A variational Bayesian based robust filter for unknown measurement bias and inaccurate noise statistics

This paper addresses the distributed state estimation over a large scale sensor network wherein each sensor may have an unknown measurement bias. In order to mitigate the influence of biases to state estimation, a bias estimator only depending on the structure of local sensor is constructed to ensure the algorithm's scalability for sensor networks. It is proved that the proposed bias estimator can effectively realize the bias estimation for the slow time-varying measurement bias. In addition, a distributed Kalman filter embedded with local bias estimator is developed to efficiently correct the biased measurements. Both consistency and stability of the filter are guaranteed under a general collective observability condition for linear time-varying systems. A numerical simulation is provided to illustrate the effectiveness of the developed results.

In this article, a novel robust Gaussian approximation smoother based on expectation–maximization (EM) algorithm is proposed for cooperative localization (CL) with faulty Doppler velocity log (DVL) and heavy-tailed measurement noise. In our model, the autonomous underwater vehicle (AUV) velocity information that is not available due to DVL failure and the bias in the underwater acoustic modem are considered as unknown inputs. Then, the Student’s t distribution is used to model the heavy-tailed measurement noise. An EM algorithm is also developed for the state-space model with heavy-tailed measurement noise. The state, noise covariance matrices, and auxiliary random variables are regarded as hidden variables to obtain the maximum likelihood estimation of unknown inputs. Gaussian smoother where modified process and measurement noise covariance are inferred by variational Bayesian (VB) approach is applied to estimate the state. The experimental results illustrate that given the heavy-tailed noise, the proposed method estimates the unknown input, and the state with a high level of accuracy. The proposed algorithm can be used as a backup algorithm for CL in cases where DVL is not available due to failure.

Inter-laboratory comparisons use the best available transfer standards to check the participants’ uncertainty analyses, identify underestimated uncertainty claims or unknown measurement biases, and improve the global measurement system. For some measurands, instability of the transfer standard can lead to an inconclusive comparison result. If the transfer standard uncertainty is large relative to a participating laboratory’s uncertainty, the commonly used standardized degree of equivalence ⩽1 criterion does not always correctly assess whether a participant is working within their uncertainty claims. We show comparison results that demonstrate this issue and propose several criteria for assessing a comparison result as passing, failing, or inconclusive. We investigate the behavior of the standardized degree of equivalence and alternative comparison measures for a range of values of the transfer standard uncertainty relative to the individual laboratory uncertainty values. The proposed alternative criteria successfully discerned between passing, failing, and inconclusive comparison results for the cases we examined.

This article examines the issue of distributed nonlinear state estimation using generalized minimum error entropy (GMEE) amidst hybrid attacks and heavy-tailed measurement noise, particularly in scenarios, where the characteristics of deception attack and measurement noise are unknown. The variational Bayesian (VB) inference is utilized to deal with the challenge of unknown characteristics of the deception attack and measurement noise. In addition, the GMEE criterion is employed to mitigate the impact of non-Gaussian additive measurement disturbances. Subsequently, a nonlinear distributed state estimation (DSE) approach utilizing covariance intersection over wireless sensor networks (WSNs) constrained by hybrid attacks is developed. In addition, the proposed method’s mean error behavior and consistency are evaluated. Finally, numerical simulations confirm the effectiveness of the proposed algorithm.

A framework for the statistical comparison of six coincident remote sounding measurements is presented, which distinguishes between additive and multiplicative biases. The relationship between multiplicative bias and error variance is explored, and three methods are proposed for producing sets of values for three comparison variables: the multiplicative bias, and the error variance for each of two instruments. We illustrate and compare the three methods through the comparison of coincident measurements of the relatively long‐lived stratospheric species O3, N2O, and HNO3 from two independent measurement sets: version 2.2 retrievals (with updated O3) from the Atmospheric Chemistry Experiment‐Fourier transform spectrometer onboard SCISAT‐1, and version 1.51 retrievals from the Earth Observing System Microwave Limb Sounder onboard Aura. We find that multiplicative bias between the two measurement sets, compared on a common vertical grid, is significant at some heights for O3 and N2O, and for all heights tested for HNO3. The most realistic estimates of measurement error are produced by a method which incorporates a third correlative data set into the analysis. Using this method, estimated error standard deviations (SDs) are comparable between the two instruments for O3 measurements, and are less than 10% of the mean measurement value between approximately 100 and 1 hPa. ACE N2O measurements are consistent with a 10% error SD at all heights tested, although the uncertainty of the estimates is large at heights above 5 hPa. Estimated MLS N2O error SDs are comparable with those for ACE in the lower stratosphere, but increase steeply with height. For HNO3, estimated error SDs are approximately 10% between 70 and 10 hPa for both instruments. At heights above 10 hPa and below 100 hPa, estimated ACE errors are significantly smaller than those for MLS.

