non-Gaussian Measurement Research Articles

Robust Minimum Error Entropy Based Cubature Information Filter With Non-Gaussian Measurement Noise

In this letter, a robust minimum error entropy based cubature information filter is proposed for state estimation in non-Gaussian measurement noise. A new combined optimization cost is defined based on the error entropy. Through cubature transform, a statistical linearization regression model is constructed, and a new information filter is then developed by minimizing the error entropy based cost. The fixed-point iteration approach is used to compute the state estimate. Further, the convergence of the proposed information filter is analyzed, and the convergence conditions are derived. Simulations are performed to demonstrate the effectiveness of the proposed algorithm. It is shown that the estimation performance of the proposed filter is more robust than that of traditional methods against the complicated non-Gaussian noises, such as outliers and noises from multimodal distributions.

A Hybrid Data Fusion Approach to AI-Assisted Indirect Centralized Integrated SINS/GNSS Navigation System During GNSS Outage

The main challenges for integration between low-cost strap-down inertial navigation system (SINS) and global navigation satellite system (GNSS) are to manage the non-Gaussian measurement noises and to access the reliable measurements during GNSS outages. Therefore, in this paper, some approaches are taken in the proposed integrated navigation system: (1) using an iterative empirical mode decomposition (EMD) interval thresholding de-noising method for low-cost inertial measurements to provide smoother and more accurate SINS measurements with less complexity, (2) designing an enhanced indirect centralized correntropy Kalman filter using a novel fuzzy parameter adjustment approach, which adaptively changes the estimation algorithm parameters to further improve the robustness of the proposed algorithm in the presence of dynamical maneuvers and non-Gaussian measurement noise, and (3) utilizing a pre-filtered nonlinear autoregressive network with exogenous inputs (PFNARX) designed to provide reliable interrupted positioning information during GNSS outages. The proposed SINS/GNSS system is experimentally evaluated through real-world flight tests. The obtained results reveal that the designed integration algorithm remarkably improves the estimation accuracy by adaptively tuning the parameters in an improved correntropy Kalman filter and an efficient and well-trained artificial neural network-based model in the absence of GNSS signal.

Robust Central Difference Kalman Filter With Mixture Correntropy: A Case Study for Integrated Navigation

In this paper, a robust central difference Kalman filter is proposed to address the process uncertainty and non-Gaussian measurement noise induced by the vehicle's severe maneuver and abnormal measurements in MEMS-SINS/GNSS integrated navigation system. Compared with the state-of-the-art noise distribution based robust filter, in the proposed filter, the process uncertainty and measurement uncertainty are simultaneously suppressed based on a new constructed cost function, which is independent of noise distribution and more insensitive to the non-Gaussian noise. To be specific, the statistical linearization approach is first presented to derive a linear-like regression model. Then, by resorting to the innovation orthogonal theory and Cholesky triangular decomposition, the fading factor of cost function is adaptively and robustly determined in the process of iteration, where the filtering performance and the stability of the algorithm under the condition of process uncertainty are extremely enhanced. Furthermore, the correntropy using the mixture of two Gaussian functions as the kernel function is incorporated into the cost function to prevent the non-Gaussian measurement noise. Our extensive simulation and car-mounted experiment demonstrate that the proposed filter can achieve higher estimation accuracy and better robustness as compared with the related state-of-the-art methods.

A flexible robust Student's t-based multimodel approach with maximum Versoria criterion

The performance of the state estimation for Gaussian state space models can be degraded if the models are affected by the non-Gaussian process and measurement noises with uncertain degree of non-Gaussianity. In this paper, we propose a flexible robust Student's t-based multimodel approach. More specifically, the degrees of freedom parameter from the Student's t-distribution is assumed unknown and modelled by a Markov chain of state values. In order to capture more information of the Student's t-distributions propagated through multiple models, we establish a model-based Versoria cost function in the form of a weighted mixture rather than the original form, and maximize the function to interact and fuse the multiple models. Simulated results prove the flexibility of the robustness of the proposed Student's t-basedmultimodel approach when the existence probability of the outliers is uncertain.

