Sequential Estimation Method Research Articles

Recursive linear continuous quaternion attitude estimator from vector observations

Attitude estimation from vector observations is widely employed in aerospace applications for accurate integrated navigation using solutions to Wahba's problem. Wahba's solutions are practical but may corrupt facing critical cases in the presence of almost collinear reference vector measurements, which is inevitable in robotic applications with redundant sensor arrays or platforms with celestial vision sensors in similar directions. Different from existing algorithms, this paper presents a novel sequential multiplicative quaternion attitude estimation method from various vector sensor outputs. The unique linear constitution of the algorithm leads to its specific name of Recursive Linear Quaternion Estimator (RLQE). The algorithm's architecture is designed to use each single pair of vector observation linearly so that the vector observations can be arbitrarily chosen and fused. The closed-form covariance of the RLQE is derived that builds up the existence of a highly reliable RLQE Kalman filter (RLQE-KF). Simulations and experiments are carried out to give the performances of our algorithm and representative ones. Compared with other works, the proposed RLQE maintains good precision, better consistency and lower variance bounds. Moreover, the attitude estimation performance with critical cases is especially much better than conventional Wahba's solution on its continuity, accuracy and variance.

Direct Instantaneous Frequency Rate Estimation to Improve the Carrier Estimation Performance in Mars Entry, Descent, and Landing Flight

This paper focuses on the carrier estimation performance improvement in Mars entry, descent, and landing (EDL) flights. Carrier reconstruction could be used for trajectory derivation and Martian atmosphere profile inversion, and is the critical information for mission operations, as it helps determine the flight status of the spacecraft, demodulate the downlink information. The current approach is maximum likelihood estimation based on a two-dimensional (2D) maximum energy search algorithm, which computes the grid energy over all the combinations of frequency cells and frequency rate cells among the search space. Although it has good performance on robust estimation, the frequency estimation accuracy is limited due to the short coherent integration. An instantaneous frequency rate tracking approach based on the cubic phase function (CPF) is proposed that directly estimates the instantaneous frequency rate over the frequency rate cells, followed by the frequency estimation among the frequency cells. A sequential estimation method is introduced to propose the sequential CPF statistics, which uses the a priori Doppler phase information to suppress the noise squaring loss inherent in the standard CPF statistics. Simulations have been made on the released Mars Science Laboratory EDL trajectory for the two approaches, which show that considerable estimation improvement has been achieved for aerobraking flight by the new algorithm.

Generalized Additive Models for Pair-Copula Constructions

ABSTRACTPair-copula constructions are flexible dependence models that use bivariate copulas as building blocks. In this article, we extend them with generalized additive models to allow covariates effects. Borrowing ideas from a traditionally univariate context, we let each pair-copula parameter depend directly on the covariates in a parametric, semiparametric, or nonparametric way. We propose a sequential estimation method that we study by simulation, and apply it to investigate the time-varying dependence structure between the intraday returns on four major foreign exchange rates. An R package, scripts reproducing the results in this article, and additional simulation results are provided as supplementary material.

Test-retest reliability of two-dimensional video analysis during running

ObjectivesTo examine test-retest reliability of two-dimensional measured frontal and sagittal plane kinematics during running, and to determine how many steps to include to reach and maintain a stable mean. DesignReliability study. SettingResearch laboratory. ParticipantsTwenty-one recreational runners. Main outcome measuresLateral trunk position, contralateral pelvic drop, femoral adduction, hip adduction, knee flexion and ankle dorsiflexion during midstance, and foot and tibia inclination at initial contact were measured with two-dimensional video analysis during running for 10 consecutive steps for both legs. All participants were tested twice one week apart. A sequential estimation method was used to determine the number of steps needed to reach a stable mean. Intraclass correlation coefficients (ICC) and smallest detectable differences (SDD) were calculated. ResultsThe minimal number of steps was 6.3 ± 0.3. Lateral trunk position, femoral adduction and foot inclination showed excellent reliability (ICC 0.90–0.99; SDD 1.3°–2.3°). Tibia inclination and ankle dorsiflexion showed good to excellent reliability (ICC 0.73–0.92; SDD 2.2°–4.8°). Hip adduction and knee flexion showed good reliability (ICC 0.82–0.89; SDD 2.3°–3.8°). Contralateral pelvic drop showed moderate to good reliability (ICC 0.59–0.77; SDD 2.7°–2.8°). ConclusionTwo-dimensional video analysis is reliable to assess running kinematics on different days. The mean of at least 7 steps should be included.

