Minimum Variance Estimation Research Articles

Unscented recursive three-step filter based unbiased minimum-variance estimation for a class of nonlinear systems

For the direct feedthrough system where unknown input affects both process equation and measurement equation, an unscented recursive three-step filter based unbiased minimum-variance (URTSF-UMV) estimation algorithm is proposed. The algorithm is based on the unbiased minimum-variance (UMV) method and uses statistical linearisation technology to approximate the nonlinear system and the nonlinear measurement function to linear regression form. The estimation of unknown input is obtained from innovation through weighted least-squares (WLS) estimation. The approximate linear regression form allows us to process the nonlinear system with unknown input direct feedthrough by using the UMV state estimation framework, and derive the filter by minimising the trace of the state error covariance of the measurement update under the unbiased condition. The URTSF-UMV requires that the unknown input distribution matrix is full column rank. We use the full rank decomposition method to deal with the nonlinear system containing the unknown input rank-deficient distribution matrix. The effectiveness of the URTSF-UMV algorithm is demonstrated through an illustrative simulation example.

Maximum correntropy unscented filter based on unbiased minimum-variance estimation for a class of nonlinear systems

Introduction: The unscented Kalman filter based on unbiased minimum-variance (UKF-UMV) estimation is usually used to handle the state estimation problem of nonlinear systems with an unknown input. When the nonlinear system is disturbed by non-Gaussian noise, the performance of UKF-UMV will seriously deteriorate.Methods: A maximum correntropy unscented filter based on the unbiased minimum variance (MCUF-UMV) estimation method is proposed on the basis of the UKF-UMV without the need for estimation of an unknown input and uses the maximum correntropy criterion (MCC) and fixed-point iterative algorithm for state estimation.Results: When the measurement noise of the nonlinear system is non-Gaussian noise, the algorithm performs well.Discussion: Our proposed algorithm also does not require estimation of an unknown input, and there is no prior knowledge available about the unknown input or any prior assumptions. The unknown input can be any signal. Finally, a simulation example is used to demonstrate the effectiveness and reliability of the algorithm.

The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction

The minimum average variance estimation (MAVE) method has proven to be an effective approach to sufficient dimension reduction. In this study, we apply the computationally efficient optimization algorithm named alternating direction method of multipliers (ADMM) to a particular approach (MAVE or minimum average variance estimation) to the problem of sufficient dimension reduction (SDR). Under some assumptions, we prove that the iterative sequence generated by ADMM converges to some point of the associated augmented Lagrangian function. Moreover, that point is stationary. It also presents some numerical simulations on synthetic data to demonstrate the computational efficiency of the algorithm.

Performance bounds for source localization using tetrahedral microphones

The Cramér-Rao Bound (CRB) quantifies the minimum variance on a given unbiased estimation parameter. It can be used to derive a lower bound on source localization error for arrays, of which there are several probabilistic models in the literature. However, existing work only considers source localization using arrays of omnidirectional sensors. This presentation describes a model of the CRB as a minimum variance estimation of localization using multiple tetrahedral microphones which have cardioid microphones. Tetrahedral microphones are commonly used to record soundfields for virtual audio reproduction. The proposed method uses the cross spectral density of signals in order to calculate the CRB. This allows for more signal parameters to be included in the model. The model of the CRB was validated with an experiment in an anechoic room with a single sound source. Experimental results show the CRB forms a lower bound at low signal-to-noise ratios.

Robust Sparse Sufficient Dimension Reduction via Adaptive Lasso Penalty

In some multi-index models applications, there is an important role for dimension reduction and variable selection (VS) methods. The ALMAVE is a method for variables selection under sufficient dimension reduction theory settings. It combines the adaptive Lasso and MAVE (minimum average variance estimation) to produce sparse and accurate solutions. The ALMAVE is a very sensitive method to outliers in the response y due to use the least-squares criterion. In this article, we proposed robust ALMAVE. Also, an efficient estimation algorithm was proposed. The simulation studies and Logo design data analysis were employed to check the effectiveness of ALMAVE.

