additive noise and packet dropout compensations. Both process noise and measurement noise are additive forms of noise that can be described as Gaussian first-order Markov processes. The stochastic uncertainty of the system is described by synchronous correlated white multiplicative noise. When the measurement information from the current epoch is lost, a compensation strategy based on measurement information prediction is used. First, the state information, process noise, and measurement noise are augmented to enable the construction of a new vector to be estimated, and the filter, predictor, and smoother of the system are designed using a Gaussian iterative estimation algorithm based on innovation analysis. The multiplicative noise in the process equation is estimated in real time. Second, a numerical implementation of the proposed algorithm is derived based on the third-degree spherical-radial Cubature Kalman filter(CKF). Finally, the proposed algorithm is compared with an extended Kalman filter (EKF) based on Taylor series expansion. The effectiveness of the proposed algorithm is verified by comparing the simulation results.

Globally Optimal Centralized and Sequential Fusion Filters for Uncertain Systems With Time-Correlated Measurement Noises

This paper is concerned with the fusion filtering problem for stochastic uncertain multi-sensor systems with time-correlated measurement noises, where the stochastic uncertainties are described by white multiplicative noises, and the additive measurement noises are first-order Gauss-Markov Processes. By introducing the recursive measurement noise estimators, the centralized fusion filter (CFF) based on the idea of batch process and sequential fusion filter (SFF) based on the idea of sequential process are designed in the linear minimum variance (LMV) sense by an innovation analysis approach, respectively. The proposed SFF can achieve the same estimation accuracy as the CFF. It is also globally optimal. The equivalence on estimation accuracy of the SFF and CFF is strictly proved by mathematical induction method. The stability and steady-state properties of the proposed fusion filters are analyzed. Two examples show the effectiveness of the proposed fusion algorithms.

Optimal control of interconnected systems with time-correlated noises: Application to vehicle platoon

This paper studies the optimal state-feedback LQG control (OSLC) of interconnected systems (ISs) with time-correlated process noises. In an IS, the information is transmitted among subsystems via the network, and the transmission time is proportional to the distance of the corresponding subsystem pairs. This means that the information received by a subsystem includes the non-real-time information, and that the information from different subsystems may be of different time indexes. This makes the optimal controller design challenging. The OSLC of ISs with time-uncorrelated process noises is studied by an independence decomposition method in the existing literature. However, the existing independence decomposition method strongly relies on the condition that the process noises are time-uncorrelated, and fails for the time-correlated process noises case. In this paper, the globally optimal LQG controller of ISs with time-correlated process noises is successfully designed. In particular, a new cost function decomposition is obtained based on the Bellman equation. Both the system state and the control input are decomposed into two independent parts by the orthogonal decomposition technique. The proposed decomposition method leads to the successful design of the globally optimal controller. The proposed theoretical results are applied to a vehicle platoon system. The simulation shows that the platoon maintains a desired state and achieves a good performance under the proposed controller.

Noise analysis in the European Pulsar Timing Array data release 2 and its implications on the gravitational-wave background search

ABSTRACTThe European Pulsar Timing Array (EPTA) collaboration has recently released an extended data set for six pulsars (DR2) and reported evidence for a common red noise signal. Here we present a noise analysis for each of the six pulsars. We consider several types of noise: (i) radio frequency independent, ‘achromatic’, and time-correlated red noise; (ii) variations of dispersion measure and scattering; (iii) system and band noise; and (iv) deterministic signals (other than gravitational waves) that could be present in the PTA data. We perform Bayesian model selection to find the optimal combination of noise components for each pulsar. Using these custom models we revisit the presence of the common uncorrelated red noise signal previously reported in the EPTA DR2 and show that the data still supports it with a high statistical significance. Next, we confirm that there is no preference for or against the Hellings–Downs spatial correlations expected for the stochastic gravitational-wave background. The main conclusion of the EPTA DR2 paper remains unchanged despite a very significant change in the noise model of each pulsar. However, modelling the noise is essential for the robust detection of gravitational waves and its impact could be significant when analysing the next EPTA data release, which will include a larger number of pulsars and more precise measurements.

Generalized bias compensated pseudolinear Kalman filter for colored noisy bearings-only measurements

Bias compensated pseudolinear Kalman filter (BC-PLKF) has been shown to solve the bias problem of pseudolinear Kalman filter (PLKF) and outperform Extended Kalman Filter (EKF) and many others in bearings-only target estimation applications with a low computational cost. However, BC-PLKF assumes that measurement noise is white, which is not a valid approximation for some applications such as weather-vane-used guided missiles where wind disturbance appears as a strongly time-correlated measurement noise, estimators performing high-frequency measurement updates, or cascaded Kalman filter-based algorithms. When the well-known noise augmentation method is applied to BC-PLKF, no straightforward solution for the bias compensation is available. First, process noise and observer matrix become coupled leading to unique bias. Second, the measurement autocovariance turns into zero whose inverse is used at the bias compensation step of BC-PLKF. Therefore, a bias analysis is performed for PLKF where the measurement noise is colored. Moreover, the generalized BC-PLKF algorithm (GBC-PLKF) for colored noise-corrupted measurements is derived. Simulations are performed to compare performances of GBC-PLKF, EKF, Cubature Kalman Filter (CKF), BC-PLKF, and colored noise augmented EKF and CKF (C-EKF and C-CKF) with typical air-to-surface missile engagement scenarios. Results verify that GBC-PLKF outperforms all comparison filters with a low computational cost for bearings-only estimation applications.