Efficient simulatability of continuous-variable circuits with large Wigner negativity

Discriminating between quantum computing architectures that can provide quantum advantage from those that cannot is of crucial importance. From the fundamental point of view, establishing such a boundary is akin to pinpointing the resources for quantum advantage; from the technological point of view, it is essential for the design of non-trivial quantum computing architectures. Wigner negativity is known to be a necessary resource for computational advantage in several quantum-computing architectures, including those based on continuous variables (CVs). However, it is not a sufficient resource, and it is an open question under which conditions CV circuits displaying Wigner negativity offer the potential for quantum advantage. In this work we identify vast families of circuits that display large, possibly unbounded, Wigner negativity, and yet are classically efficiently simulatable, although they are not recognized as such by previously available theorems. These families of circuits employ bosonic codes based on either translational or rotational symmetries (e.g., Gottesman-Kitaev-Preskill or cat codes), and can include both Gaussian and non-Gaussian gates and measurements. Crucially, within these encodings, the computational basis states are described by intrinsically negative Wigner functions, even though they are stabilizer states if considered as codewords belonging to a finite-dimensional Hilbert space. We derive our results by establishing a link between the simulatability of high-dimensional discrete-variable quantum circuits and bosonic codes.

Efficient Evaluation of Remaining Wall Thickness in Corroded Water Pipes Using Pulsed Eddy Current Data

In order to analyse failures of an ageing water pipe, some methods such as the loss-of-section require remaining wall thickness (RWT) along the pipe to be fully known, which can be measured by the magnetism based non-destructive evaluation sensors though they are practically slow due to the magnetic penetrating process. That is, fully measuring RWT at every location in a water pipe is not really practical if RWT inspection causes disruption of water supply to customers. Thus, this paper proposes a new data prediction approach that can increase amount of RWT data of a corroded water pipe collected in a given period of time by only measuring RWT on a part (e.g. 20%) of the total pipe surface area and then employing the measurements to predict RWT at unmeasured area. It is proposed to utilize a marginal distribution to convert the non-Gaussian RWT measurements to the standard normally distributed data, which can then be input into a 3-dimensional Gaussian process model for efficiently predicting RWT at unmeasured locations on the pipe. The proposed approach was implemented in two real-life in-service pipes, and the obtained results demonstrate its practicality.

Reaching small scales with low-frequency imaging: applications to the Dark Ages.

The initial conditions for the density perturbations in the early Universe, which dictate the large-scale structure and distribution of galaxies we see today, are set during inflation. Measurements of primordial non-Gaussianity are crucial for distinguishing between different inflationary models. Current measurements of the matter power spectrum from the cosmic microwave background only constrain this on scales up to k ∼ 0.1 Mpc-1. Reaching smaller angular scales (higher values of k) can provide new constraints on non-Gaussianity. A powerful way to do this is by measuring the HI matter power spectrum at [Formula: see text]. In this paper, we investigate what values of k can be reached for the Low-Frequency Array (LOFAR), which can achieve [Formula: see text]1″ resolution at approximately 50 MHz. Combining this with a technique to isolate the spectrally smooth foregrounds to a wedge in [Formula: see text]-k⊥ space, we demonstrate what values of k we can feasibly reach within observational constraints. We find that LOFAR is approximately five orders of magnitude away from the desired sensitivity, for 10 years of integration time. This article is part of a discussion meeting issue 'Astronomy from the Moon: the next decades'.

Multiple least mean kurtosis adaptive filters for blind source separation

In this paper, a novel use of adaptive filters for blind source separation is presented. The known independent component analysis algorithm separates signals from their mixtures based on the observation that a mixture of statistically independent signals is more Gaussian than the separate signals. Similarly, an adaptive filter, that is designed to minimize the Gaussianity of its output, relies on the same hypothesis. The proposed adaptive filter uses all the mixture signals, the observation signals, as its inputs—one as the main input, and the rest as reference inputs. The filter is iteratively modified, using gradient descent, such that the measure of non-Gaussianity of its output is maximized, leading to the separation of one source signal at its output. To separate the N source signals from the given N mixtures, N such adaptive filters are used. The proposed method has been successfully applied to the blind separation of multiple signals.