Sequential source localisation and range estimation based on shrinkage algorithm

This study presents the shrinkage-based sequential source localisation and range estimation algorithms. The shrinkage factor is found using the variance of the estimate in the existing shrinkage algorithm. However, the variance of the estimate is difficult to calculate when the form of the estimate is complex. To circumvent this problem, the authors propose a shrinkage algorithm that employs the Cramer-Rao lower bound (CRLB) instead of the variance for the maximum likelihood (ML) estimate. The variance of the ML estimate and CRLB were found to be similar in simulation results. Furthermore, Stein's unbiased risk estimator and Ledoit-Wolf methods are used to determine the shrinkage factor. The resulting estimation accuracy of the proposed shrinkage-based sequential source localisation and range estimation methods was similar with that of the existing shrinkage algorithm.

Sequential Parameter Estimation Using Modal Dispersion Curves in Shallow Water**Supported by the National Natural Science Foundation of China under Grant Nos 11434012, 11774374, 11404366 and 41561144006.

Existing sequential parameter estimation methods use the acoustic pressure of a line array as observations. The modal dispersion curves are employed to estimate the sound speed profile (SSP) and geoacoustic parameters based on the ensemble Kalman filter. The warping transform is implemented to the signals received by a single hydrophone to obtain the dispersion curves. The experimental data are collected at a range-independent shallow water site in the South China Sea. The results indicate that the SSPs are well estimated and the geoacoustic parameters are also well determined. Comparisons of the observed and estimated modal dispersion curves show good agreement.

Sequential fusion estimation for clustered sensor networks

We consider multi-sensor fusion estimation for clustered sensor networks. Both sequential measurement fusion and state fusion estimation methods are presented. It is shown that the proposed sequential fusion estimation methods achieve the same performance as the batch fusion one, but are more convenient to deal with asynchronous or delayed data since they are able to handle the data that are available sequentially. Moreover, the sequential measurement fusion method has lower computational complexity than the conventional sequential Kalman estimation and the measurement augmentation methods, while the sequential state fusion method is shown to have lower computational complexity than the batch state fusion one. Simulations of a target tracking system are presented to demonstrate the effectiveness of the proposed results.

Stochastic parameterization identification using ensemble Kalman filtering combined with maximum likelihood methods

For modelling geophysical systems, large-scale processes are described through a set of coarse-grained dynamical equations while small-scale processes are represented via parameterizations. This work proposes a method for identifying the best possible stochastic parameterization from noisy data. State-of-the-art sequential estimation methods such as Kalman and particle filters do not achieve this goal successfully because both suffer from the collapse of the posterior distribution of the parameters. To overcome this intrinsic limitation, we propose two statistical learning methods. They are based on the combination of the ensemble Kalman filter (EnKF) with either the expectation–maximization (EM) or the Newton–Raphson (NR) used to maximize a likelihood associated to the parameters to be estimated. The EM and NR are applied primarily in the statistics and machine learning communities and are brought here in the context of data assimilation for the geosciences. The methods are derived using a Bayesian approach for a hidden Markov model and they are applied to infer deterministic and stochastic physical parameters from noisy observations in coarse-grained dynamical models. Numerical experiments are conducted using the Lorenz-96 dynamical system with one and two scales as a proof of concept. The imperfect coarse-grained model is modelled through a one-scale Lorenz-96 system in which a stochastic parameterization is incorporated to represent the small-scale dynamics. The algorithms are able to identify the optimal stochastic parameterization with good accuracy under moderate observational noise. The proposed EnKF-EM and EnKF-NR are promising efficient statistical learning methods for developing stochastic parameterizations in high-dimensional geophysical models.

Parametric estimation of dispersive viscoelastic layered media with application to structural health monitoring