SchWARMA: A model-based approach for time-correlated noise in quantum circuits

Temporal noise correlations are ubiquitous in quantum systems, yet often neglected in the analysis of quantum circuits due to the complexity required to accurately characterize and model them. Autoregressive moving average (ARMA) models are a well-known technique from time series analysis that model time correlations in data. By identifying the space of completely positive trace reserving (CPTP) quantum operations with a particular matrix manifold, we generalize ARMA models to the space of CPTP maps to parameterize and simulate temporally correlated noise in quantum circuits. This approach, denoted Schr\"odinger Wave ARMA (SchWARMA), provides a natural path for generalization of classic techniques from signal processing, control theory, and system identification for which ARMA models and linear systems are essential. This enables the broad theory of classical signal processing to be applied to quantum system simulation, characterization, and noise mitigation.

Transmission spectroscopy with VLT FORS2: a featureless spectrum for the low-density transiting exoplanet WASP-88b

ABSTRACT We present ground-based optical transmission spectroscopy of the low-density hot Jupiter WASP-88b covering the wavelength range of 4413−8333 Å with the FOcal Reducer Spectrograph (FORS2) on the Very Large Telescope. The FORS2 white light curves exhibit a significant time-correlated noise that we model using a Gaussian process and remove as a wavelength-independent component from the spectroscopic light curves. We analyse complementary photometric observations from the Transiting Exoplanet Survey Satellite and refine the system properties and ephemeris. We find a featureless transmission spectrum with increased absorption towards shorter wavelengths. We perform an atmospheric retrieval analysis with the aura code, finding tentative evidence for haze in the upper atmospheric layers and a lower likelihood for a dense cloud deck. While our retrieval analysis results point towards clouds and hazes, further evidence is needed to definitively reject a clear-sky scenario.

Multiband Transit Follow-up Observations of Five Hot Jupiters with Critical Noise Treatments: Improved Physical Properties

Abstract The most challenging limitation in transit photometry arises from the noises in the photometric signal. In particular, the ground-based telescopes are heavily affected by the noise due to perturbation in the Earth’s atmosphere. Use of telescopes with large apertures can improve the photometric signal-to-noise ratio to a great extent. However, detecting a transit signal out of a noisy light curve of the host star and precisely estimating the transit parameters call for various noise reduction techniques. Here, we present multiband transit photometric follow-up observations of five hot Jupiters e.g., HAT-P-30 b, HAT-P-54 b, WASP-43 b, TrES-3 b, and XO-2 N b, using the 2 m Himalayan Chandra Telescope at the Indian Astronomical Observatory, Hanle, and the 1.3 m J. C. Bhattacharya Telescope at the Vainu Bappu Observatory, Kavalur. Our critical noise treatment approach includes techniques such as wavelet denoising and Gaussian process regression, which effectively reduce both time-correlated and time-uncorrelated noise components from our transit light curves. In addition to these techniques, use of our state-of-the-art model algorithms have allowed us to estimate the physical properties of the target exoplanets with a better accuracy and precision compared to the previous studies.

Impact of correlations and heavy tails on quantum error correction

We show that space- and time-correlated single-qubit rotation errors can lead to high-weight errors in a quantum circuit when the rotation angles are drawn from heavy-tailed distributions. This leads to a breakdown of quantum error correction, yielding reduced or, in some cases, no protection of the encoded logical qubits. While heavy-tailed phenomena are prevalent in the natural world, there is very little research as to whether noise with these statistics exists in current quantum processing devices. Furthermore, it is an open problem to develop tomographic or noise spectroscopy protocols that could test for the existence of noise with such statistics. These results suggest the need for quantum characterization methods that can reliably detect or reject the presence of such errors together with continued first-principles studies of the origins of space- and time-correlated noise in quantum processors. If such noise does exist, physical or control-based mitigation protocols must be developed to mitigate this noise as it would severely hinder the performance of fault-tolerant quantum computers.