Robust Cubature Kalman Filter for SINS/GPS Integrated Navigation Systems With Unknown Noise Statistics

to the vehicle’s severe maneuver and abnormal measurements of GPS in practical applications, the statistic of process noise in SINS/GPS integrated navigation system may be unknown and the measurement noise may not follow the Gaussian distribution, which results in a deteriorated performance for the conventional cubature Kalman filter. To address this issue, we propose in this paper a new robust cubature Kalman filter based on the adaptive information entropy theory. In the proposed filter, the process uncertainty and non-Gaussian measurement noise are simultaneously suppressed based on a new constructed cost function using the maximum correntropy and residual orthogonal principle based weighted least squares technology, which is independent of noise distribution and more insensitive to the non-Gaussian noise. Moreover, a multiple-channel adaptive strategy for the better process uncertainty suppression is given. Furthermore, some improvements are proposed to avoid the numerical problem and implement the proposed robust filter effectively. Extensive simulation and car-mounted experiment demonstrate that the proposed filter can achieve higher estimation accuracy and better robustness as compared with the related state-of-the-art methods.

Optimal PMU placement approach for power systems considering non-Gaussian measurement noise statistics

This paper investigates how to add a limited number of Phasor Measurement Units (PMUs) to the existing monitoring system so as to improve the estimation accuracy further. The existing methods are usually based on Gaussian noise assumption and the weighted least squares (WLS) estimator is taken into account. However, the Gaussian noise assumption is not always true in reality and the WLS is non-robust in this case. This paper proposes a new optimal PMU placement approach where the distribution of measurement noise can be non-Gaussian or Gaussian and many robust estimators such as the maximum likelihood estimator, Multiple-Segment, Quadratic-Linear, Square-Root and Schweppe-Huber Generalized-M estimator are considered. Based on the new Gain matrix obtained from the influence function approximation, the D-optimal and E-optimal experiment criterions are exploited in the optimal PMU placement problem. A convex relaxation in conjunction with an optimization improvement method based on the Fedorov exchange algorithm is utilized to solve the optimizing problem. Simulations on the IEEE 57-bus system and the Polish 2383-bus system are carried out to evaluate the effective performance of the proposed approach.

Real-time robust forecasting-aided state estimation of power system based on data-driven models

This paper presents a real-time robust power system forecasting-aided state estimation method based on the Bayesian framework, deep learning, and Gaussian mixture model to dynamically estimate the non-Gaussian measurement noise in the real-time power system. The approach is data driven and model independent. A non-linear mapping function between measurement and state is formulated based on the historical operating data of the power system and the Gaussian process. Then combine the anomaly detection technology in machine learning and the Gaussian mixture model to accurately judge and delete the abnormal data in measurement information. Thus, a power system state forecasting model based on long-short term memory neural network is established, which can solve the problem of missing data combining power flow calculation. Numerical simulations carried out on the IEEE 118-bus and IEEE 300-bus test system reveal that the proposed method has high accuracy and robustness.

Quantifying non-Gaussianity via the Hellinger distance

Non-Gaussianity is an important resource for quantum information processing with continuous variables. We introduce a measure of the non-Gaussianity of bosonic field states based on the Hellinger distance and present its basic features. This measure has some natural properties and is easy to compute. We illustrate this measure with typical examples of bosonic field states and compare it with various measures of non-Gaussianity. In particular, we highlight its similarity to and difference from the measure based on the Bures distance (or, equivalently, fidelity).

