Estimate Co Variance Research Articles

On the efficiency of the hybrid and the exact second-order sampling formulations of the EnKF: a reality-inspired 3-D test case for estimating biodegradation rates of chlorinated hydrocarbons at the port of Rotterdam

Abstract. This study considers the assimilation problem of subsurface contaminants at the port of Rotterdam in the Netherlands. It involves the estimation of solute concentrations and biodegradation rates of four different chlorinated solvents. We focus on assessing the efficiency of an adaptive hybrid ensemble Kalman filter and optimal interpolation (EnKF-OI) and the exact second-order sampling formulation (EnKFESOS) for mitigating the undersampling of the estimation and observation errors covariances, respectively. A multi-dimensional and multi-species reactive transport model is coupled to simulate the migration of contaminants within a Pleistocene aquifer layer located around 25 m below mean sea level. The biodegradation chain of chlorinated hydrocarbons starting from tetrachloroethene and ending with vinyl chloride is modeled under anaerobic environmental conditions for 5 decades. Yearly pseudo-concentration data are used to condition the forecast concentration and degradation rates in the presence of model and observational errors. Assimilation results demonstrate the robustness of the hybrid EnKF-OI, for accurately calibrating the uncertain biodegradation rates. When implemented serially, the adaptive hybrid EnKF-OI scheme efficiently adjusts the weights of the involved covariances for each individual measurement. The EnKFESOS is shown to maintain the parameter ensemble spread much better leading to more robust estimates of the states and parameters. On average, a well tuned hybrid EnKF-OI and the EnKFESOS respectively suggest around 48 and 21 % improved concentration estimates, as well as around 70 and 23 % improved anaerobic degradation rates, over the standard EnKF. Incorporating large uncertainties in the flow model degrades the accuracy of the estimates of all schemes. Given that the performance of the hybrid EnKF-OI depends on the quality of the background statistics, satisfactory results were obtained only when the uncertainty imposed on the background information is relatively moderate.

Estimation and asymptotic covariance matrix for stochastic volatility models

In this paper we compute the asymptotic variance-covariance matrix of the method of moments estimators for the canonical Stochastic Volatility model. Our procedure is based on a linearization of the initial process via the log-squared transformation of Breidt and Carriquiry (Modelling and prediction, honoring Seymour Geisel. Springer, Berlin, 1996). Knowledge of the asymptotic variance-covariance matrix of the method of moments estimators offers a concrete possibility for the use of the classical testing procedures. The resulting asymptotic standard errors are then compared with those proposed in the literature applying different parameter estimates. Applications on simulated data support our results. Finally, we present empirical applications on the daily returns of Euro-US dollar and Yen-US dollar exchange rates.

Hybrid estimators for mean aboveground carbon per unit area

Carbon accounting is at the heart of efforts to mitigate the effects of climate change. One approach for estimating population parameters for live tree stem carbon entails three primary steps: (1) construction of an individual tree, allometric carbon model, (2) application of the model to tree-level data for a probability sample of plots, and (3) use of a probability-based (design-based) estimator of mean carbon per unit area for a population of interest. Compliance with the IPCC good practice guidance requires satisfaction of two criteria, one related to minimizing bias and one related to minimizing uncertainty. For this carbon estimation procedure, the portion of uncertainty attributed to the variance of the probability-based estimator of the population mean using the plot-level predictions is usually correctly estimated, but the portion attributed to the variance of the allometric model estimator is usually ignored. The result is that the total variance of the population mean estimator cannot be asserted to comply with the IPCC good practice criteria because not only is it not minimized, it is not even correctly estimated.Within the framework of what is coming to be characterized as hybrid inference, model-based inferential methods were used to estimate the variance of the tree-level allometric model estimator which was then propagated through to the variance of the probability-based estimator of mean carbon per unit area. This combined estimator, consisting of a model-based estimator used to predict a variable for a probability sample of a population followed by a probability-estimator of the population total or mean using the sample predictions, is characterized as a hybrid estimator. For this study, two probability-based estimators of the mean were considered, simple random sampling estimators and model-assisted regression estimators that used airborne laser scanning (ALS) data as auxiliary information. The variance of the allometric model estimator incorporated variances of distributions of diameter and height measurement errors, covariances of model parameter estimators, model residual variance, and variances of distributions of wood densities and carbon content proportions.The novel features of the study included the hybrid inferential framework, consideration of six sources of uncertainty including the variances of distributions of wood densities and carbon content proportions, use of ALS data with model-assisted regression estimators of the population mean, and use of confidence intervals for the population mean as the basis for comparisons rather than intermediate products such as model prediction accuracy. The primary conclusions were that the variance of the allometric model estimator was negligible or marginally negligible relative to the variance of the probability estimator when using species-specific allometric models and simple random sampling estimators, but non-negligible when using species-specific models and model-assisted regression estimators and when using a non-specific model with either estimator.