A suitable jump Markov system (JMS) filtering approach provides an efficient technique for tracking surface targets. In complex surface target tracking situations, due to the joint influences of lost measurements with an unknown probability and heavy-tailed measurement noise (HTMN), the estimation accuracy of conventional interacting multiple model (IMM) methods may be seriously degraded. Aiming to address the filtering issues in JMSs with HTMNs and random measurement losses, this paper presents an IMM filtering approach with the adaptive estimation of unknown measurement loss probability. In this study, we assumed that the measurement noises obey student’s t-distributions and then proposed Bernoulli random variables (BRVs) to characterize the random measurement loss. Notably, by converting the two likelihood functions from the weighted sum form to exponential multiplication, we established hierarchical Gaussian state space models to directly utilize the variational inference method. The system state vectors, unknown distribution parameters, BRVs, and unknown measurement loss probabilities were estimated simultaneously according to the variational Bayesian inference in the IMM framework. The results of maneuvering target tracking simulations verified that the presented filtering approach demonstrated superior estimation accuracy compared to existing IMM filters.

Aims. Calibrating the point spread function (PSF) is a fundamental part of weak gravitational lensing analyses. Even with corrected galaxy images, imperfect calibrations can introduce biases. We propose an analytical framework for quantifying PSF-induced systematics as diagnostics for cross-correlation measurements of weak lensing with density tracers; for example, galaxy-galaxy lensing. We show how those systematics propagate to physical parameters of the density tracers. Those diagnostics only require a shape catalog of PSF stars and foreground galaxy positions. Methods. We considered the PSF-induced multiplicative bias, and introduced three second-order statistics as additive biases. We computed both biases for the weak-lensing derived halo mass of spectroscopic foreground galaxy samples; in particular, their effect on the tangential shear and fit halo mass as a function of stellar mass. In addition, we assessed their impact on the recently published black-hole – halo-mass relation for type I active galactic nuclei (AGNs). Results. Using weak-lensing catalogs from the Ultraviolet Near Infrared Optical Northern Survey (UNIONS) and the Dark Energy Survey (DES), we find the multiplicative biases in the tangential shear to be less than 0.5%. No correlations between additive bias and galaxy properties of the foreground sample are detected. The combined PSF systematics affect low-mass galaxies and small angular scales; halo mass estimates can be biased by up to 18% for a sample of central galaxies in the stellar mass range of 9.0 ≤ log M*/M⊙ < 9.5. Conclusions. The PSF-induced multiplicative bias is a subdominant contribution to current studies of weak-lensing – density cross-correlations, but might become significant for upcoming stage IV surveys. For samples with a low tangential shear, additive PSF systematics can induce a significant bias on derived properties such as the halo mass.

Tele-correlation refers to the correlation of galaxy shapes with large angular separations (e.g., > 100 degrees). Since there are no astrophysical reasons causing such a correlation on cosmological scales, any detected tele-correlation could disclose systematic effects in shear-shear correlation measurement. If the shear estimators are measured on single exposures, we show that the field distortion (FD) signal associated with the galaxy position on the CCD can be retained and used in tele-correlation to help us directly calibrate the multiplicative and additive biases in shear-shear correlations.We use the DECaLS shear catalog produced by the Fourier_Quad pipeline to demonstrate this idea.To our surprise, we find that significant multiplicative biases can arise (up to more than 10%) due to redshift binning of the galaxies. Correction for this bias leads to about 1σ increase of the best-fit value of S 8 from 0.760+0.015 -0.017 to 0.777+0.016 -0.019 in our tomography study.

We propose to use a low order autoregressive (AR) model to describe the temporal structure of source. Then we adopt Variational Bayesian (VB) method for source separation which models additive noise into the mixing system. The approach integrates the source probabilistic model and noise probabilistic model. Its goal is to approximate the actual probability density function of hidden variables and parameters using its approximating posterior distribution by minimizing the misfit between them. The advantage of our VB-AR algorithm is that it can exploit the temporal nature of source signals and avoid overfitting in the separating process. This algorithm can also identify the AR order. Experiments on artifact and real-world speech signals are used to verify our proposed algorithms. As a result, the lower AR source model improves the separation. The performance of the algorithm is compared with that of i.i.d. separation algorithm and the second-order separation algorithm.

Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli–Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model.

We derive a new relation between cosological distances, valid in any (statistically) isotropic space-time and independent of cosmological parameters or even the validity of the field equation of General Relativity. In particular, this relation yields an equation between those distance ratios which are the geometrical factors determining the strength of the gravitational lensing effect of mass concentrations. Considering a combination of weak lensing shear ratios, based on lenses at two different redshifts, and sources at three different redshifts, we derive a relation between shear-ratio tests which must be identically satisfied. A redshift-dependent multiplicative bias in shear estimates will violate this relation, and thus can be probed by this generalized shear-ratio test. Combining the lensing effect for lenses at three different redshifts and three different source redshifts, a relation between shear ratios is derived which must be valid independent of a multiplicative bias. We propose these generalized shear-ratio tests as a diagnostic for the presence of systematics in upcoming weak lensing surveys.

