Problem Of Simultaneous Estimation Research Articles

Joint Data Compression and Parameter Estimation for Kronecker Product Structure

Due to the existence of high-dimensional data originating from observation matrices with the Kronecker product structure, it is possible to achieve cost-effective data processing by utilizing such a structure. This paper proposes an open issue, i.e., the problem of simultaneous data compression and parameter estimation for Kronecker product structure. Three joint compression–estimation schemes with different compression dimensions are derived. The first scheme is a lossless compression (LLC) estimator, where both the compressor and the estimator are Kronecker factorizable to ensure computational advantages. It shows that there is a deterministic data compression dimension equal to the rank of the observation matrix in the LLC estimator. Without satisfying this dimension, the second scheme is a general lossy compression (GLC) estimator that achieves compressed data of arbitrary dimension. The last one is a structured lossy compression estimator that reduces the number and dimension of compressed data segments suitable to special compression dimensions and has less computational burden than the GLC estimator. In addition, the performance of the three estimators is theoretically analyzed. Finally, the simulation results show the effectiveness of the proposed schemes.

Hierarchical Empirical Bayes Estimation of Two Sample Means Under Divergence Loss

We consider the problem of simultaneous estimation of two population means when one suspects that the two means are nearly equal. It is shown that the hierarchical empirical Bayes estimators which shrink the sample means towards the suspected hypothesis dominate the sample mean vectors in simultaneous estimation under the divergence loss function.

UKF‐based soft sensor design for joint estimation of chemical processes with multi‐sensor information fusion and infrequent measurements

Having a proper and real-time process monitoring and control requires accurate and frequent measurement of process variables. However, using a particular sensor for an important variable has high cost and low precision limitations. In such cases, laboratory analyses are an excellent choice for their high precision, but as their measurements are obtained manually and infrequently, they are not practical for every application in industries. This study presents an advanced soft sensor for a highly non-linear continuous stirred-tank reactor (CSTR) system which is observed with multiple sensors with different sampling rates under the assumption that there are different kinds of non-idealities in data acquisition for sensors. Some rules are assigned in order to vanquish these non-idealities in joint estimation algorithm. Therefore, the problem of simultaneous state and parameter estimation based on data fusion technique and unscented Kalman filter (UKF) is presented, and the effectiveness of the proposed method is investigated. Moreover, the proposed method is such that the effects of the inaccurate sensor on the parameter estimation are reduced. Simulation results on the estimation of four states and two parameters in a typical CSTR process show the proficiency of the proposed approach.

Optimality and identification of dynamic models in systems biology: an inverse optimal control framework.

Optimality principles have been used to explain many biological processes and systems. However, the functions being optimized are in general unknown a priori. Here we present an inverse optimal control framework for modeling dynamics in systems biology. The objective is to identify the underlying optimality principle from observed time-series data and simultaneously estimate unmeasured time-dependent inputs and time-invariant model parameters. As a special case, we also consider the problem of optimal simultaneous estimation of inputs and parameters from noisy data. After presenting a general statement of the inverse optimal control problem, and discussing special cases of interest, we outline numerical strategies which are scalable and robust. We discuss the existence, relevance and implications of identifiability issues in the above problems. We present a robust computational approach based on regularized cost functions and the use of suitable direct numerical methods based on the control-vector parameterization approach. To avoid convergence to local solutions, we make use of hybrid global-local methods. We illustrate the performance and capabilities of this approach with several challenging case studies, including simulated and real data. We pay particular attention to the computational scalability of our approach (with the objective of considering large numbers of inputs and states). We provide a software implementation of both the methods and the case studies. The code used to obtain the results reported here is available at https://zenodo.org/record/1009541. Supplementary data are available at Bioinformatics online.

Uniformly efficient simulation for extremes of Gaussian random fields

AbstractIn this paper we consider the problem of simultaneously estimating rare-event probabilities for a class of Gaussian random fields. A conventional rare-event simulation method is usually tailored to a specific rare event and consequently would lose estimation efficiency for different events of interest, which often results in additional computational cost in such simultaneous estimation problems. To overcome this issue, we propose a uniformly efficient estimator for a general family of Hölder continuous Gaussian random fields. We establish the asymptotic and uniform efficiency of the proposed method and also conduct simulation studies to illustrate its effectiveness.

