Combined Parameter Estimation Research Articles

DOA Estimation Based on Combined Unitary ESPRIT for Coprime MIMO Radar

Direction of arrival (DOA) estimation for coprime multiple-input multiple-output radar is studied, and a combined unitary estimation of signal parameters via rotational invariance technique (ESPRIT)-based algorithm is proposed. The transmitter and the receiver adopt coprime arrays, which are sparse but still uniform. Therefore, unitary ESPRIT is first used to obtain arbitrary ambiguous DOA estimations based on the rotational invariances of transmit and receive arrays, respectively. After recovering all the other estimations, unique DOA estimation is achieved by finding the coincide results from transmit and receive arrays based on the coprimeness. The proposed algorithm obtains more accurate DOA estimation, achieves higher angle resolution, and identifies more targets than conventional methods. Multiple simulations are conducted to verify the improvement of the proposed algorithm.

On Sequential Learning for Parameter Estimation in Particle Algorithms for State-Space Models

Particle methods, also known as Sequential Monte Carlo, have been ubiquitous for Bayesian inference for state-space models, particulary when dealing with nonlinear non-Gaussian scenarios. However, in many practical situations, the state-space model contains unknown model parameters that need to be estimated simultaneously with the state. In this paper, We discuss a sequential analysis for combined parameter and state estimation. An online learning method is proposed to approach the distribution of the model parameter by tuning a flexible proposal mixture distribution to minimize their Kullback-Leibler divergence. We derive the sequential learning method by using a truncated Dirichlet processes normal mixture and present a general algorithm under a framework of the auxiliary particle filtering. The proposed algorithm is verified in a blind deconvolution problem, which is a typical state-space model with unknown model parameters. Furthermore, in a more challenging application that we call meta-modulation, which is a more complex blind deconvolution problem with sophisticated system evolution equations, the proposed method performs satisfactorily and achieves an exciting result for high efficiency communication.

Resolver angle estimation using parameter and state estimation

Abstract In this paper, a new type of a resolver angle estimator that utilizes a combined parameter and state estimation scheme is proposed. A state-space model of a resolver is first developed with unknown parameters. Least square estimation is employed to obtain some unknown model parameters by using the measurements up to the current time. Based on the state-space model with estimated parameters, a constrained state estimator with finite memory is constructed to estimate the resolver angle. It is shown through simulation that the proposed scheme is very effective in suppressing noise and overcoming amplitude and phase imbalances compared with common angle tracking observers.

Modeling the impacts of temperature and precipitation changes on soil CO2 fluxes from a Switchgrass stand recently converted from cropland

Switchgrass (Panicum virgatum L.) is a perennial C4 grass native to North America and successfully adapted to diverse environmental conditions. It offers the potential to reduce soil surface carbon dioxide (CO2) fluxes and mitigate climate change. However, information on how these CO2 fluxes respond to changing climate is still lacking. In this study, CO2 fluxes were monitored continuously from 2011 through 2014 using high frequency measurements from Switchgrass land seeded in 2008 on an experimental site that has been previously used for soybean (Glycine max L.) in South Dakota, USA. DAYCENT, a process-based model, was used to simulate CO2 fluxes. An improved methodology CPTE [Combining Parameter estimation (PEST) with “Trial and Error” method] was used to calibrate DAYCENT. The calibrated DAYCENT model was used for simulating future CO2 emissions based on different climate change scenarios. This study showed that: (i) the measured soil CO2 fluxes from Switchgrass land were higher for 2012 which was a drought year, and these fluxes when simulated using DAYCENT for long-term (2015–2070) provided a pattern of polynomial curve; (ii) the simulated CO2 fluxes provided different patterns with temperature and precipitation changes in a long-term, (iii) the future CO2 fluxes from Switchgrass land under different changing climate scenarios were not significantly different, therefore, it can be concluded that Switchgrass grown for longer durations could reduce changes in CO2 fluxes from soil as a result of temperature and precipitation changes to some extent.