Model-Based Bayesian Compressive Sensing of Non-stationary Images Using a Wavelet-Domain Triplet Markov Fields Model

In this paper, a new model-based Bayesian compressive sensing technique for non-stationary images is proposed. Our algorithm is based on the recently addressed triplet Markov fields (TMF) model. The TMF model is well appropriate for non-stationary image processing, owing to the introduction of a third random field which reflects different non-stationarity of images. Furthermore, TMF can extract the interactions among the neighboring sites of an image in a more complete way than the classic hidden Markov models do. In this paper, the inter-scale dependencies between the wavelet coefficients is exploited explicitly in the proposed TMF model, which results in the wavelet domain TMF model. Our proposed model considers the intra- and inter-scale dependencies and the non-stationarity of images simultaneously. Also, we have developed our proposed algorithm for both Gaussian and non-Gaussian measurement noises, and we have modeled the non-Gaussianity of the noise via Laplace distribution. To approximate the posterior distributions of the hidden variables, we resort to a variational Bayesian expectation–maximization algorithm. Simulation results in both the optical and synthetic aperture radar images show that this model leads to an improvement over state-of-the-art algorithms in terms of the reconstruction error and the structural similarity.

Phase tracking for sub-shot-noise-limited receivers

Non-conventional receivers for phase-coherent states based on non-Gaussian measurements such as photon counting surpass the sensitivity limits of shot-noise-limited coherent receivers, the quantum noise limit (QNL). These non-Gaussian receivers can have a significant impact in future coherent communication technologies. However, random phase changes in realistic communication channels, such as optical fibers, present serious challenges for extracting the information encoded in coherent states. While there are methods for correcting random phase noise with conventional heterodyne detection, phase-tracking for non-Gaussian receivers surpassing the QNL is still an open problem. Here we demonstrate phase tracking for non-Gaussian receivers to correct for time-varying phase noise while allowing for decoding beyond the QNL. The phase-tracking method performs real-time parameter estimation and correction of phase drifts using the data from the non-Gaussian discrimination measurement, without relying on phase reference pilot fields. This method enables non-Gaussian receivers to achieve higher sensitivities and rates of information transfer than ideal coherent receivers in realistic channels with time-varying phase noise. This demonstration makes sub-QNL receivers a more robust, feasible, and practical quantum technology for classical and quantum communications.

Maximum Correntropy Rauch–Tung–Striebel Smoother for Nonlinear and Non-Gaussian Systems

We propose a new robust recursive fixed-interval smoother for nonlinear systems under non-Gaussian process and measurement noises, i.e., the nominal Gaussian noise is polluted by large noise from unknown distributions. Taking advantage of correntropy in handling non-Gaussian noise, a robust Rauch-Tung-Striebel smoother is derived according to the maximum-correntropy-criterion-based cost functions with nonlinear functions linearized by their first-order Taylor series expansions, where two weights are utilized to adjust the estimation gains of forward filtering and backward smoothing, respectively. Simulation results demonstrate the effectiveness of the proposed smoother in the presence of various non-Gaussian process and measurement noises, especially the shot sequences and multimodal noise.

Optimal distributed quantum sensing using Gaussian states

We find and investigate the optimal scheme of quantum distributed Gaussian sensing for estimation of the average of independent phase shifts. We show that the ultimate sensitivity is achievable by using an entangled symmetric Gaussian state, which can be generated using a single-mode squeezed vacuum state, a beam-splitter network, and homodyne detection on each output mode in the absence of photon loss. Interestingly, the maximal entanglement of a symmetric Gaussian state is not optimal although the presence of entanglement is advantageous as compared to the case using a product symmetric Gaussian state. It is also demonstrated that when loss occurs, homodyne detection and other types of Gaussian measurements compete for better sensitivity, depending on the amount of loss and properties of a probe state. None of them provide the ultimate sensitivity, indicating that non-Gaussian measurements are required for optimality in lossy cases. Our general results obtained through a full-analytical investigation will offer important perspectives to the future theoretical and experimental study for quantum distributed Gaussian sensing.