Research on the ascending path of traditional media’s intelligent transformation based on multivariate statistical analysis

Abstract Under the background of the new technological revolution and the rise of new media, traditional media try to innovate the media form, update the internal resource structure, enhance the ability of environmental adaptation, and then reshape their competitive advantages through intelligent transformation. In this paper, we comprehensively use factor analysis, cluster analysis, case study, and other methods in multivariate statistical analysis to conduct systematic research according to the ascending path of “the reasons for the continuous decline in the competitive advantage of traditional media → intelligent transformation strategy of traditional media → intelligent transformation to reshape the competitive advantage of traditional media”. Using factor analysis, we aim to obtain the minimum variance estimation of all residuals to construct a model that empirically analyzes the mechanism of intelligent transformation to reshape the competitive advantage of traditional media. The results of the study show that there is a complex group relationship between intelligence maturity, resource base, dynamic capability, resource orchestration capability, and the competitive performance of traditional media, and the consistency and overall consistency of the four conditional groupings are greater than the critical value of 0.80, and explain 58.7% of the cases. It indicates that intelligence maturity, resource base, dynamic capability, and resource orchestration capability constitute the competitive advantages of traditional media’s intelligent transformation and drive traditional media’s business development.

Fast Construction of Optimal Composite Likelihoods

A composite likelihood is a combination of low-dimensional likelihood objects useful in applications where the data have complex structure. Although composite likelihood construction is a crucial aspect influencing both computing and statistical properties of the resulting estimator, currently there does not seem to exist a universal rule to combine low-dimensional likelihood objects that is statistically justified and fast in execution. This paper develops a methodology to select and combine the most informative low-dimensional likelihoods from a large set of candidates while carrying out parameter estimation. The new procedure minimizes the distance between composite likelihood and full likelihood scores subject to a constraint representing the afforded computing cost. The selected composite likelihood is sparse in the sense that it contains a relatively small number of informative sub-likelihoods while the noisy terms are dropped. The resulting estimator is found to have asymptotic variance close to that of the minimum-variance estimator constructed using all the low-dimensional likelihoods.

Uncertainty propagation in absolute metabolite quantification for in vivo MRS of the human brain.

Absolute spectral quantification is the standard method for deriving estimates of the concentration from metabolite signals measured using in vivo proton MRS (1 H-MRS). This method is often reported with minimum variance estimators, specifically the Cramér-Rao lower bound (CRLB) of the metabolite signal amplitude's scaling factor from linear combination modeling. This value serves as a proxy for SD and is commonly reported in MRS experiments. Characterizing the uncertainty of absolute quantification, however, depends on more than simply the CRLB. The uncertainties of metabolite-specific (T1m , T2m ), reference-specific (T1ref , T2ref ), and sequence-specific (TR , TE ) parameters are generally ignored, potentially leading to an overestimation of precision. In this study, the propagation of uncertainty is used to derive a comprehensive estimate of the overall precision of concentrations from an internal reference. The propagated uncertainty is calculated using analytical derivations and Monte Carlo simulations and subsequently analyzed across a set of commonly measured metabolites and macromolecules. The effect of measurement error from experimentally obtained quantification parameters is estimated using published uncertainties and CRLBs from in vivo 1 H-MRS literature. The additive effect of propagated measurement uncertainty from applied quantification correction factors can result in up to a fourfold increase in the concentration estimate's coefficient of variation compared to the CRLB alone. A case study analysis reveals similar multifold increases across both metabolites and macromolecules. The precision of absolute metabolite concentrations derived from 1 H-MRS experiments is systematically overestimated if the uncertainties of commonly applied corrections are neglected as sources of error.