Iterative Methods for Subspace and DOA Estimation in Nonuniform Noise

Usually, direction-of-arrival (DOA) estimators are derived under the assumption of uniform white noise, whose covariance matrix is a scaled identity matrix. However, in practice, the noise can be nonuniform with an arbitrary unknown diagonal covariance matrix. In this situation, the performance of DOA estimators may be deteriorated considerably if the noise nonuniformity is ignored. To tackle this problem, iterative approaches to subspace estimation are developed and the corresponding subspace-based DOA estimators are addressed. In our proposed methods, the signal subspace and noise covariance matrix are first determined by maximizing the log-likelihood (LL) function or solving a least-squares (LS) minimization problem, both of which are accomplished in an iterative manner. Then, the DOAs are determined from the subspace estimate and/or noise covariance matrix estimate with the help of traditional DOA estimators. As the signal subspace and noise covariance matrix can be computed in closed-form in each iteration, the proposals are computationally attractive. Furthermore, the signal subspace is directly calculated without the requirement of the exact knowledge of the array manifold, enabling us to handle array uncertainties by incorporating conventional subspace-based calibration algorithms. Simulations and experimental results are included to demonstrate the superiority of the proposed approaches.

Mean‐square filtering for polynomial discrete‐time systems with Poisson noises

The discrete-time state estimation problem for a class of stochastic non-linear polynomial systems confused with Poisson noises over linear observations is presented in this study. The filtering problem is solved computing the time-update and measurement-update equations for the state estimate and error covariance matrix. A finite number of filtering equations can be obtained by expressing the conditional expectations of polynomial terms as functions of the estimate and error covariance. The finite-dimensional filtering equations are explicitly derived in a closed form for third degree polynomial systems. Numerical simulations are performed for a third degree polynomial system and the performance of the designed filter is compared to the performances of the filter designed for polynomial systems confused with additive white Gaussian noises and the extended Kalman filter.

MIMO Precoding for Networked Control Systems with Energy Harvesting Sensors

In this paper, we consider a MIMO networked control system with an energy harvesting sensor, where an unstable MIMO dynamic system is connected to a controller via a MIMO fading channel. We focus on the energy harvesting and MIMO precoding design at the sensor so as to stabilize the unstable MIMO dynamic plant subject to the energy availability constraint at the sensor. Using the Lyapunov optimization approach, we propose a closed-form dynamic energy harvesting and dynamic MIMO precoding solution, which has an event-driven control structure. Furthermore, the MIMO precoding solution is shown to have an eigenvalue water-filling structure, where the water level depends on the state estimation covariance, energy queue and the channel state, and the sea bed level depends on the state estimation covariance. The proposed scheme is also compared with various baselines and we show that significant performance gains can be achieved.

A Continuous Updating Weighted Least Squares Estimator of Tail Dependence in High Dimensions

Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can be hard to compute in higher dimensions. An adaptive weighted least-squares procedure matching nonparametric estimates of the stable tail dependence function with the corresponding values of a parametrically specified proposal yields a novel minimum-distance estimator. The estimator is easy to calculate and applies to a wide range of sampling schemes and tail dependence models. In large samples, it is asymptotically normal with an explicit and estimable covariance matrix. The minimum distance obtained forms the basis of a goodness-of-fit statistic whose asymptotic distribution is chi-square. Extensive Monte Carlo simulations confirm the excellent finite-sample performance of the estimator and demonstrate that it is a strong competitor to currently available methods. The estimator is then applied to disentangle sources of tail dependence in European stock markets.

