Combined Parameter Estimation Research Articles

Space and frequency diversity characterization of mobile GNSS receivers in multipath fading channels

Diversity reception of multipath Global Navigation Satellte System (GNSS) signals offers a new insight into carrier phase-based high-precision positioning. The focus of this paper is to demonstrate the fading independence between space and frequency diversity GNSS signals. In harsh urban environments, multipath components arrive to the mobile receiver antenna with different phases and Doppler shifts, therefore giving rise to the discontinuity of code and Doppler observations and large tracking errors. In this paper, an empirical model of fading GNSS signals is constructed, including power fluctuations and spread metrics. Based on this model, real BeiDou Navigation Satellite System (BDS) signals from two GNSS dual-frequency antennas are characterized, at both information and signal level. The block processing algorithm is utilized for signal investigation. Results show that: (1) a high proportion of asynchronous loss-of-lock (around 16%) is experienced by observations of diversity signals; and (2) power fluctuations of fading signals are uncorrelated in frequency separated branches unconditionally, yet for space diversity signals the independency exists in dynamic fading channels only. The results above corroborate the significant potential gain of diversity reception, and could be further implemented in researches of diversity combined GNSS parameter estimation in dense fading conditions.

Combined state and parameter estimation in level-set methods

Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous learning algorithm for state and parameter estimation with level-set methods. A Bayesian approach based on data assimilation is introduced. Data assimilation is enabled by the ensemble Kalman filter and smoother, which are used in their probabilistic formulations. The level-set data assimilation framework is verified in one-dimensional and two-dimensional test cases, where state estimation, parameter estimation and uncertainty quantification are performed. The statistical performance of the proposed ensemble Kalman filter and smoother is quantified by twin experiments. In the twin experiments, the combined state and parameter estimation fully recovers the reference solution, which validates the proposed algorithm. The level-set data assimilation framework is then applied to the prediction of the nonlinear dynamics of a forced premixed flame, which exhibits the formation of sharp cusps and intricate topological changes, such as pinch-off events. The proposed physics-informed statistical learning algorithm opens up new possibilities for making reduced-order models of interfaces quantitatively predictive, any time that reference data is available.

State and Parameter Estimation from Observed Signal Increments.

The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean–Vlasov equations as the starting point to derive ensemble Kalman–Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems.

A Novel Model-Based Estimation Scheme for Battery-Double-Layer Capacitor Hybrid Energy Storage Systems

Battery-double-layer capacitor (DLC) units are becoming popular hybrid energy storage systems (HESS) for vehicle propulsion, auxiliary power units, and renewable energy applications. Safe and optimal operation of the HESS requires real-time monitoring of its constituent subsystems. In this paper, we use a model-based approach to monitor HESS behavior and propose an online combined state and parameter estimation scheme using coupled electrical–thermal dynamical models for each subsystem. In particular, we focus on an HESS composed of a lead–acid (PbA) battery and a DLC for which experiments have been designed to identify the initial model parameters. The estimation scheme uses a novel cascaded observer-based structure which: 1) is designed based on sliding mode methodology and 2) exploits the coupling of the electrical and thermal dynamics. Using Lyapunov’s arguments, theoretical conditions are derived which characterize the convergence of the state and parameter estimates in the presence of uncertainties. The effectiveness of the estimation scheme is evaluated via simulation and experimental studies on the PbA battery, the DLC, and the HESS system.

A Resonance Tracking Approach from Adaptive Control

Resonance tracking is an approach to measuring concentrations, forces or viscosities. Such vibration-based measurements appear to be particularly well suited for applications at the micro- or even nano-scale. In order to monitor more than one parameter or parameter ratio simultaneously, a new kind of resonance tracking is developed with methods from adaptive control. It combines parameter estimation methods and state observers to adopt the resonant excitation to vibrating systems with time-varying parameters. At the same time, these parameters are measured. This approach is exemplified at two single-input-single-output (SISO) systems: a linear spring-mass-damper oscillator and a weakly nonlinear oscillator of Duffing-type.

