Tomographic SAR imaging based on GTD model and compressed sensing

The Bayes principle is applied to the joint model selection and parameter estimation of GTD model to explore the prior information. An algorithm using RJ-MCMC is designed. It not only has better model selection and parameter estimation performance than the non-Bayes algorithms, but also solves the mixed parameter estimation problem in GTD model effectively. The advantage of this algorithm is especially evident at low SNR, for short data and with closely-spaced components. Simulations verify the effectiveness of this algorithm.

Undirected graphical models such as Markov random fields or Boltzmann machines prove useful in many signal processing and machine learning tasks. However, parameter estimation in these models is difficult due to the intractable normalising constant in their probability density functions. One powerful technique for parameter estimation in such models is score matching. This technique makes use of an objective function which is independent of the normalising constant and constitutes locally consistent estimators for the parameters of such models. However, score matching is only applicable to fully-observed models. In this paper, we extend the applicability of score matching to models with latent variables. Our estimators are unbiased, based on Monte Carlo integration. Unbiased gradient estimators open the way to optimisation through stochastic approximation. We demonstrate the performance of our methodology on two synthetic problems.

Many existing software reliability models are based on the assumption of statistical independence among successive software failures. In reality, this assumption could be easily violated. In recent years, efforts have been made to relax this unrealistic assumption and a software reliability modeling framework considering failure correlation was developed by Goseva-Popstojanova and Trivedi. However, some important issues that are crucial to the proposed modeling framework to be used in practice remain unstudied, such as the method of estimation of model parameters. In this paper, we study the parameter estimation problem for the software reliability modeling framework developed in. We propose a relationship function among model parameters which could be essential to the reduction of the number of parameters to be estimated as well as to the reliability prediction using the proposed modeling framework. Two parameter estimation methods are developed based on deferent types of data available, using Maximum Likelihood Estimation (MLE) method. Simulation results preliminarily show that the accuracy of both proposed estimation methods seem to be satisfactory.

Wind power curve (WPC) is an important index of wind turbines, and it plays an important role in wind power prediction and condition monitoring of wind turbines. Motivated by model parameter estimation of logistic function in WPC modelling, aimed at the problem of selecting initial value of model parameter estimation and local optimum result, based on the combination of genetic algorithm and least square estimation method, a genetic least square estimation (GLSE) method of parameter estimation is proposed, and the global optimum estimation result can be obtained. Six evaluation indices including the root mean square error, the coefficient of determination R2, the mean absolute error, the mean absolute percentage error, the improved Akaike information criterion and the Bayesian information criterion are used to select the optimal power curve model in the different candidate models, and avoid the model’s over-fitting. Finally, to predict the annual energy production and output power of wind turbines, a two-component Weibull mixture distribution wind speed model and five-parameter logistic function power curve model are applied in a wind farm of Jiangsu Province, China. The results show that the GLSE approach proposed in this paper is feasible and effective in WPC modelling and wind power prediction, which can improve the accuracy of model parameter estimation, and five-parameter logistic function can be preferred compared with high-order polynomial and four-parameter logistic function when the fitting accuracy is close.

In order to solve the problem of parameter estimation of nonlinear model in chemical engineering, a novel heuristic optimization approach is presented. The proposed approach develops and employs particle swarm optimization (PSO) technique to search for optimal solution of the parameter estimation. Firstly, the proposed approach converts the problem of parameter estimation of nonlinear model into an equation solving problem that is prone to be optimized. Secondly, two extrema of PSO are used as the target, and all the particles synchronously move through the solution space roundly and efficiently to find the optimum parameter estimation. The feasibility of the proposed method is demonstrated by the parameter estimation example of the pyrolysis model for fir.

Online estimates of unknown environment dynamics are used for the control of robotic contact tasks. The Hunt-Crossley nonlinear dynamic model of environments has been shown to be more consistent with the physics of contact, compared to the classical linear models, such as Kelvin-Voigt. This paper proposes a new method for online parameter estimation of Hunt-Crossley model and provides a mild set of conditions for guaranteed unbiased estimation. The rate and the sensitivity of convergence to parameter initialization and system parameter changes are numerically evaluated and compared for both the proposed method and an existing 2-stage identification method.

Light detection and ranging (LiDAR) is commonly used to create high-resolution maps; however, the efficiency and convergence of parameter estimation are difficult. To address this issue, we evaluated the structural characteristics of received LiDAR signals by decomposing them into Gaussian functions and applied the variable projection algorithm of the separable nonlinear least-squares problem to the process of waveform fitting. First, using a variable projection algorithm, we separated the linear (amplitude) and nonlinear (center position and width) parameters in the Gaussian function model; the linear parameters are expressed with nonlinear parameters by the function. Thereafter, the optimal estimation of the characteristic parameters of the Gaussian function components was transformed into a least-squares problem only comprising nonlinear parameters. Finally, the Levenberg–Marquardt algorithm was used to solve these nonlinear parameters, whereas the linear parameters were calculated simultaneously in each iteration, and the estimation results satisfying the nonlinear least-square criterion were obtained. Five groups of waveform decomposition simulation data and ICESat/GLAS satellite LiDAR waveform data were used for the parameter estimation experiments. During the experiments, for the same accuracy, the separable nonlinear least-squares optimization method required fewer iterations and lesser calculation time than the traditional method of not separating parameters; the maximum number of iterations was reached before the traditional method converged to the optimal estimate. The method of separating variables only required 14 iterations to obtain the optimal estimate, reducing the computational time from 1128 s to 130 s. Therefore, the application of the separable nonlinear least-squares problem can improve the calculation efficiency and convergence speed of the parameter solution process. It can also provide a new method for parameter estimation in the Gaussian model for LiDAR waveform decomposition.

Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models

Time delay estimation is of great significance in multipath propagation to recover overlapped signals and identify the channel characteristics. However, achieving a high accuracy in this purpose may pose many problems in ultra-wideband (UWB) applications. In UWB systems, capturing a signal with high sampling rates cannot readily be done; hence classical methods for time delay estimation substantially lose their precision. To overcome this challenge, the authors incorporate a robust estimation approach and supplementary sampling process in a unified algorithm to retrieve time delays from signals with low sampling rates. Toward that pursuit, a model based least squares estimator is proposed as the main approach to calculate time delays and a modified method based on multiple signal classification (MUSIC) is also presented for comparison aim. Then, the authors have developed the algorithm by embedding two additional pre-processing steps of under sampling and interpolation to achieve a higher sampling rate and a better resolution. To show the high accuracy of work, root mean square error is computed in different values of time delay. Simulation and experiment results show the considerably higher precision of the proposed algorithm in comparison with presented MUSIC type method and also previously proposed methods in literature.

Recursive formulae for repeated integration of a continuous-time function with uniformly sampled data using Simpson's 1/3 and 3/8 integrating rules are derived. Combined with the recursive algorithm of the least-squares solution, a method for recursive parameter estimation of transfer function matrix models in multiple-input-multiple-output systems is proposed. It is demonstrated that the use of the popular integrating rules for parameter estimation can be as effective as sophisticated methods that use orthogonal functions and the associated operational properties reported in the literature. The proposed algorithm is suitable for on-line applications and computer programming. Three numerical examples are included to illustrate the applicability of the proposed method.

BackgroundIdentifying a proper model structure, using methods that address both structural and parameter uncertainty, is a crucial problem within the systems approach to biology. And yet, it has a marginal presence in the recent literature. While many existing approaches integrate methods for simulation and parameter estimation of a single model to address parameter uncertainty, only few of them address structural uncertainty at the same time. The methods for handling structure uncertainty often oversimplify the problem by allowing the human modeler to explicitly enumerate a relatively small number of alternative model structures. On the other hand, process-based modeling methods provide flexible modular formalisms for specifying large classes of plausible model structures, but their scope is limited to deterministic models. Here, we aim at extending the scope of process-based modeling methods to inductively learn stochastic models from knowledge and data.ResultsWe combine the flexibility of process-based modeling in terms of addressing structural uncertainty with the benefits of stochastic modeling. The proposed method combines search trough the space of plausible model structures, the parsimony principle and parameter estimation to identify a model with optimal structure and parameters. We illustrate the utility of the proposed method on four stochastic modeling tasks in two domains: gene regulatory networks and epidemiology. Within the first domain, using synthetically generated data, the method successfully recovers the structure and parameters of known regulatory networks from simulations. In the epidemiology domain, the method successfully reconstructs previously established models of epidemic outbreaks from real, sparse and noisy measurement data.ConclusionsThe method represents a unified approach to modeling dynamical systems that allows for flexible formalization of the space of candidate model structures, deterministic and stochastic interpretation of model dynamics, and automated induction of model structure and parameters from data. The method is able to reconstruct models of dynamical systems from synthetic and real data.

A methodology is proposed to aid parameter estimation in fundamental models of pharmaceutical processes. This methodology addresses situations with insufficient data to reliably estimate all parameters, when the estimation is complicated by uncertain independent variables. The proposed method uses an augmented sensitivity matrix to rank the combined set of parameters and uncertain inputs from most estimable to least estimable. An updated mean‐squared‐error criterion is then used to determine the appropriate parameters and inputs that should be estimated, based on the ranked list. A model for one step in a batch pharmaceutical production process with an uncertain initial reactant concentration is used to illustrate the method, revealing that the initial reactant concentration in each batch should be estimated along with three out of six model parameters. Non‐estimable parameters are fixed at their initial values to prevent overfitting. The method will aid error‐in‐variables parameter estimation in many situations involving limited data.

An important issue in social network analysis refers to the development of algorithms for estimating parameters of a social network model, using data available from the network itself. This entails solving an optimization problem. In the paper, we propose a new method for parameter estimation in a specific social network model, namely, the so‐calledp‐star random graph model with three parameters. The method is based on the mean‐field approximation of the moments associated with the three subgraphs defining the model, namely: the mean numbers of edges, 2‐stars, and triangles. A modified gradient ascent method is applied to maximize the log‐likelihood function of thep‐star model, in which the components of the gradient are computed using approximate values of the moments. Compared to other existing iterative methods for parameter estimation, which are computationally very expensive when the number of vertices becomes large, such as gradient ascent applied to maximum log‐likelihood and maximum log‐pseudo‐likelihood estimation, the proposed approach has the advantage of a much cheaper cost per iteration, which is practically independent of the number of vertices.

The primary challenge of software reliability growth model is to find the unknown model parameters that are used to validate on software failure dataset. Though, numerical estimation technique plays a vital role in parameter estimation of software reliability growth models, they are not optimal as they suffer from constraints sucha as sample size, biasing, and initialisation of parameters. In this study, a parameter estimation of software reliability growth model that utilises a variant of harmony search is proposed. Extensive experiments are conducted on seven different software datasets of varying complexity. A robust experimental setup is developed employing an orthogonal array and Taguchi method. Two‐fold performance comparisons are performed. First, the authors tested their proposed approach against Cuckoo search and numerical method (least square estimation) considering mean square error and Theil's statistics as a quality measure. Second, the authors applied statistical tests are performed that demonstrate the superiority of their approach over the others. The underlying motivation to conduct this study is to motivate researchers to utilise their approach for a better estimation of model parameters.

Parameter and uncertainty estimation in stochastic differential equation models with multi-rate data and nonstationary disturbances