A New Method for State of Charge Estimation of Lithium-Ion Battery Based on Strong Tracking Cubature Kalman Filter

The estimation of state of charge (SOC) is a crucial evaluation index in a battery management system (BMS). The value of SOC indicates the remaining capacity of a battery, which provides a good guarantee of safety and reliability of battery operation. It is difficult to get an accurate value of the SOC, being one of the inner states. In this paper, a strong tracking cubature Kalman filter (STCKF) based on the cubature Kalman filter is presented to perform accurate and reliable SOC estimation. The STCKF algorithm can adjust gain matrix online by introducing fading factor to the state estimation covariance matrix. The typical second-order resistor-capacitor model is used as the battery’s equivalent circuit model to dynamically simulate characteristics of the battery. The exponential-function fitting method accomplishes the task of relevant parameters identification. Then, the developed STCKF algorithm has been introduced in detail and verified under different operation current profiles such as Dynamic Stress Test (DST) and New European Driving Cycle (NEDC). Making a comparison with extended Kalman filter (EKF) and CKF algorithm, the experimental results show the merits of the STCKF algorithm in SOC estimation accuracy and robustness.

基于无源定位观测方程的一类伪线性加权最小二乘定位闭式解及其理论性能分析

Utilizing a type of special measurement equation from the passive location problem, a novel theoretical analysis framework, which transforms nonlinear localization equations into pseudo-linear equalities and locates the source with a closed-form solution, is presented. An algebraic model is constructed for pseudo-linearizing the nonlinear localization equations, and the corresponding pseudo-linear weighted least-squares solution, namely Pwls-a, is provided under the assumption that system errors (i.e., observer position and velocity perturbations) are not present. Moreover, the estimation covariance matrix of solution Pwls-a is derived through a first-order perturbation analysis method, and its theoretical performance is proved to attain the corresponding Cramer-Rao bound (CRB). Furthermore, the statistical covariance matrix is also mathematically analyzed in a case in which system errors exist; the result shows that its asymptotical estimation variance cannot reach the relevant CRB in the presence of system errors. As a consequence, a pseudo-linear weighted least-squares solution, namely Pwls-b, is proposed to mitigate the effects of system errors, and its statistical performance is proved to be asymptotically equal to the CRB under the existence of system errors. In addition, the solution Pwls-b is extended into a scenario in which multiple targets are present. Finally, a location scenario with AOA/TDOA/GROA measurements is used as an example to describe the application of the pseudo-linearization method. Simulation experiments are conducted to show the effectiveness of the theoretical analysis and the advantages of the location solutions in this paper.

Special issue on Co-prime sampling and arrays

Co-prime sampling and co-prime arrays have recently been shown to improve active and passive sensing in radar and under-water acoustics using both narrowband and wideband signal plat-forms. Co-prime processing provides a systematical framework for sparse sampling and array configuration with increased aperture and improved spatial resolution. Co-prime based approaches to sampling and arrays can combat ambiguity and provide unique answers to target coordinates under forced coarse sampling in time, frequency, and space. Temporal and spatial co-prime samplings make advances in direction-of-arrival (DOA) estimation, spectrum sensing, and sparse covariance sketching. They find broad applications in synthetic aperture radar (SAR), radio frequency (RF) surveillance, target localization, wideband urban radar processing, space–time adaptive processing, and nonstationary array processing utilizing Doppler signatures and instantaneous frequency source characteristics.