Evaluating bulk flow estimators for CosmicFlows–4 measurements

ABSTRACT For over a decade there have been contradictory claims in the literature about whether the local bulk flow motion of galaxies is consistent or in tension with the ΛCDM model. While it has become evident that systematics affect bulk flow measurements, systematics in the estimators have not been widely investigated. In this work, we thoroughly evaluate the performance of four estimator variants, including the Kaiser maximum likelihood estimator (MLE) and the minimum variance estimator (MVE). We find that these estimators are unbiased, however their precision may be strongly correlated with the survey geometry. Small biases in the estimators can be present leading to underestimated bulk flows, which we suspect are due to the presence of non-linear peculiar velocities. The uncertainty assigned to the bulk flows from these estimators is typically underestimated, which leads to an overestimate of the tension with ΛCDM. We estimate the bulk flow for the CosmicFlows–4 data and use mocks to ensure the uncertainties are appropriately accounted for. Using the MLE we find a bulk flow amplitude of 408 ± 165 kms−1 at a depth of $49\, \mathrm{Mpc} h^{-1}$, in reasonable agreement with ΛCDM. However using the MVE which can probe greater effective depths, we find an amplitude of 428 ± 108 kms−1 at a depth of $173\, \mathrm{Mpc} h^{-1}$, in tension with the model, having only a 0.11 per cent probability of obtaining a larger χ2. These measurements appear directed towards the Great Attractor region where more data may be needed to resolve tensions.

Unbiased minimum-variance estimation and dynamic event-driven disturbance rejection control for discrete time-varying systems

This paper studies a dynamic event-driven disturbance rejection control problem for a class of linear discrete time-varying systems with unknown external disturbances, random process and measurement noises. To obtain the accurate estimates of both the system states and external disturbances, simultaneously, an unbiased minimum-variance time-varying extended state observer is designed, and the stability of the estimation error system is analyzed. Then, a dynamic event-driven disturbance rejection controller is designed by minimizing the upper bound of the cost function of the closed-loop system over a finite horizon. It can be shown that, by applying the proposed control approach, not only the transmission frequency of the control signal is reduced, but also the external disturbances are compensated actively. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed control approaches.

Robust Z-Estimators for Semiparametric Moment Condition Models.

In the present paper, we introduce a class of robust Z-estimators for moment condition models. These new estimators can be seen as robust alternatives for the minimum empirical divergence estimators. By using the multidimensional Huber function, we first define robust estimators of the element that realizes the supremum in the dual form of the divergence. A linear relationship between the influence function of a minimum empirical divergence estimator and the influence function of the estimator of the element that realizes the supremum in the dual form of the divergence led to the idea of defining new Z-estimators for the parameter of the model, by using robust estimators in the dual form of the divergence. The asymptotic properties of the proposed estimators were proven, including here the consistency and their asymptotic normality. Then, the influence functions of the estimators were derived, and their robustness is demonstrated.

Explicit construction of the minimum error variance estimator for stochastic LTI-ss systems

We showcase the derivation of the optimal (minimum error variance) estimator, when one part of the stochastic LTI system outputs is not measured but is able to be predicted from the measured system outputs.

Model-free adaptive robust control method for high-speed trains

Abstract Aiming at the robustness issue in high-speed trains (HSTs) operation control, this article proposes a model-free adaptive control (MFAC) scheme to suppress disturbance. Firstly, the dynamic linearization data model of train system under the action of measurement disturbance is given, and the Kalman filter (KF) based on this model is derived under the minimum variance estimation criterion. Then, according to the KF, an anti-interference MFAC scheme is designed. This scheme only needs the input and output data of the controlled system to realize the MFAC of the train under strong disturbance. Finally, the simulation experiment of CRH380A HSTs is carried out and compared with the traditional MFAC and the MFAC with attenuation factor. The proposed control algorithm can effectively suppress the measurement disturbance, and obtain smaller tracking error and larger signal to noise ratio with better applicability.

Uncorrelated compensated isocurvature perturbations from kinetic Sunyaev-Zeldovich tomography

Compensated isocurvature perturbations (CIPs) are relative density perturbations in which a baryon-density fluctuation is accompanied by a dark matter density fluctuation such that the total-matter density is unperturbed. These fluctuations can be produced primordially if multiple fields are present during inflation, and therefore they can be used to differentiate between different models for the early Universe. Kinetic Sunyaev-Zeldovich (kSZ) tomography allows for the reconstruction of the radial-velocity field of matter as a function of redshift. This technique can be used to reconstruct the total-matter-overdensity field, independent of the galaxy-density field obtained from large-scale galaxy surveys. We leverage the ability to measure the galaxy- and matter-overdensity fields independently to construct a minimum-variance estimator for the primordial CIP amplitude, based on a mode-by-mode comparison of the two measurements. We forecast that a configuration corresponding to CMB-S4 and VRO will be able to detect (at $2\sigma$) a CIP amplitude $A$ (for a scale-invariant power spectrum) as small as $A\simeq 5\times 10^{-9}$. Similarly, a configuration corresponding to SO and DESI will be sensitive to a CIP amplitude $A\simeq 1\times 10^{-7}$. These values are to be compared to current constraints $A \leq {\cal O}(0.01)$.