An adaptive sliding‐mode observer for a class of uncertain nonlinear systems

SummaryIn this paper, the problem of simultaneous state and parameter estimation is studied for a class of uncertain nonlinear systems. A nonlinear adaptive sliding‐mode observer is proposed based on a nonlinear parameter estimation algorithm. It is shown that such a nonlinear algorithm provides a rate of convergence faster than exponential, ie, faster than the classic linear algorithm. Then, the proposed parameter estimation algorithm is included in the structure of a sliding‐mode state observer, providing an ultimate bound for the full estimation error and attenuating the effects of the external disturbances. Moreover, the synthesis of the observer is given in terms of linear matrix inequalities. The corresponding proofs of convergence are developed based on the Lyapunov function approach and input‐to‐state stability theory. Some simulation results illustrate the efficiency of the proposed adaptive sliding‐mode observer.

Some Results on Simultaneous Input and State Estimation for Linear Systems

This paper is concerned with the problem of simultaneous input and state estimation for linear discrete-time systems with missing measurements. First, in order to simultaneously estimate the input and state in the sense of unbiased minimum variance, a recursive estimator is designed in terms of one Lyapunov equation and one Riccati equation. Then some mild conditions for the existence of the infinite horizon estimator are presented. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approach.

Simultaneous estimation of multiple sensor and process faults for non-linear discrete-time systems

The paper deals with the problem of simultaneous estimation of sensor and process faults. For that purpose, a novel scheme is proposed and its complete design procedure is described. The approach results in a robust estimation strategy with guaranteed convergence. In particular, apart from simultaneous estimation ability the proposed approach makes it possible to attenuate the exogenous disturbances up to the predefined level. Finally, the design procedure boils down to solving a set of linear matrix inequalities. The last part of the paper shows an illustrative example with the application dedicated to the laboratory twin-rotor aero-dynamical MIMO system.

Minimum-variance unbiased unknown input and state estimation for multi-agent systems with direct feedthrough by using distributed cooperative filters

This paper addresses the problem of simultaneous estimation of unknown inputs and states in multi-agent systems with direct feedthrough. A group of cooperative distributed recursive filters, in the sense of minimum-variance unbiased (MVU), is developed, where the estimations of the unknown input and state are interconnected. Theoretical and numerical analyses show that the existing condition of the proposed filters is significantly relaxed compared with that of the conventional decentralized filters.

Novel hybrid estimator based on model reference adaptive system and extended Kalman filter for speed-sensorless induction motor control

This paper presents a novel hybrid estimator consisting of an extended Kalman filter (EKF) and an active power-based model reference adaptive system (AP-MRAS) in order to solve simultaneous estimation problems of the variations in stator resistance ([Formula: see text]) and rotor resistance ([Formula: see text]) for speed-sensorless induction motor control. The EKF simultaneously estimates the stator stationary axis components ([Formula: see text] and [Formula: see text]) of stator currents, the stator stationary axis components ([Formula: see text] and [Formula: see text]) of stator fluxes, rotor angular velocity ([Formula: see text]), load torque ([Formula: see text]) and [Formula: see text], while the AP-MRAS provides the online [Formula: see text] estimation to the EKF. Both the AP-MRAS, whose adaptation mechanism is developed with the help of the least mean squares method in this paper, and the EKF only utilize the measured stator voltages and currents. Performances of the proposed hybrid estimator in this paper are tested by challenging scenarios generated in simulations and real-time experiments. The obtained results demonstrate the effectiveness of the introduced hybrid estimator, together with a [Formula: see text] reduction in the processing time and size of the estimation algorithm in terms of previous studies performing the same estimations of the states and parameters. From this point of view, it is the first such study in the literature, to our knowledge.