Research on reconstruction method for two-dimensional temperature field in solid using ultrasound

Reconstruction method has played a fundamental and significant role in measuring internal temperature fields using ultrasound. A new method is proposed to reconstruct internal two dimensional temperature fields in solid structure using ultrasonic thermometry technique in this paper. Based on ultrasonic travel time changes with temperature, a mathematical model of temperature measurement using ultrasonic is established, which effectively describes the cumulative amount of temperature distribution on the propagation path of wave. Meanwhile, two-dimensional acoustic propagation path prediction method is developed using the ray acoustics. Then, combining parameter estimation method and path prediction method, two-dimensional temperature field reconstruction method is presented. To demonstrate the robustness and practicability of temperature field reconstruction method, a comprehensive analysis is conducted using dimensionless analysis to investigate the influences of two factors, that is measurement error and measuring point position distribution. Numerical experiments show that this reconstruction method developed in this paper has high precision, strong noise immunity and good applicability. Therefore, it can be helpful for realizing high-resolution reproduction of internal temperature field in solid structure.

Effects of estimating the ionospheric and thermospheric parameters on electron density forecasts

Based on the thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIEGCM), a thermospheric-ionospheric data assimilation and forecast system is developed. Using this system, we estimated the oxygen ions, neutral temperature, wind, and composition by assimilating the simulated data from Formosa Satellite 3/Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) occultation electron density profiles to evaluate their effects on the ionospheric forecast. An ensemble Kalman filter data assimilation scheme and combined state and parameter estimation methods are used to estimate the unobserved parameters in the model. The statistical results show that the neutral and ion compositions are more effective than the neutral temperature and wind for improving the forecast of the ionospheric electron density, whose root mean square errors in the assimilation period decreased by approximately 40%, 30%, and 10% due to the estimations of the neutral composition, oxygen ions, and neutral temperature, respectively. Due to the different physical and chemical processes that these parameters primarily affect, their e-folding times differ greatly from longer than 12 h for neutral composition to approximately 6 h for oxygen ions and 3 h for neutral temperature. The effect of estimating the neutral composition on improving the ionospheric forecast is greater than that of estimating the oxygen ions, which can be also be seen in an actual data assimilation experiment. This indicates that the neutral composition is the most important thermospheric parameter in ionospheric data assimilations and forecasts.

Retrospective Cost Subsystem Estimation and Smoothing for Linear Systems with Structured Uncertainty

Two algorithms for the combined state and parameter estimation (CSPE) of a linear, time-invariant system are presented. Retrospective cost subsystem estimation is formulated under the assumption that the initial state is known. A smoother algorithm based on this formulation is developed for the case in which the initial state is unknown. It is numerically demonstrated that these algorithms are more accurate for CSPE than the extended Kalman filter and the unscented Kalman filter.

State filtering‐based least squares parameter estimation for bilinear systems using the hierarchical identification principle

This study presents a combined parameter and state estimation algorithm for a bilinear system described by its observer canonical state-space model based on the hierarchical identification principle. The Kalman filter is known as the best state filter for linear systems, but not applicable for bilinear systems. Thus, a bilinear state observer (BSO) is designed to give the state estimates using the extremum principle. Then a BSO-based recursive least squares (BSO-RLS) algorithm is developed. For comparison with the BSO-RLS algorithm, by dividing the system into three fictitious subsystems on the basis of the decomposition–coordination principle, a BSO-based hierarchical least squares algorithm is proposed to reduce the computation burden. Moreover, a BSO-based forgetting factor recursive least squares algorithm is presented to improve the parameter tracking capability. Finally, a numerical example illustrates the effectiveness of the proposed algorithms.

Parameter inference to motivate asymptotic model reduction: An analysis of the gibberellin biosynthesis pathway

Developing effective strategies to use models in conjunction with experimental data is essential to understand the dynamics of biological regulatory networks. In this study, we demonstrate how combining parameter estimation with asymptotic analysis can reveal the key features of a network and lead to simplified models that capture the observed network dynamics. Our approach involves fitting the model to experimental data and using the profile likelihood to identify small parameters and cases where model dynamics are insensitive to changing particular individual parameters. Such parameter diagnostics provide understanding of the dominant features of the model and motivate asymptotic model reductions to derive simpler models in terms of identifiable parameter groupings.We focus on the particular example of biosynthesis of the plant hormone gibberellin (GA), which controls plant growth and has been mutated in many current crop varieties. This pathway comprises two parallel series of enzyme-substrate reactions, which have previously been modelled using the law of mass action (Middleton et al., 2012). Considering the GA20ox-mediated steps, we analyse the identifiability of the model parameters using published experimental data; the analysis reveals the ratio between enzyme and GA levels to be small and motivates us to perform a quasi-steady state analysis to derive a reduced model. Fitting the parameters in the reduced model reveals additional features of the pathway and motivates further asymptotic analysis which produces a hierarchy of reduced models. Calculating the Akaike information criterion and parameter confidence intervals enables us to select a parsimonious model with identifiable parameters. As well as demonstrating the benefits of combining parameter estimation and asymptotic analysis, the analysis shows how GA biosynthesis is limited by the final GA20ox-mediated steps in the pathway and generates a simple mathematical description of this part of the GA biosynthesis pathway.