We present a sequential Bayesian estimation method to estimate the material parameters that govern the one-dimensional propagation of shear waves through continuous, layered, viscoelastic solids. While the proposed estimation method is generic, namely, can be applied to waveform inversion problems that satisfy the above conditions, we here employ it for system identification of building structures. We approximate the linear-elastic response of building structures subjected to low-amplitude earthquake base excitations by a multilayer dispersive shear beam model with Kelvin-Voigt material subjected to vertically propagating shear waves. Utilizing the proposed sequential Bayesian estimation method, we sequentially update the probability distribution function of the unknown parameters to reduce the discrepancies between the estimated and measured frequency response functions. We next verify and validate the performance of the proposed estimation method and investigate the limitations of the presented structural system identification approach using two case studies. In the first case study, we use the simulated structural response of a three-dimensional 52-story building model subjected to bi-directional low-amplitude ground shakings. We estimate the frequency-dependent phase velocity and damping ratio, as well as the mass distribution along the building height. Then, we verify the structural damage detection and localization capabilities of the presented system identification approach by comparing the wave model parameters estimated from simulated response of undamaged and damaged structural models. In the second case study, we use data measured from a shake table experiment on a full-scale five-story reinforced concrete building specimen, where the estimated wave model parameters capture the progressive structural damage in the test specimen. The validation studies suggest that the sequential Bayesian estimation method based on viscoelastic dispersive wave propagation can be used for system and damage identification of building structures.

Direction-Of-Arrival Estimation and Tracking Based on a Sequential Implementation of C-SPICE with an Off-Grid Model.

This paper focuses on the problem of estimating and tracking time-varying direction-of-arrivals (DoAs) with an antenna array. A sequential DoA estimation method is proposed by extending the capon and sparse iterative covariance-based estimation (C-SPICE) method, which is an iterative off-grid method for estimating constant DoAs. Then, a moving average initialization technique is introduced such that the spatial spectrum information estimated in this snapshot can be utilized in the next one. In uniform linear arrays (ULAs), we replace the uniform grid in direction domain with that in a “frequency” domain, to improve estimation accuracy without additional complexity in practical applications. The validity and efficiency of the proposed methods are demonstrated through numerical experiments.

O-38 The influence of body composi-tion on paediatric drug dosing

Background Body size is an important patient covariate in scaling drug doses. While total body weight has been the most commonly used size descriptor, fat free mass (FFM) has been advocated as an alternative size descrip-tor to scale drug doses in adults and children. FFM de-scribes the non-fat component of the body thus having a better correlation with the metabolic rate and drug clear-ance (CL). The aim of this work was to evaluate FFM as a covariate in a PK model of unfractionated heparin (UFH) developed in a paediatric population. Methods Data from 64 infants and children who re-ceived 75–100 IU/kg of UFH during cardiac angiography were analysed. Four plasma samples were collected at baseline and at 15, 30, 45, and 120 min post-dose. UFH concentration (231 measurements) was quantified using a protamine titration assay. UFH effect (164 mea-surements) was quantified using activated partial throm-boplastin time (aPTT). A PKPD model was fitted to the data using the non-linear mixed effects modelling (in NONMEM v7.2). Various patient covariates such as age, weight (Wt), body surface area, and FFM were tested. The final model was evaluated using the likelihood ratio test and visual predictive checks (VPCs). Results A one-compartment model with linear elimina-tion provided the best fit for the dose-concentration data. Wt and FFM had substantial influence on model fit; FFM was preferred statistically. A linear model provided the best fit for the concentration-effect data using the PPP and D sequential estimation method. Censored PD data (above the upper limit of quantification) were accounted for us-ing likelihood estimation. The PKPD model performed well using visual predictive checks. Conclusion A PKPD model to describe the time-course of UFH effect was developed in a paediatric population which received a high single bolus dose. FFM was shown to describe drug disposition well and can potentially be used in dose calculation after appropriate evaluation.

An analytical model of sequential hypothesis estimation for femtocell network optimisation

ABSTRACTFemto Base Stations (FBSs) are small cells that provide radio coverage for low-power-consuming smart mobile devices in indoors. In this article, we contemplate on the networks optimisation issue of a number of FBSs which anticipate joint network coverage in commercial area. In such a situation, FBSs reduce coverage overlapping, network holes and make sure a balanced traffic load is distributed among them. We apply sequential hypothesis estimation methods to quantify the probabilistic accuracy of a provided femtocell (small cell) configuration at runtime. If any disobeying is observed in providing the required standard of quality service, a self-optimisation process is enabled to build on the present configuration.

Estimation of gravity‐wave parameters to alleviate the delay in the Antarctic vortex breakup in general circulation models

The impact of optimal parameters in a non‐orographic gravity‐wave drag parametrization on the middle atmosphere circulation of the Southern Hemisphere is examined. Optimal parameters are estimated using a data assimilation technique. The proposed technique aims to reduce the delay in the winter vortex breakdown of the Southern Hemisphere found in general circulation models, which may be associated with a poor representation of gravity‐wave activity. We introduce two different implementations of the parameter estimation method: an offline estimation method and a sequential estimation method. The delay in the zonal‐mean zonal‐wind transition is largely alleviated by the optimal gravity‐wave parameters. The sequential method diminishes the model biases during winter vortex evolution, through gravity‐wave drag alone. On the other hand, the offline method accounts better for unresolved–resolved wave interactions and the zonal‐wind transition. We show that the final warmings in the lower mesosphere are driven mainly by planetary‐wave breaking. These are affected by changes in the gravity‐wave drag that are responsible for stratospheric preconditioning. Parameter estimation during the vortex breakdown is a challenging task that requires the use of sophisticated estimation techniques, because there are strong interactions between unresolved gravity‐wave drag and planetary waves.