The New Kumaraswamy Kumaraswamy Family of Generalized Distributions with Application

Finding the best fitted distribution for data set becomes practically an important problem in world of data sets so that it is useful to use new families of distributions to fit more cases or get better fits than before. In this paper, a new generating family of generalized distributions so called the Kumaraswamy - Kumaraswamy (KW-KW) family is presented. Four important common families of distributions are illustrated as special cases from the KW KW family. Moments, probability weighted moments, moment generating function, quantile function, median, mean deviation, order statistics and moments of order statistics are obtained. Parameters estimation and variance covariance matrix are computed using maximum likelihood method. A real data set is used to illustrate the potentiality of the KW KW weibull distribution (which derived from the kw kw family) compared with other distributions.

On-Board Event-Based State Estimation for Trajectory Approaching and Tracking of a Vehicle.

For the problem of pose estimation of an autonomous vehicle using networked external sensors, the processing capacity and battery consumption of these sensors, as well as the communication channel load should be optimized. Here, we report an event-based state estimator (EBSE) consisting of an unscented Kalman filter that uses a triggering mechanism based on the estimation error covariance matrix to request measurements from the external sensors. This EBSE generates the events of the estimator module on-board the vehicle and, thus, allows the sensors to remain in stand-by mode until an event is generated. The proposed algorithm requests a measurement every time the estimation distance root mean squared error (DRMS) value, obtained from the estimator's covariance matrix, exceeds a threshold value. This triggering threshold can be adapted to the vehicle's working conditions rendering the estimator even more efficient. An example of the use of the proposed EBSE is given, where the autonomous vehicle must approach and follow a reference trajectory. By making the threshold a function of the distance to the reference location, the estimator can halve the use of the sensors with a negligible deterioration in the performance of the approaching maneuver.

Huber’s M-Estimation-Based Process Uncertainty Robust Filter for Integrated INS/GPS

The integration of the inertial navigation system and the global positioning system (INS/GPS) is a widely used procedure for position and attitude determination applications. The Kalman type filter (KTF) is the primary mechanism to perform the integration. In the KTF, the process noise is always assumed to be Gaussian distribution, which may be violated by the vehicle's severe maneuver, resulting in a much degraded performance. In this paper, the Huber's M-estimation methodology is investigated to suppress the process uncertainty, founded on the cascaded form of the M-estimation-based Kalman filter. An iterated algorithm is designed to construct the weighted matrix to rescale the prior state estimate covariance. The proposed process uncertainty robust algorithm is embedded into the newly derived modified unscented quaternion estimator to perform the standard inertial navigation equations-based INS/GPS integration. The car-mounted experiments are carried out to validate the proposed method against the process uncertainty.

Fast Kalman filter using hierarchical matrices and a low-rank perturbative approach

We develop a fast algorithm for a Kalman filter applied to the random walk forecast model. The key idea is an efficient representation of the estimate covariance matrix at each time step as a weighted sum of two contributions—the process noise covariance matrix and a low-rank term computed from a generalized eigenvalue problem, which combines information from the noise covariance matrix and the data. We describe an efficient algorithm to update the weights of the preceding terms and the computation of eigenmodes of the generalized eigenvalue problem. The resulting algorithm for the Kalman filter with a random walk forecast model scales as in memory and in computational cost, where N is the number of grid points. We show how to efficiently compute measures of uncertainty and conditional realizations from the state distribution at each time step. An extension to the case with nonlinear measurement operators is also discussed. Numerical experiments demonstrate the performance of our algorithms, which are applied to a synthetic example from monitoring CO2 in the subsurface using travel-time tomography.

Increased Incidence of Thromboembolic Event Rates in Patients Diagnosed with Polycythemia Vera: Results from an Observational Cohort Study