Impact of the Heat Emission System on the Identification of Grey-box Models for Residential Buildings

Grey-box modelling is a system identification technique that combines parameter estimation methods to quantify the model parameters and physical knowledge to define the model structure. Consequently, the potential of grey-box modelling lies, in addition to the application of reduced-order models in e.g. control strategies or district simulations, in the characterization of the thermal properties of buildings. Nevertheless, the quality of the obtained model is governed by the dynamic information that is available in the training data. Thereby, the required accuracy of the models, and thus the requirements of the training data, differ from application to application.This paper analyses how the significant difference in dynamic behavior of a slow floor heating system compared to a highly responsive radiator heating system results in a variation of the time constants of the building that are excited by the system and therefore identifiable in the system identification process. The performance of grey-box models for prediction and simulations are contrasted for cases with radiators and floor heating and the physical interpretability of the model parameters is demonstrated.

Mechanical Parameter Estimation of Permanent-Magnet Synchronous Machines With Aiding From Estimation of Rotor PM Flux Linkage

This paper proposes a combined parameter estimation for permanent-magnet synchronous machines (PMSMs), by which the rotor permanent-magnet (PM) flux linkage and mechanical parameters, such as the combined moment of inertia and viscous friction coefficient, are estimated without the aid from nominal machine parameter values. The proposed estimation of rotor PM flux linkage is based on the addition of position offsets and does not need the information of other machine parameters or injection of currents. With the aid from estimated rotor PM flux linkage, the electromagnetic torque can be consequently calculated for the estimation of mechanical parameters at no-load condition, and a two-step method is employed to achieve a higher ratio of signal to noise. This combined parameter estimation is finally validated on a surface-mounted PMSM (SPMSM) and an interior PMSM (IPMSM), respectively. It is found that the estimation error of combined moment of inertia with reference to its nominal value can be less than 10 $\%$ even if it (the combined moment of inertia) is lower than $1\times 10^{-3} \hbox{kg}\cdot \hbox{m}^{2} $ , while the estimation error will be further decreased to less than 3 $\%$ if it is higher than $7\times 10^{-3} \hbox{kg}\cdot \hbox{m}^{2}$ .

Joint Estimation of States and Parameters for an Input Nonlinear State-Space System with Colored Noise Using the Filtering Technique

This paper concerns the state and parameter estimation problem for an input nonlinear state-space system with colored noise. By using the data filtering and the over-parameterization technique, we transform the original nonlinear state-space system into two identification models with filtered states: one containing the system parameters and the other containing the noise model's parameters. A combined state and parameter estimation algorithm is developed for identifying the state-space system. The key is that the estimation of system parameters uses the estimated states, and the estimation of states uses the preceding parameter estimates. A simulation example is provided to show that the proposed algorithm can work well.

The estimation of time-invariant parameters of noisy nonlinear oscillatory systems

The inverse problem of estimating time-invariant (static) parameters of a nonlinear system exhibiting noisy oscillation is considered in this paper. Firstly, a Markov Chain Monte Carlo (MCMC) simulation is used for the time-invariant parameter estimation which exploits a non-Gaussian filter, namely the Ensemble Kalman Filter (EnKF) for state estimation required to compute the likelihood function. Secondly, a recently proposed Particle Filter (PF) (that uses the EnKF for its proposal density for the state estimation) has been adapted for combined state and parameter estimation. Numerical illustrations highlight the strengths and limitations of the MCMC, EnKF and PF algorithms for time-invariant parameter estimation. For low measurement noise and dense measurement data, the performances of the MCMC, EnKF and PF algorithms are comparable. For high measurement noise and sparse observational data, the EnKF fails to provide accurate parameter estimates. Hence the adapted PF algorithm becomes necessary in order to obtain parameter estimates comparable in accuracy to the MCMC simulation with EnKF. It highlights the fact that the augmented state space model for the combined state and parameter estimation contains stronger nonlinearity than the original state space model. Hence the EnKF effectively handles the state estimation of the original state space model, but it fails for the combined state and parameter estimation using the augmented system. The effectiveness of the EnKF for the state estimation is therefore leveraged in the MCMC simulation for the time-invariant parameter estimation. In order to obtain accurate parameter estimates using the augmented system, the adapted PF becomes necessary to match the parameter estimates obtained using the MCMC simulation complemented by EnKF for likelihood function computation.