Robust estimation and model identification for longitudinal data varying-coefficient model

ABSTRACTIt is well known that M-estimation is a widely used method for robust statistical inference and the varying coefficient models have been widely applied in many scientific areas. In this paper, we consider M-estimation and model identification of bivariate varying coefficient models for longitudinal data. We make use of bivariate tensor-product B-splines as an approximation of the function and consider M-type regression splines by minimizing the objective convex function. Mean and median regressions are included in this class. Moreover, with a double smoothly clipped absolute deviation (SCAD) penalization, we study the problem of simultaneous structure identification and estimation. Under approximate conditions, we show that the proposed procedure possesses the oracle property in the sense that it is as efficient as the estimator when the true model is known prior to statistical analysis. Simulation studies are carried out to demonstrate the methodological power of the proposed methods with finite samples. The proposed methodology is illustrated with an analysis of a real data example.

Simultaneous estimation of means of two sensitive variables

ABSTRACTIn this paper, we introduce a new problem of simultaneous estimation of means of two quantitative sensitive variables by using only one randomized response another pseudo response from a respondent in a sample. The proposed estimators are extended to stratified random sampling, and the relative efficiency values are computed for equal, proportional, and optimum allocation with respect to the newly introduced naïve estimators.

SVD-Based Kalman Filter Derivative Computation

Recursive adaptive filtering methods are often used for solving the problem of simultaneous state and parameters estimation arising in many areas of research. The gradient-based schemes for adaptive Kalman filtering (KF) require the corresponding filter sensitivity computations. The standard approach is based on the direct differentiation of the KF equations. The shortcoming of this strategy is a numerical instability of the conventional KF (and its derivatives) with respect to roundoff errors. For decades, special attention has been paid in the KF community for designing efficient filter implementations that improve robustness of the estimator against roundoff. The most popular and beneficial techniques are found in the class of square-root (SR) or UD factorization-based methods. They imply the Cholesky decomposition of the corresponding error covariance matrix. Another important matrix factorization method is the singular value decomposition (SVD) and, hence, further encouraging KF algorithms might be found under this approach. Meanwhile, the filter sensitivity computation heavily relies on the use of matrix differential calculus. Previous works on the robust KF derivative computation have produced the SR- and UD-based methodologies. Alternatively, in this paper we design the SVD-based approach. The solution is expressed in terms of the SVD-based KF covariance quantities and their derivatives (with respect to unknown system parameters). The results of numerical experiments illustrate that although the newly-developed SDV-based method is algebraically equivalent to the conventional approach and the previously derived SR- and UD-based strategies, it outperforms the mentioned techniques for estimation accuracy in ill-conditioned situations.

Simultaneous estimation of multiple channel faults for two-dimensional linear systems

ABSTRACTThis study focuses on the problem of simultaneous estimation of multiple channel faults for two-dimensional linear systems, which are described by Fornasini–Marchesini second (FM-II) model, and the faults that exist in state equation and measurement equation. By transforming the fault in the measurement equation as augmented state, the FM-II model with faults in the state equation and measurement equation can be rewritten into a singular system. Hence, several observers are proposed for the singular systems, and then the estimation of the faults in the state equation and measurement equation can be obtained. Using Lyapunov stability theory, sufficient conditions for the existence of the asymptotically stable observer and uniformly ultimately bounded observer are derived in the context of time domain. For the bounded observer, the upper bound of estimation error can be provided referring to the fault bound. Numerical and practical examples are given to demonstrate the effectiveness of the proposed method.

A Discontinuous Adaptive Sliding-Mode Observer for a Class of Uncertain Nonlinear Systems

In this paper the problem of simultaneous state and parameter estimation is studied for a class of uncertain nonlinear systems. A discontinuous adaptive sliding-mode observer is proposed based on a discontinuous nonlinear parameter estimation algorithm. It is shown that such an algorithm provides a rate of convergence faster than exponential. Then, the proposed discontinuous parameter estimation algorithm is included in the structure of a sliding-mode state observer providing an ultimate bound for the full estimation error. Some simulation results illustrate the feasibility of the proposed adaptive sliding-mode observer.