Background: Polycythemia vera (PV) is a rare hematologic neoplasm with significant morbidities. Blood hyperviscosity reflected by elevated hematocrit (HCT) levels is believed to contribute to most disease symptoms and complications including thrombotic events (TE), which are among the most serious clinical manifestations of PV. Concurrent with ongoing Phase III trials in PV, this study assesses treatment patterns, TE event rates, and direct costs associated with PV in real-world practice settings. Preliminary results on incidence of TE events in a privately insured US population are presented here.Methods: Data for this retrospective observational study were taken from the MarketScan database containing medical and drug utilization data for ~40 million unique individuals enrolled in employer-sponsored private health insurance plans in the United States. Patients with at least two claims of a PV diagnosis (International Classification of Diseases, 9th Clinical Modification [ICD-9-CM] code 238.4) at least 30 days apart, between July 1, 2008 and December 31, 2011, were selected for study inclusion. Using propensity score (PS) methods, we identified a non-PV control group matched with PV cases on demographics and comorbidities. PS matching is frequently used in observational studies to achieve balance on observed covariates between cases and controls. Incident TE events were identified using ICD-9 diagnosis codes and were assessed from the index date (first PV diagnosis) until the earliest of plan disenrollment or end of the database. Both fatal and nonfatal events were included, although a distinction could not be ascertained in these data. The TE event rate was defined as the number of unique patients with a new TE occurrence (i.e., incident cases) per 1000 person-years (PYs) of observation time. Unadjusted TE event rates and incident rate ratios (RR) expressing the increased frequency of events in PV cases relative to controls were estimated for overall (i.e., any), cerebral, arterial, and venous TE events. Kaplan-Meyer (KM) analyses were performed to estimate time to event for each of the event categories listed above.Results: The cohort comprised 8,124 PV patients with mean age of 51 years; 71% of patients were male. Table 1 describes the quality of balance between cases and matched controls for selected variables that differed significantly before PS matching. As shown in Figure 1, TE event rates were significantly higher among PV cases compared to matched controls (overall: 14.3 vs. 4.9/1000 PYs [RR 2.90 (95% CI: 2.28-3.68)], cerebral: 3.5 vs. 1.3/1000 PYs [RR 2.66 (95% CI: 1.66-4.24)], arterial: 6.9 vs. 2.4/1000 PYs [RR 3.16 (95% CI: 2.05-4.87)], and venous: 4.7 vs. 1.5/1000 PYs [RR 2.94 (95% CI: 2.08-4.15)]). KM analyses showed that event probabilities over time were significantly higher among PV cases (Figure 2). Due to high censoring in both the groups, median time to TE event could not be calculated. However, among those with an event, median time to event was shorter (but not statistically significant) among PV cases compared to controls for overall (7.0 vs. 9.7 months [P=0.0817]), cerebral (8.5 vs. 13.1 months [P=0.0634]), and arterial (9.2 vs. 14.7 months [P=0.0768]), but slightly higher for venous (5.3 vs. 4.8 months [P=0.5583]).Conclusion: Patients with PV have significantly higher rate of TE events compared with matched controls. This rate may be higher in patients with HCT > 45%. Further analyses in this ongoing study will assess patient level predictors of cardiovascular and TE events and their impact on overall economic burden of PV.Table 1Comparison of Baseline Characteristics between PV Cases and Matched ControlsPV Cases (n=8124)Control (n=8124)P-value ‡PercentAge Group (years)<181.71.70.2418 - 4419.919.045 - 5958.459.960 - 6420.119.4GenderMale71.571.20.65Geographic regionNorth Central20.620.90.48North East16.516.7South40.841.1West19.218.1Unknown3.03.2Year of diagnosis200817.317.60.16200927.729.0201027.527.2201127.526.2Charlson comorbidity index (CCI) score (mean [SD])0.8 (1.4)0.7 (1.4)0.00Note: Other covariates in the PS estimation include payer type, plan type, employment status, and relationship to employee.‡P-values based on McNemar’s test for categorical variables and Wilcoxon Signed Rank Sum test for continuous variables. [Display omitted] [Display omitted] DisclosuresGoyal:Novartis Pharmaceuticals Corp: Employee of RTI Health Solutions, which received research funding for this work. Other. Davis:Novartis Pharmaceuticals Corporation: Research Funding. Mounedji:Novartis Pharma: Employment. Kaye:Novartis Pharmaceuticals Corp: Employee of RTI Health Solutions, which received research funding for this work. Other.