Modelling quasi-periodic signals in geodetic time-series using Gaussian processes

SUMMARY Seasonal signals in geodetic time-series have long been recognized to be associated with environmental phenomena such as polar motion, atmospheric loading, groundwater loading and other hydrological processes. Modelling these periodic signals is crucial for the geophysical interpretation of these time-series. The most common approach used for resolving seasonal (annual and semi-annual) signals is their approximation by sinusoidal functions with constant amplitudes. However, because of their environmental source, seasonal signals are likely to be quasi-periodic. In this study, we investigate a Gaussian process (GP) to model quasi-periodic signals in geodetic time-series, a flexible method that allows capturing the variability structure in the data using covariance functions. We use the Markov Chain Monte Carlo method to evaluate the posterior probability density function. To test its effectiveness, we apply this method to a synthetic time-series in the presence of time-correlated noise. We find that the GP model provides a better fit to the time-series, resulting in time-series residuals with fewer systematic effects. We use the GP model to estimate the secular velocity of selected GPS sites from Antarctica and Alaska, as well as an example of Gravity Recovery and Climate Experiment time-series. The Bayesian aspect of the GP model allows inferring the linear velocity ensemble in the vicinity of the true solution while taking into account the quasi-periodic systematics in the time-series.

Discrete-time quantum walk with time-correlated noise

We investigate the dynamics of discrete-time quantum walk subject to time correlated noise. Noise is described as an unitary coin-type operator before each step, and attention is focused on the noise generated by a Gaussian Ornstein Uhlenbeck process, going beyond the usual telegraph noise, where the random variables are consist of only -1 and 1. Under the first-order approximation of BCH formula, the master equation of noisy discrete-time quantum walk is derived. The dynamics given by the master equation are in good agreement with those given by numerical simulations within a certain period of steps, which is controlled by noise parameters. Two remarker behaviors of long time noisy dynamics are observed in numerical simulations, corresponding to two opposite noise regimes: in slow noise regime, with the increase of the noise amplitude, the quantum coherence is suppressed, and the dynamics of noisy discrete-time quantum walk gradually transits to that of classical random walk. In fast noise regime, the walker is confined into few lattice sites, and the width of wave packet is much narrower compared with that in slow noise regime.

Randomized benchmarking in the presence of time-correlated dephasing noise

Randomized benchmarking has emerged as a popular and easy-to-implement experimental technique for gauging the quality of gate operations in quantum computing devices. A typical randomized benchmarking procedure identifies the exponential decay in the fidelity as the benchmarking sequence of gates increases in length, and the decay rate is used to estimate the fidelity of the gate. That the fidelity decays exponentially, however, relies on the assumption of time-independent or static noise in the gates, with no correlations or significant drift in the noise over the gate sequence, a well-satisfied condition in many situations. Deviations from the standard exponential decay, however, have been observed, usually attributed to some amount of time correlations in the noise, though the precise mechanisms for deviation have yet to be fully explored. In this work, we examine this question of randomized benchmarking for time-correlated noise---specifically for time-correlated dephasing noise for exact solvability---and elucidate the circumstances in which a deviation from exponential decay can be expected.

Finite-time higher-order moment state estimation for Markov jump linear system with time-correlated measurement noise

In the present study, a higher-order moment state estimation problem in a finite time interval for the discrete-time Markov jump linear systems (MJLS) is investigated. Moreover, time-correlated noise in measurements is considered. Initially, the measruement differencing approach is applied to convert the time-correlated measurement noise to an uncorrelated noise. Then the cumulant generating function is utilized to solve the stochastic jumping problem of MJLS, by which the discrete-time MJLS is transformed into a deterministic system. In this way, the transformed deterministic system has the same norm with a higher-order moment of the original state. Finally, a finite-time state estimation algorithm is proposed to guarantee that the higher-order moment of error trajectory remains within a pre-specified bound over a given time interval. In order to evaluate the performance of the proposed method, some test cases are applied. Obtained results prove the accuracy and efficiency of the proposed method.

Using time-correlated noise to encourage exploration and improve autonomous agents performance in Reinforcement Learning

Intelligent autonomous agents need to know how to carry out actions based on reasoning, perception, and analysis. Therefore, reinforcement learning algorithms guide the agent to reach this goal by performing steps that guarantee the most significant reward. The problem with this approach is that when the agent finds an optimal action with a considerable premium, it tends to stop exploring the environment to guarantee only that great reward. In this way, the agent stops making a great exploration to find new ways and learn alternatives that could generate a bigger bonus in the face of a change in its context. To alleviate this problem, some techniques, such as Soft Actor-Critic (SAC) and Asynchronous Advantage Actor-Critic (A3C), use entropy regulation to improve policy optimization in reinforcement learning. Thus, the greater the entropy, the lower the probability of the agent’s certainty in a given action. Despite entropy, these algorithms are not immune to local optimal and require additional exploration mechanisms. Therefore, this work proposes an approach that helps the agent’s exploitation policy during reinforcement learning training and improves its performance during the test time. We use the latest state-of-the-art (SOTA) approaches, that is, Asynchronous Advantage Actor-Critic (A3C), Proximal Policy Optimization (PPO), and Soft Actor-Critic (SAC) in this work. We created a time-correlated noise in the agent’s policy network from the use of a random disturbance generated with the Ornstein-Uhlenbeck process. According to the experiments carried out and the results obtained, we can see that our proposal allowed the agent to explore the environment more during training and improve its performance during the testing time, increasing the reward received in different learning contexts.