A Probabilistic Approach for Reliability and Life Prediction of Electronics in Drilling and Evaluation Tools

The capability to predict performance and lifetime of drilling electronics is the key to preventing costly downhole tool failures and ensuring success of any drilling operation. Drilling electronics operate under extremely harsh downhole environments with temperatures beyond 150C and vibration levels exceeding 15g. In addition to temperature and vibration, there are several factors affecting electronic reliability that have high uncertainty and cannot be accurately measured. There is a growing trend in the oil and gas industry to drill faster and operate at higher temperatures and pressures, forcing tools to operate beyond design specifications. This has resulted in increased failure rate leading to higher maintenance costs and system downtime for drilling operators as well as service providers. This paper develops a methodology to estimate the life of drilling electronics by using operational data, drilling dynamics and historical maintenance information. The methodology combines parameter estimation techniques, statistical reliability analysis and Bayesian math in a probabilistic framework. Parameter estimation is used to calibrate statistical equations to field data and probabilistic analysis is used to obtain the likelihood of failure. In the paper, the model parameters are represented as random variables, each with a probability distribution. Drilling electronics under downhole conditions can have several failure modes and each failure mode can be caused by the interaction of several variables. When information on each failure mechanism is not readily available, the failure is expressed in terms of several candidate models. Bayesian updating is used to incorporate real time operational history for a specific part and select the most accurate failure model for that part. Tis is for the first time, a systematic approach is developed for predicting the life of electronics in downhole drilling environments using statistical modeling and probabilistic methods on life cycle history and operational data from the field.

State filtering and parameter estimation for state space systems with scarce measurements

This paper considers the state filtering and parameter estimation problems for state space systems with scarce output availability. When the scarce states are available, a least squares based algorithm and an observer based parameter estimation algorithm are developed to estimate the system parameter matrices and states. For the case with unknown states, a combined parameter estimation and state filtering algorithm is presented for canonical state space models, using the reconstructed states for the parameter estimation. Finally, an example is provided to test the effectiveness of the proposed algorithms.

Combining techniques for screening and evaluating interaction terms on high-dimensional time-to-event data

BackgroundMolecular data, e.g. arising from microarray technology, is often used for predicting survival probabilities of patients. For multivariate risk prediction models on such high-dimensional data, there are established techniques that combine parameter estimation and variable selection. One big challenge is to incorporate interactions into such prediction models. In this feasibility study, we present building blocks for evaluating and incorporating interactions terms in high-dimensional time-to-event settings, especially for settings in which it is computationally too expensive to check all possible interactions.ResultsWe use a boosting technique for estimation of effects and the following building blocks for pre-selecting interactions: (1) resampling, (2) random forests and (3) orthogonalization as a data pre-processing step. In a simulation study, the strategy that uses all building blocks is able to detect true main effects and interactions with high sensitivity in different kinds of scenarios. The main challenge are interactions composed of variables that do not represent main effects, but our findings are also promising in this regard. Results on real world data illustrate that effect sizes of interactions frequently may not be large enough to improve prediction performance, even though the interactions are potentially of biological relevance.ConclusionScreening interactions through random forests is feasible and useful, when one is interested in finding relevant two-way interactions. The other building blocks also contribute considerably to an enhanced pre-selection of interactions. We determined the limits of interaction detection in terms of necessary effect sizes. Our study emphasizes the importance of making full use of existing methods in addition to establishing new ones.