Optimization of the Data Transmission Flow from Moving Object to Nonhomogeneous Network of Base Stations

One of the common aims of an Unmanned Aerial Vehicle (UAV) performing an autonomous mission consists in data collection. Often the collected data needs to be transmitted immediately while the UAV is still in the air. This can be done through the net of receiving base stations by means of wireless communication. The problem is that any of the stations chosen for data transmission may be in different and a priori unknown state. Moreover, the transmission channel with any base station is variable due to the weather conditions, varying distance or obstacles between the station and the UAV. This randomly changing environment makes the selection of a station to communicate rather important, so the optimal data transmission problem should involve an auxiliary problem of the transmission channel state (TCS) estimation. In order to estimate the TCS one can use the information available to the on-board transmitter: since the probability of packet loss depends on the channel state, counting the number of lost packets may provide indirect measurements of the state. Thus the only resource for the solution of both the estimation and the optimal control problems becomes the transmitted packets, whose number is restricted by the transmitter capabilities and the UAV power source. In this work we give a statement of this new class of simultaneous estimation and stochastic control problems and provide the solution in a feedback form.

Quantum multiparameter estimation with generalized balanced multimode NOON-like states

The simultaneous multi-parameter estimation problem using a class of multi-mode entangled states is investigated in this paper. Specifically, the problem of optical phase imaging is considered and the quantum probe is taken to be a balanced coherent superposition of components with an arbitrary quantum state in one mode and vacuum states in all the other modes, which is a generalization of the multi-mode NOON state. The analytical form for the quantum Cramer-Rao bound (QCRB) is presented, which shows the performance by providing a lower bound of the estimation uncertainty. It is shown that the NOON state has the worst performance among those in the class of the entangled states considered. We also analyze in detail four different scenarios, which are the NOON state, the entangled coherent state, the entangled squeezed coherent state, and the entangled squeezed vacuum state. From the comparison among these four states, we find that when the mean photon number is fixed, the squeezed vacuum state has the smallest QCRB, followed by the squeezed coherent state, entangled coherent state, and NOON state. We also illustrate that the balanced entangled state can perform better than a more generalized unbalanced form studied in previous works for certain scenarios. Finally, we give an experimental setup for producing a two-mode entangled state that can beat the NOON state in quantum metrology.

Bayes minimax estimation of the mean matrix of matrix-variate normal distribution under balanced loss function

This note considers the problem of simultaneous estimation of matrix-variate normal mean matrix using a balanced loss function when common variance σ2 is unknown. We first find a class of minimax estimators for this problem and show that the maximum likelihood estimator is inadmissible. We obtain a large class of (proper and generalized) Bayes minimax estimators for the mean matrix.

Simultaneous Robust Fault and State Estimation for Linear Discrete-Time Uncertain Systems

We consider the problem of robust simultaneous fault and state estimation for linear uncertain discrete-time systems with unknown faults which affect both the state and the observation matrices. Using transformation of the original system, a new robust proportional integral filter (RPIF) having an error variance with an optimized guaranteed upper bound for any allowed uncertainty is proposed to improve robust estimation of unknown time-varying faults and to improve robustness against uncertainties. In this study, the minimization problem of the upper bound of the estimation error variance is formulated as a convex optimization problem subject to linear matrix inequalities (LMI) for all admissible uncertainties. The proportional and the integral gains are optimally chosen by solving the convex optimization problem. Simulation results are given in order to illustrate the performance of the proposed filter, in particular to solve the problem of joint fault and state estimation.

Motion Estimation and Correction in Photoacoustic Tomographic Reconstruction

Motion, e.g., due to patient movement or improper device calibration, is inevitable in many imaging modalities such as photoacoustic tomography (PAT) by a rotating system and can lead to undesirable motion artifacts in image reconstructions, if ignored. In this paper, we establish a hybrid-type model for PAT that incorporates motion in the model. We introduce an approximate continuous model and establish two uniqueness results for some specific parametrized motion models. Then we formulate the discrete problem of simultaneous motion estimation and image reconstruction as a separable nonlinear least squares problem and describe an automatic approach to detect and eliminate motion artifacts during the reconstruction process. Numerical examples validate our methods.