Foreground-immune CMB lensing reconstruction with polarization

Extragalactic foregrounds are known to generate significant biases in temperature-based CMB lensing reconstruction. Several techniques, which include ``source hardening'' and ``shear-only estimators'' have been proposed to mitigate contamination and have been shown to be very effective at reducing foreground-induced biases. Here we extend both techniques to polarization, which will be an essential component of CMB lensing reconstruction for future experiments, and investigate the ``large-lens'' limit analytically to gain insight on the origin and scaling of foreground biases, as well as the sensitivity to their profiles.Using simulations of polarized point sources, we estimate the expected bias to both Simons Observatory and CMB-S4 like (polarization-based) lensing reconstruction, finding that biases to the former are minuscule while those to the latter are potentially non-negligible at small scales ($L\sim1000-2000$). In particular, we show that for a CMB-S4 like experiment, an optimal linear combination of point-source hardened estimators can reduce the (point-source induced) bias to the CMB lensing power spectrum by up to two orders of magnitude, at a $\sim4\%$ noise cost relative to the global minimum variance estimator.

Global Ocean Wind Speed Retrieval From GNSS Reflectometry Using CNN-LSTM Network

Ocean surface winds play an essential role in regulating the earth’s weather and climate, and the Cyclone GNSS (CYGNSS) mission launched in 2016 is designed specially to monitor the ocean wind speed. In this study, an innovative model is developed based on a deep learning method to retrieve the ocean wind speed by making full use of the spatiotemporal information of CYGNSS observations. The proposed model named CNN-LSTM is established based on two modules, i.e., the Convolution Neural Network (CNN) module that extracts the spatial features around the Specular Point (SP) from a Two-Dimensional matrix of delay-Doppler Map (DDM) and the Long Short-Term Memory (LSTM) module which extracts the temporal features over a time series. The performance of the ocean wind speed derived from CNN-LSTM is assessed with the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5) products. The results show that the wind speed derived from CNN-LSTM reveals an accuracy of 1.34 m/s in terms of root mean square error (RMSE) values, showing an improvement of about 36.8%, 14.6%, 6.3%, when compared to the official retrieval algorithm called Minimum Variance Estimator (MVE), Multilayer Perceptron (MLP) net, and the CNN, respectively, confirming the feasibility and effectiveness of the designed method. Among all the experiments in this study which apply machine learning-based algorithms, the wind speed achieved by CNN-LSTM presents the smallest RMSE value. Furthermore, the error analyses of the wind speed retrieval in spatial and temporal scale are also discussed, which indicate the robust performance of CNN-LSTM model. The results show that the CNN-LSTM model proposed in this study contributes to offering efficient processing of Global Navigation Satellite Systems Reflectometry (GNSS-R) observations and fully exploits the capabilities of high-accurate ocean wind speed retrieval on a global scale.

Robust Unscented Kalman Filter-Based Decentralized Multisensor Information Fusion for INS/GNSS/CNS Integration in Hypersonic Vehicle Navigation

INS/GNSS/CNS (inertial navigation system/global navigation satellite system/celestial navigation system) integration is a favourable navigation mode for hypersonic vehicles. However, since the measurements from GNSS and CNS are easily interfered during highly dynamic maneuvers, this integration is very difficult to achieve optimal navigation solution with existing information fusion techniques. This paper proposes a new method of decentralized multi-sensor information fusion based on robust UKF (unscented Kalman filter) for INS/GNSS/CNS integration to solve the above issue. Firstly, a fault detection-based robust UKF is established for local state estimation, in which a hypothesis test is constructed via the Mahalanobis distance of innovation to detect abnormal measurements in GNSS and CNS; and subsequently, a scalar factor is determined and further introduced into the innovation covariance to decrease the Kalman gain to improve the UKF robustness against abnormal measurements. Secondly, the traditional multi-sensor optimal data fusion technique is extended to nonlinear systems by use of unscented transformation in the framework of minimum variance estimation to fuse the local state estimations from INS/GNSS and INS/CNS subsystems. The proposed information fusion method can achieve the globally optimal fusion estimation results against abnormal measurements for hypersonic vehicle navigation with INS/GNSS/CNS integration. Semi-physical simulations and comparison analysis have validated the superior performance of the proposed method.