Adaptive Kalman filter for actuator fault diagnosis

An adaptive Kalman filter is proposed in this paper for actuator fault diagnosis in discrete time stochastic time varying systems. By modeling actuator faults as parameter changes, fault diagnosis is performed through joint state-parameter estimation in the considered stochastic framework. Under the classical uniform complete observability–controllability conditions and a persistent excitation condition, the exponential stability of the proposed adaptive Kalman filter is rigorously analyzed. In addition to the minimum variance property of the combined state and parameter estimation errors, it is shown that the parameter estimation within the proposed adaptive Kalman filter is equivalent to the recursive least squares algorithm formulated for a fictive regression problem. Numerical examples are presented to illustrate the performance of the proposed algorithm.

Combined state and parameter estimation for a bilinear state space system with moving average noise

This paper considers the identification problem of bilinear systems with measurement noise in the form of the moving average model. In particular, we present an interactive estimation algorithm for unmeasurable states and parameters based on the hierarchical identification principle. For unknown states, we formulate a novel bilinear state observer from input-output measurements using the Kalman filter. Then a bilinear state observer based multi-innovation extended stochastic gradient (BSO-MI-ESG) algorithm is proposed to estimate the unknown system parameters. A linear filter is utilized to improve the parameter estimation accuracy and a filtering based BSO-MI-ESG algorithm is presented using the data filtering technique. In the numerical example, we illustrate the effectiveness of the proposed identification methods.

Toward Rapid Transient Identification and Characterization of Kilonovae

Abstract With the increasing sensitivity of advanced gravitational-wave (GW) detectors, the first joint detection of an electromagnetic and GW signal from a compact binary merger will hopefully happen within this decade. However, current GW likelihood sky areas span , and thus it is a challenging task to identify which, if any, transient corresponds to the GW event. In this study, we make a comparison between recent kilonova/macronova light-curve models for the purpose of assessing potential light-curve templates for counterpart identification. We show that recent analytical and parameterized models for these counterparts result in qualitative agreement with more complicated radiative transfer simulations. Our analysis suggests that with improved light-curve models with smaller uncertainties it will become possible to extract information about ejecta properties and binary parameters directly from the light-curve measurement. Even tighter constraints are obtained in cases for which GW and kilonova parameter estimation results are combined. It will therefore be important to make comparisons and potentially combine parameter estimation with the kilonova and GW results. However, to be prepared for upcoming detections, more realistic kilonova models are needed. These will require numerical relativity with more detailed microphysics, better radiative transfer simulations, and a better understanding of the underlying nuclear physics.

DOA Estimation of Noncircular Signals with Combined ESPRIT for Coprime Linear Array

Direction of arrival (DOA) estimation of noncircular signals for coprime linear array is investigated, and a combined estimation of signal parameters via rotational invariance technique (ESPRIT) based algorithm is proposed. The coprime linear array can be de-composed into two uniform linear arrays, so ESPRIT is firstly used to obtain ambiguous DOA estimations, then unique DOA estimation is achieved by finding the coincide results from the two decomposed subarrays based on the coprimeness. The proposed algorithm increase the degree of freedom, enhance the performance of angle estimation, and identifies more targets than conventional methods. Numerical simulations are conducted to demonstrate the improvement of the proposed algorithm.

Optimal estimation and scheduling in aquifer management using the rapid feedback control method

Abstract Management of water resources systems often involves a large number of parameters, as in the case of large, spatially heterogeneous aquifers, and a large number of “noisy” observations, as in the case of pressure observation in wells. Optimizing the operation of such systems requires both searching among many possible solutions and utilizing new information as it becomes available. However, the computational cost of this task increases rapidly with the size of the problem to the extent that textbook optimization methods are practically impossible to apply. In this paper, we present a new computationally efficient technique as a practical alternative for optimally operating large-scale dynamical systems. The proposed method, which we term Rapid Feedback Controller (RFC), provides a practical approach for combined monitoring, parameter estimation, uncertainty quantification, and optimal control for linear and nonlinear systems with a quadratic cost function. For illustration, we consider the case of a weakly nonlinear uncertain dynamical system with a quadratic objective function, specifically a two-dimensional heterogeneous aquifer management problem. To validate our method, we compare our results with the linear quadratic Gaussian (LQG) method, which is the basic approach for feedback control. We show that the computational cost of the RFC scales only linearly with the number of unknowns, a great improvement compared to the basic LQG control with a computational cost that scales quadratically. We demonstrate that the RFC method can obtain the optimal control values at a greatly reduced computational cost compared to the conventional LQG algorithm with small and controllable losses in the accuracy of the state and parameter estimation.