The constant image brightness (CIB) assumption assumes that the intensities of corresponding points in two images are equal. This assumption is central to much of computer vision. However, surprisingly little work has been performed to support this assumption, despite the fact the many of algorithms are very sensitive to deviations from CIB. An examination of the images contained in the SRI JISCT stereo database revealed that the constant image brightness assumption is indeed often false. Moreover, the simple additive/multiplicative models of the form I/sub L/=/spl beta/I/sub R/+/spl alpha/ do not adequately represent the observed deviations. A comprehensive physical model of the observed deviations is difficult to develop. However, many potential sources of deviations can be represented by a nonlinear monotonically increasing relationship between intensities. Under these conditions, we believe that an expansion/contraction matching of the intensity histograms represents the best method to both measure the degree of validity of the CIB assumption and correct for it. Dynamic histogram warping (DHW) is closely related to histogram specification. It is shown that histogram specification introduces artifacts that do not occur with dynamic histogram warping. Experimental results show that image histograms are closely matched after DHW, especially when both histograms are modified simultaneously. DHW is also capable of removing simple constant additive and multiplicative biases without derivative operations, thereby avoiding amplification of high frequency noise. DHW can improve the estimates from stereo and optical flow estimators.

A new scheme for the traceability ensuring, called the Metrological Measurements Network, was proposed. It is not an alternative to the existing scheme but is only another form of implementation of the traceability scheme. It is about the main principle of construction of the Metrological Measurements Network and its advantages over the existing scheme. The main reason is that each laboratory calibrates its own object for measurement using its measurement standard and sends it for calibration to a laboratory-participant and, almost simultaneously, receives a similar object from another laboratory-participant that calibrated it. If each participant, at the same time as the others, makes at least four such calibrations and transfers between laboratories-participants, it will form a common and very precise Metrological Measurement Network in a very short time. It can cover hundreds and even thousands of laboratories in a short period of time. The joint processing of a large number of such measurements will help to define the additive and/or multiplicative biases of each measurement standards. Moreover, the reference conditions are imposed that the sum of additive and, separately, the sum of multiplicative biases for all measurement standards is equal to zero regardless of the number of network participants.

The error characterization of soil moisture products, for example, obtained from microwave remote sensing data, is a key requirement for using these products in applications like numerical weather prediction. The error variance and root-mean-square error are among the most popular metrics: they can be estimated consistently for three datasets using triple collocation (TC) without assuming any dataset to be free of errors. This technique can account for additive and multiplicative biases; that is, it assumes that the three products are linearly related. However, its susceptibility to nonlinear relations (e.g., due to sensor saturation and scale mismatch) has not been addressed. Here, a simulation study investigates the impact of quadratic relations on the TC error estimates [also when the products are first rescaled using the nonlinear cumulative distribution function (CDF) matching technique] and on those by two novel methods. These methods—based on error-in-variables regression and probabilistic factor analysis—extend standard TC by also accounting for nonlinear relations using quadratic polynomials. The relative differences between the error estimates of the ASCAT remotely sensed product by the quadratic and the linear methods are predominantly smaller than 10% in a case study based on remotely sensed, reanalysis, and in situ measured soil moisture over the contiguous United States. Exceptions with larger discrepancies indicate that nonlinear relations can pose a challenge to traditional TC analyses, as the simulations show they can introduce biases of either sign. In such cases, the use of nonlinear methods may complement traditional approaches for the error characterization of soil moisture products.

It usually suffers from long observing time and interference sensitivity when a radar transmits the high-range-resolution stepped-frequency chirp signal. Motivated by this, only partial pulses of the stepped-frequency chirp are utilized. For the obtained incomplete frequency data, a Bayesian model based on transfer learning is proposed to reconstruct the corresponding full-band frequency data. In the training phase, a complex beta process factor analysis (CBPFA) model is utilized to statistically model each aspect-frame from a set of given full-band frequency data, whose probability density function (pdf) can be learned from this CBPFA model. It is important to note that the numbers of factors and dictionaries are automatically learned from the data. The inference of CBPFA can be performed via the variational Bayesian (VB) method. In the reconstruction phase for the incomplete frequency data that "related" to the training samples, its corresponding full-band frequency data can be analytically reconstructed via the compressive sensing (CS) method and Bayesian criterion based on the transfer knowledge of the previous pdfs learned from the training phase. About the "relatedness" between each training frame and the incomplete test frequency data, we utilize the frame condition distribution of incomplete test frequency data to represent. The proposed method is validated on the measured high range resolution (HRR) data.