A weight modification sequential method for VSC-MTDC power system state estimation

This paper presents an effective sequential approach based on weight modification for VSC-MTDC power system state estimation, called weight modification sequential method. The proposed approach simplifies the AC/DC system state estimation algorithm through modifying the weight of state quantity to keep the matrix dimension constant. The weight modification sequential method can also make the VSC-MTDC system state estimation calculation results more ccurate and increase the speed of calculation. The effectiveness of the proposed weight modification sequential method is demonstrated and validated in modified IEEE 14 bus system.

Ensemble-based release estimation for accidental river pollution with known source position

Dispersion model is an important tool for decision makers to accurately assess risks and effectively plan countermeasures during river pollution accidents, but their applications suffer from significant modeling uncertainties, primarily due to the scarce information of the source. A fully sequential inverse estimation method is proposed to reconstruct the temporal release for accidental river pollution. The method is based on a one-dimensional advection-dispersion model in conjunction with the augmented ensemble Kalman filter method. Detailed analysis of the ensemble background error covariance (BEC) matrix is conducted to elucidate the “flow-dependent” mechanism, which enables the inversion method to simultaneously take into account the uncertainties in the hydrological parameters (mean flow velocity and longitudinal dispersion coefficient). The method is evaluated with six field tracer experiments with various mean flow velocities, ranging from 0.085 to 0.889ms−1, and also compared with the commonly used Tikhonov regularization inverse estimation method to demonstrate its performance improvement. The results indicate that it successfully reconstructs the temporal release and reduces the relative errors of the total release estimation by about 12.4% on average compared with the Tikhonov method, since the errors caused by the uncertainties in mean flow velocity and longitudinal dispersion coefficient are effectively alleviated.

Hybrid Sequential Fusion Estimation for Asynchronous Sensor Network-Based Target Tracking

This brief presents a sequential fusion estimation method for maneuvering target tracking in asynchronous wireless sensor networks. The modeling error caused by asynchronous sampling and communication uncertainties is considered and compensated for by introducing a time-varying fading factor into the unscented Kalman filter (UKF). A square root form of the unscented strong tracking filter (SR-USTF) based on QR decomposition is proposed to improve the stability and performance of the USTF. Moreover, a hybrid sequential fusion estimation method is presented to estimate the state of the target, and the proposed sequential fusion estimation method combines the superiorities of both the SR-USTF and the conventional UKF, and is able to deal with communication uncertainties such as time delay and packet loss in a unified framework. Both simulations and experiments of an E-puck robot tracking example are provided to demonstrate the effectiveness and superiorities of the proposed sequential fusion estimation method.

Rapid Inverse Method to Measure Thermal Diffusivity of Low-Moisture Foods.

Thermal diffusivity is an important transport property needed in modeling and computations of transient heat transfer in basic food processing operations. In addition, the prediction of nutritional and microbial changes occurring in food during thermal processing requires knowledge of thermal diffusivity of foods. The objectives of this study were to develop a new nonisothermal and nonlinear determination method of thermal diffusivity and to measure the thermal diffusivity of low-moisture foods using that new method. Thermal diffusivities of 5 kinds of low-moisture foods (almond meal, corn meal, wheat flour, chocolate fudge, and peanut butter) were estimated using an inverse technique. Samples were canned and heated at the surface in a water bath at about 70 °C. The 1-dimensional transient heat conduction problem for radial coordinates was solved with a finite-difference model. The thermal diffusivity of each of the 5 samples was determined by the ordinary least squares and sequential estimation methods, respectively. Predicted and observed temperature matched well, with maximum residuals of 0.9 °C. The thermal diffusivity values of the samples ranged from 9.8 × 10-8 to 1.3 × 10-7 m2 /s. The advantages of this method are that the device and the estimation method are simple, inexpensive, rapid, and can handle large spatial temperature gradients, such as those experienced during heating of low-moisture foods. The results obtained in this study will be useful in the design of equipment and in calculations for the thermal processing of low-moisture foods.