Signal selection for local module identification in linear dynamic networks: A graphical approach

In a dynamic network of interconnected transfer functions, it is not necessary to use all the node signals for estimating a local transfer function. Given the network topology, detailed conditions are available for selecting inputs and outputs in a (MIMO) predictor model that warrants consistent and minimum variance estimation of a target module through the so-called local direct method. Motivated by the existing minimum-input signal selection approach that gradually incorporates additional signals, an alternative graphical algorithm for signal selection is developed in this work by directly exploiting the complete network graph. Then, as a straightforward application of existing analytical results, graphical conditions for consistent identification are derived for the novel signal selection approach. We show by an example that in some cases, for the consistent estimation of the target module, the developed method leads to fewer selected signals than the original minimum-input method.

Adaptive Modified Unbiased Minimum-Variance Estimation for Highly Maneuvering Target Tracking With Model Mismatch

Due to the complexity, time variability, and mutability of the noncooperative maneuvering target, the dynamic tracking model of the target does not match with the actual state, which reduces the tracking accuracy or even completely tracking loss. In this article, an expectation maximization-based adaptive modified unbiased minimum-variance estimation (EM-AMUMVE) algorithm is proposed for highly maneuvering target tracking with model mismatch. First, the virtual maneuvering noise and the first-order Markov process model are integrated to quantitatively describe the maneuvering acceleration according to the boundness of the maneuvering acceleration. Then, the maneuvering acceleration and state estimation are derived based on the unbiased minimum-variance criterion, and the expectation maximization (EM) is introduced in the updating procedure of the quadratic Bayesian filter to adaptively estimate the mean and covariance of virtual maneuvering noise and thus to improve the accuracy of maneuvering acceleration estimation. Finally, the optimality of the adaptive modified maneuvering acceleration estimation is theoretically proved, and the tracking scenarios of time-varying maneuvering target with model mismatch and reentry gliding trajectory of typical hypersonic vehicle hypersonic technology vehicle 2 (HTV-2) are built to demonstrate the validness, convergence, sensitivity, and engineering practicability of the proposed algorithm.

Optimal Reconstruction of Human Motion From Scarce Multimodal Data

Wearable sensing has emerged as a promising solution for enabling unobtrusive and ergonomic measurements of the human motion. However, the reconstruction performance of these devices strongly depends on the quality and the number of sensors, which are typically limited by wearability and economic constraints. A promising approach to minimize the number of sensors is to exploit dimensionality reduction approaches that fuse <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">prior</i> information with insufficient sensing signals, through minimum variance estimation. These methods were successfully used for static hand pose reconstruction, but their translation to motion reconstruction has not been attempted yet. In this work, we propose the usage of functional principal component analysis to decompose multimodal, time-varying motion profiles in terms of linear combinations of basis functions. Functional decomposition enables the estimation of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> covariance matrix, and hence the fusion of scarce and noisy measured data with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information. We also consider the problem of identifying which elemental variables to measure as the most informative for a given class of tasks. We applied our method to two different datasets of upper limb motion D1 (joint trajectories) and D2 (joint trajectories + EMG data) considering an optimal set of measures (four joints for D1 out of seven, three joints, and eight EMGs for D2 out of seven and twelve, respectively). We found that our approach enables the reconstruction of upper limb motion with a median error of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.013 \pm 0.006$</tex-math></inline-formula> rad for D1 (relative median error 0.9%), and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.038 \pm 0.023$</tex-math></inline-formula> rad and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.003 \pm 0.002$</tex-math></inline-formula> mV for D2 (relative median error 2.9% and 5.1%, respectively).