Practical uncertainty quantification analysis involving statistically dependent random variables

This article presents a practical refinement of generalized polynomial chaos expansion for uncertainty quantification under dependent input random variables. Unlike the Rodrigues-type formula, which exists for select probability measures, a three-step computational algorithm is put forward to generate a sequence of any approximate measure-consistent multivariate orthonormal polynomials. For uncertainty quantification analysis under dependent random variables, two regression methods, comprising existing standard least-squares and newly developed partitioned diffeomorphic modulation under observable response preserving homotopy (D-MORPH), are proposed to estimate the coefficients of generalized polynomial chaos expansion for the very first time. In contrast to the existing regression devoted so far to the classical polynomial chaos expansion, no tensor-product structure is required or enforced. The partitioned D-MORPH regression is applicable to either an underdetermined or overdetermined system, thus substantially enhancing the ability of the original D-MORPH regression. Numerical results obtained for Gaussian and non-Gaussian probability measures with rectangular or non-rectangular domains point to highly accurate orthonormal polynomials produced by the three-step algorithm. More significantly, the generalized polynomial chaos approximations of mathematical functions and stochastic responses from solid-mechanics problems, in tandem with the partitioned D-MORPH regression, provide excellent estimates of the second-moment properties and reliability from only hundreds of function evaluations or finite element analyses.

Solving phase retrieval via graph projection splitting

Phase retrieval with prior information can be cast as a nonsmooth and nonconvex optimization problem. To decouple the signal and measurement variables, we introduce an auxiliary variable and reformulate it as an optimization with an equality constraint. We then solve the reformulated problem by graph projection splitting (GPS), where the two proximity subproblems and the graph projection step can be solved efficiently. With slight modification, we also propose a robust graph projection splitting (RGPS) method to stabilize the iteration for noisy measurements. Contrary to intuition, RGPS outperforms GPS with fewer iterations to locate a satisfying solution even for noiseless case. Based on the connection between GPS and Douglas–Rachford iteration, under mild conditions on the sampling vectors, we analyze the fixed point sets and provide the local convergence of GPS and RGPS applied to noiseless phase retrieval without prior information. For noisy case, we provide the error bound of the reconstruction. Compared to other existing methods, thanks for the splitting approach, GPS and RGPS can efficiently solve phase retrieval with prior information regularization for general sampling vectors which are not necessarily isometric. For Gaussian phase retrieval, compared to existing gradient flow approaches, numerical results show that GPS and RGPS are much less sensitive to the initialization. Thus they markedly improve the phase transition in noiseless case and reconstruction in the presence of noise respectively. GPS shows sharpest phase transition among existing methods including RGPS, while it needs more iterations than RGPS when the number of measurement is large enough. RGPS outperforms GPS in terms of stability for noisy measurements. When applying RGPS to more general non-Gaussian measurements with prior information, such as support, sparsity and TV minimization, RGPS either outperforms state-of-the-art solvers or can be combined with state-of-the-art solvers to improve their reconstruction quality.

A method for efficiently estimating non-Gaussianity of continuous-variable quantum states

We develop a method for efficiently calculating non-Gaussianity of quantum states in Wigner function representation based on the sine metric. In contradistinction to the known non-Gaussianity measures, we seek the corresponding reference Gaussian counterpart via the cumulant-expansion techniques of quantum state. We analyze this quantity for some non-Gaussian quantum states, which can not be well detected or quantified by other non-Gaussianity measures such as the degree of Gaussianity, the Hilbert-Schmidt metric and the relative entropy metric, thereby providing a good measure to quantify a genuine non-Gaussian state.

Nonlinear Non-Gaussian Estimation Using Maximum Correntropy Square Root Cubature Information Filtering

This paper concerns the nonlinear filter designing methods in the information space of the nonlinear systems with non-Gaussian noises. Firstly, the prediction information vector is obtained by the traditional square root cubature information filtering algorithm. Then, under the maximum correntropy criterion, the prediction information vector is corrected with the contribution information vector obtained by the non-Gaussian measurement. The information filtering gain is obtained by utilizing the state information correntropy matrix and the measurement information correntropy matrix, in which, the state prediction is taken as the state value. In order to improve the advantage of the above nonlinear non-Gaussian information filter in filtering accuracy, with the help of fixed-point theory, an iterative computation method is further developed to update the estimation information vector and the state estimate. The effectiveness of the two proposed nonlinear non-Gaussian filtering methods is illustrated in final four simulation examples.