Consider unobservable uncertain parameters using radio beacon navigation during Mars entry

This paper presents a navigation algorithm based on the extended consider Kalman filter (ECKF) to mitigate the adverse effects of unobservable uncertain parameters using radio measurements during Mars entry phase. Consistency of the Mars entry navigation using a radio beacon navigation scheme is also demonstrated. A nonlinear consider approach is utilized by incorporating the covariances of the unobservable uncertain atmospheric density and the ballistic coefficient into the state estimate covariance; parameters are specifically not estimated directly to improve the navigation accuracy and robustness during the Mars entry phase. Perturbation is introduced to analyze the navigation state errors from each unobservable uncertain parameter. Numerical simulations show that the presented ECKF-based navigation algorithm is more accurate and robust than the augmented extended Kalman filter for unobservable uncertain parameters.

A Gaussian pseudolikelihood approach for quantile regression with repeated measurements

To enhance the efficiency of regression parameter estimation by modeling the correlation structure of correlated binary error terms in quantile regression with repeated measurements, we propose a Gaussian pseudolikelihood approach for estimating correlation parameters and selecting the most appropriate working correlation matrix simultaneously. The induced smoothing method is applied to estimate the covariance of the regression parameter estimates, which can bypass density estimation of the errors. Extensive numerical studies indicate that the proposed method performs well in selecting an accurate correlation structure and improving regression parameter estimation efficiency. The proposed method is further illustrated by analyzing a dental dataset.

Optimal Sensor Scheduling in Batch Processes Using Convex Relaxations and Tchebycheff Systems Theory

In several industrial processes, measurements are limited due to time or cost constraints. Hence, scheduling of these measurements to obtain maximally informative and accurate estimates of the states becomes important. The focus of this contribution is to determine a schedule of measurements that maximizes the quality of the estimates at the end of a finite time horizon. This work finds applications in batch chemical processes. The estimate covariance matrix as obtained by applying standard Kalman filtering theory is approximated and the original problem is relaxed and reformulated as a cone program. For a certain class of systems, the approximated covariance matrix is parameterized in terms of a point belonging to a moment space induced by a Tchebycheff system. The theory of Tchebycheff systems is used to determine an improved upper bound on the guaranteed minimum number of measurements. A tractable solution methodology to obtain the optimal cost and a parsimonious discrete schedule using the theory of cone programming, generalized barrier functions and Tchebycheff systems is described.

Asymptotically Efficient Distributed Estimation With Exponential Family Statistics

This paper studies the problem of distributed parameter estimation in multiagent networks with exponential family observation statistics. A certainty-equivalence type distributed estimator of the consensus-plus-innovations form is proposed in which, at each observation sampling epoch, agents update their local parameter estimates by appropriately combining the data received from their neighbors and the locally sensed new information (innovation). Under global observability of the networked sensing model, i.e., the ability to distinguish between different instances of the parameter value based on the joint observation statistics, and mean connectivity of the inter-agent communication network, the proposed estimator is shown to yield consistent parameter estimates at each network agent. Further, it is shown that the distributed estimator is asymptotically efficient, in that, the asymptotic covariances of the agent estimates coincide with that of the optimal centralized estimator, i.e., the inverse of the centralized Fisher information rate. From a technical viewpoint, the proposed distributed estimator leads to non-Markovian mixed time-scale stochastic recursions and the analytical methods developed in this paper contribute to the general theory of distributed stochastic approximation.

Recursive identification of time-varying systems: Self-tuning and matrix RLS algorithms

In this paper, a new parallel adaptive self-tuning recursive least squares (RLS) algorithm for time-varying system identification is first developed. Regularization of the estimation covariance matrix is included to mitigate the effect of non-persisting excitation. The desirable forgetting factor can be self-tuning estimated in both non-regularization and regularization cases. We then propose a new matrix forgetting factor RLS algorithm as an extension of the conventional RLS algorithm and derive the optimal matrix forgetting factor under some reasonable assumptions. Simulations are given which demonstrate that the performance of the proposed self-tuning and matrix RLS algorithms compare favorably with two improved RLS algorithms recently proposed in the literature.