REVIEW: Identifying links between vital rates and environment: a toolbox for the applied ecologist

Summary In a rapidly changing world, understanding and predicting population change is a central aim of applied ecologists, and this involves studying the links between environmental variation and vital rates (survival, fecundity, etc.). Demographic analysis and modelling can be daunting for practicing ecologists, and here we provide an overview of some of the most important issues and methods. Collection of demographic data should follow standardized protocols and the statistical power to detect links with environment is critically dependent on long time‐series. Candidate environmental covariates should be carefully selected with a view to reducing the risk of spurious correlations. The relevant sample size for environment–demography links is typically the number of years and mixed models with random year effects offer a powerful framework to enforce this. Data on individually marked animals are the best source of information on demography. These data can be analysed and demographic parameters estimated using a wide variety of capture–mark–recapture models, available in standard software packages. Population models integrate all demographic variables and provide estimates of population growth rate. Two common classes of models are matrix models and integrated population models, where the latter combine parameter estimation and dynamic modelling. Synthesis and applications. Careful demographic analysis and modelling has provided solutions for many real‐world problems in population management, as well as assisting the development of general principles. The tools currently available are flexible and powerful, and the main limitations to their more general use are data availability and training.

Floating Sensor Networks for River Studies

Free-floating sensor packages that take local measurements and track flows in water systems, known as drifters, are a standard tool in oceanography, but are new to estuarial and riverine studies. A system based on drifters for making estimates on a hydrodynamic system requires the drifters themselves, a communication network, and a method for integrating the gathered data into an estimate of the state of the hydrodynamics. This paper presents a complete drifter system and documents a pilot experiment in a controlled channel. The utility of the system for making measurements in unknown environments is highlighted by a combined parameter estimation and data assimilation algorithm using an extended Kalman filter. The performance of the system is illustrated with field data collected at the Hydraulic Engineering Research Unit, Stillwater, OK.

Application of model reduced 4D-Var to a 1D ecosystem model

The model reduced 4D-Var (Vermeulen and Heemink, 2006) is investigated to test its feasibility in ecosystem application. Ecological models are known for their high nonlinearity and issues with non-differentiability. However, since the method is performed in the reduced space, the implementation of the adjoint of the tangent linear approximation of the original model is not required.Twin experiments are conducted in a 1D ecological model. Surface phytoplankton data are used, with 30% log-normally distributed measurement error. Three parameters are chosen for calibration. The method performs very well in the setup where a perfect initial condition is used, as well as for the combined parameter and initial condition estimation. A relatively well calibrated initial condition contributes to accurate parameter estimations. Not accounting for the wrongly assigned initial condition leads to incorrectly calibrated parameters.

Sampling-free linear Bayesian updating of model state and parameters using a square root approach

We present a sampling-free implementation of a linear Bayesian filter based on a square root formulation. It employs spectral series expansions of the involved random variables, one such example being Wiener's polynomial chaos. The method is compared to several related methods, as well as a full Bayesian update, on a simple scalar example. Additionally it is applied to a combined state and parameter estimation problem for a chaotic system, the well-known Lorenz-63 model. There, we compare it to the ensemble square root filter (EnSRF), which is essentially a probabilistic implementation of the same underlying estimator. The spectral method is found to be more robust than the probabilistic one, especially for variance estimation. This is to be expected due to the sampling-free implementation.

Combined model state and parameter estimation with an ensemble Kalman filter in a North Sea station 1-D numerical model

The combined estimation of model state and parameters is investigated by using an ensemble Kalman filter in a 1-D numerical study of the temperature profile at a North Sea station located at 55°30’ North and 0°55’ East. This simplified model implementation allows to test many configurations for the sampling of the model error for the model state as well as for the parameters. Temperature profiles from thermistor data are assimilated. The influence of a vertically or non-vertically correlated model error is examined through the computation of correlation coefficients, root mean square errors, and model bias. As the CS station is located in the North Sea region stratified in summer, vertically non-correlated model error terms have a slight positive impact on the assimilative runs. The benefit of the combined estimation of the model state and parameters is examined by comparison of a simulation where the model parameters are not adjusted to simulations with the combined estimation of the model state either with one parameter or with a set of parameters related to the surface heat exchange. The optical attenuation coefficient, the sensible, and latent heat exchange coefficients are considered. The best results are obtained when a set of parameters are simultaneously adjusted.