Combined state and parameter identification of nonlinear structural dynamical systems based on Rao-Blackwellization and Markov chain Monte Carlo simulations

The problem of combined state and parameter estimation in nonlinear state space models, based on Bayesian filtering methods, is considered. A novel approach, which combines Rao-Blacicwellized particle filters for state estimation with Markov chain Monte Carlo (MCMC) simulations for parameter identification, is proposed. In order to ensure successful performance of the MCMC samplers, in situations involving large amount of dynamic measurement data and (or) low measurement noise, the study employs a modified measurement model combined with an importance sampling based correction. The parameters of the process noise covariance matrix are also included as quantities to be identified. The study employs the Rao-Blackwellization step at two stages: one, associated with the state estimation problem in the particle filtering step, and, secondly, in the evaluation of the ratio of likelihoods in the MCMC run. The satisfactory performance of the proposed method is illustrated on three dynamical systems: (a) a computational model of a nonlinear beam moving oscillator system, (b) a laboratory scale beam traversed by a loaded trolley, and (c) an earthquake shake table study on a bending-torsion coupled nonlinear frame subjected to uniaxial support motion. (C) 2017 Elsevier Ltd. All rights reserved.

Utilizing the Ensemble Kalman Filter and Ensemble Kalman Smoother for Combined State and Parameter Estimation of a Three-Dimensional Towed Underwater Cable Model

Abstract A finite difference method (FDM) solving the coupled partial differential equations governing three-dimensional (3D) motions of a towed underwater cable has been implemented in a combined ensemble Kalman filter (EnKF) and ensemble Kalman smoother (EnKS), as a new approach to combined state and parameter estimation for towed underwater cables. A simulation study of the method applied to a seismic streamer has been performed. Cable state variables as well as model parameters are estimated. Parameters estimated are crossline ocean current varying with time as well as cable tangential drag coefficient. The presented results indicate that the method is able to estimate state as well as parameters for seismic streamers.

Adaptive Kalman Filter for Actuator Fault Diagnosis

An adaptive Kalman filter is proposed in this paper for actuator fault diagnosis in discrete time stochastic time varying systems. By modeling actuator faults as parameter changes, fault diagnosis is performed through joint state-parameter estimation in the considered stochastic framework. Under the classical uniform complete observability-controllability conditions and a persistent excitation condition, the exponential stability of the proposed adaptive Kalman filter is rigorously analyzed. The minimum variance property of the combined state and parameter estimation errors is also demonstrated. Numerical examples are presented to illustrate the performance of the proposed algorithm.

Fault estimation of wind turbines using combined adaptive and parameter estimation schemes

SummaryThis paper addresses the problem of fault estimation in wind turbines using a joint fault and state estimation scheme. The scheme assumes a set of possible faults affecting the dynamics of the wind turbine. Then, a combined adaptive and parameter estimation scheme is developed taking into consideration that process disturbances and sensor noises are unknown but bounded in an ellipsoid. Two subcases are considered depending on the satisfaction of a certain rank condition. The proposed approach is applied to a wind turbine based on a benchmark system model. The benchmark represents relevant fault scenarios, including sensor, actuator, and process faults. The proposed approach focuses on the last group of faults. Finally, the obtained results show that a satisfactory fault estimation is achieved against a set of predefined fault scenarios.

Performance of an Algorithm for Estimation of Flux, Background, and Location on One-dimensional Signals

Optimal estimation of signal amplitude, background level, and photocenter location is crucial to the combined extraction of astrometric and photometric information from focal plane images, in particular from the one-dimensional measurements performed by Gaia on intermediate to faint magnitude stars. Our goal is to define a convenient maximum likelihood framework that is suited to the efficient iterative implementation and assessment of noise level, bias, and correlation among variables. The analytical model is investigated numerically and verified by simulation over a range of magnitude and background values. The estimates are unbiased, with a well-understood correlation between amplitude and background, and with a much lower correlation of either of them with location, further alleviated in case of signal symmetry. Two versions of the algorithm are implemented and tested against each other, respectively, for independent and combined parameter estimation. Both are effective and provide consistent results, but the latter is more efficient because it takes into account the flux-background estimate correlation.