Determinants of route choice behavior: A comparison of shop versus work trips using the Potential Path Area - Gateway (PPAG) algorithm and Path-Size Logit

This paper presents an in-depth comparison of route choice models for work and shop vehicle trips—with emphasis on the interactions between route attributes and individual characteristics—to better understand the route choice determinants that are assumed to vary by trip purpose. Insights into the route choice behavior involving two dominant vehicle trip purposes—work and shop trips—will help in the design of traffic facilities and implementation of measures to influence route choice in the desired direction.In this study, we show that the utility and scale parameters for separate models of work and shop trips differ by direct comparison using a sequential scaling estimation method and likelihood ratio tests, and highlight the differences in route choice behavior by considering the interaction of route attributes and individual characteristics using Path-Size Logit modeling. In the process, we used Potential Path Area - Gateway (PPAG) algorithm—that generates feasible route choice sets for route choice modeling from GPS trajectories of observed routes.The results show that, indeed, route choice behavior varies by trip, which suggests that drivers attach value to route choice determinants relative to trip purpose. The inclusion of interaction terms in model specifications further indicates that work route choice behavior tends to be restrictive compared to the nonrestrictive route choice for shop trips—a generalization consistent with the mandatory and discretionary nature of work and shop trips, respectively. Specifically, individual characteristics such as personal income, age, gender, tenure, household size, and access to public transit affect route choice behavior.

Mode shift behavior of commuters due to the introduction of new rail transit mode

Abstract The cities of developing countries are undertaking implementation of rail based transit systems, especially metro rail, as a solution to the problems of urban traffic congestion and rapidly increasing travel demand, keeping in view the goal of sustainable development. Traffic congestion mainly finds its roots in the ever increasing number of private vehicles, which in turn is primarily attributed to low levels of service provided by existing public transport. After the introduction of metro system, however, an analysis as to whether the system has been successful in veering the masses away from their private modes and onto the new metro mode is of crucial importance. This paper presents such an investigation on the mode shifting behavior towards a newly operational metro rail mode in Mumbai city, India, so as to understand the key tangibles perceived most important by the end user responsible for the mode shift. The investigation involves designing, implementing and analyzing Revealed and Stated Preference questionnaire surveys. The Revealed Preference (RP) survey has been conducted on commuters using the newly operational metro rail line which has provided the much needed east-west connectivity in Mumbai city, whereas an appropriately designed Stated Preference (SP) experiment has been administered on the commuters living within the catchment of a proposed additional metro rail line. The RP and SP datasets collected are used for estimating econometric mode choice models by analyzing the combined dataset using the sequential estimation method. Separate models are estimated for private vehicle users and public transit users. Before the development of a combined RP and SP model of mode choice, a discrete choice model using only the RP data explaining the mode shift behavior of commuters of new metro rail is developed and presented. The RP survey shows approximately 80% of respondents were using public transport even before shifting to the new metro line, whereas approximately 60% of the respondents from SP survey who are currently using private vehicle show willingness to shift to the proposed metro rail line, showing the need for the metro rail alignment along the corridor. Results of this analysis have been used in updating parameters of existing transportation planning model and estimation of ridership on the proposed transit system along the new corridor, and realistically determining the value commuters assign to travel time savings and comfort inside transit vehicles.

Sequential multi-nuclide emission rate estimation method based on gamma dose rate measurement for nuclear emergency management

In case of a nuclear accident, the source term is typically not known but extremely important for the assessment of the consequences to the affected population. Therefore the assessment of the potential source term is of uppermost importance for emergency response. A fully sequential method, derived from a regularized weighted least square problem, is proposed to reconstruct the emission and composition of a multiple-nuclide release using gamma dose rate measurement. The a priori nuclide ratios are incorporated into the background error covariance (BEC) matrix, which is dynamically augmented and sequentially updated. The negative estimations in the mathematical algorithm are suppressed by utilizing artificial zero-observations (with large uncertainties) to simultaneously update the state vector and BEC. The method is evaluated by twin experiments based on the JRodos system. The results indicate that the new method successfully reconstructs the emission and its uncertainties. Accurate a priori ratio accelerates the analysis process, which obtains satisfactory results with only limited number of measurements, otherwise it needs more measurements to generate reasonable estimations. The suppression of negative estimation effectively improves the performance, especially for the situation with poor a priori information, where it is more prone to the generation of negative values.