Moving horizon observer with regularisation for detectable systems without persistence of excitation

A constrained moving horizon observer is developed for nonlinear discrete-time systems. The algorithm is proved to converge exponentially under a detectability assumption with the data being exciting at all times. However, in many practical estimation problems, such as combined state and parameter estimation, the data may not be exciting for every period of time. The algorithm therefore has regularisation mechanisms to ensure robustness and graceful degradation of performance in cases when the data are not exciting. This includes the use of a priori estimates in the moving horizon cost function, and the use of thresholded singular value decomposition to avoid ill-conditioned or ill-posed inversion of the associated nonlinear algebraic equations that define the moving horizon cost function. The latter regularisation relies on monitoring of the rank of an estimate of a Hessian-like matrix and conditions for uniform exponential convergence are given. The method is in particular useful with augmented state space models corresponding to mixed state and parameter estimation problems, or dynamics that are not asymptotically stable, as illustrated with two simulation examples.

Parameterising hydrological models – Comparing optimisation and robust parameter estimation

In most conditions, calibration is a prerequisite for successfully applying conceptual and physically based rainfall–runoff models. The goal of this paper is to comparatively analyse the potential of both event-based automatic calibration (PEST) as described in Skahill and Doherty (2006) and robust parameter estimation (ROPE) as proposed by Bardossy and Singh (2008). The results of our modelling study in the Rietholzbach catchment (Switzerland) show that ROPE performs better in validation of small to medium sized events. This indicates that ROPE might be better suited to parameterise models when the modellers intention is focussed on a maximising the generalisation capacity of the model, e.g. for evaluating transient process characteristics. We base our study on the hydrological model WaSiM-ETH, using a combined ROPE and automatic parameter estimation approach to investigate optimal parameter sets. The PEST algorithm used in this study outperforms the ROPE application by a factor of roughly 100 in terms of time required for computation.

Image-Driven Parameter Estimation in Absorption-Diffusion Models of Chromoscopy

The administration of dyes and subsequent examination, with a colorimetry visual criterion, is a gastroenterology procedure for distinguishing, in endoscopic images, normal and aberrant colonic crypts. These are thought to be possible precursors of colon cancer. In this paper a combined image segmentation and parameter estimation model is proposed for in vivo colonic crypt images, obtained with chromoscopic colonoscopy. The parameter estimation is an inverse problem. It is formulated as a PDE constrained optimization problem, and involves an absorption-diffusion equation. A Lagrange multiplier formulation is employed and analyzed for resolving this inverse problem. Using only the segmentation of the medical endoscopic image, which separates normal and aberrant crypts, the mathematical model proposed in this paper performs a mathematical and dimensionless quantification (medically noninvasive) of the dye absorption and diffusion coefficients, as well as the dye absorbed, in normal and aberrant colonic crypts. This mathematical quantification can be important for clinicians if it is able to provide a distinction between individuals with and without cancer. Numerical simulations, on a test image and on some medical endoscopic images, are presented for the validation and evaluation of the proposed mathematical model.

On the Choice of Prior in Bayesian Model Averaging

Bayesian model averaging attempts to combine parameter estimation and model uncertainty in one coherent framework. The choice of prior is then critical. Within an explicit framework of ignorance we define a ‘suitable’ prior as one which leads to a continuous and suitable analog to the pretest estimator. The normal prior, used in standard Bayesian model averaging, is shown to be unsuitable. The Laplace (or lasso) prior is almost suitable. A suitable prior (the Subbotin prior) is proposed and its properties are investigated.