Problem Of Simultaneous Estimation Research Articles

A process fault estimation strategy for non-linear dynamic systems

The paper deals with the problem of simultaneous state and process fault estimation for non-linear dynamic systems. Instead of estimating the fault directly, its product with state and the state itself are estimated. To derive the fault from the product, a simple algebraic approach is proposed. The estimation strategy is based on the quadratic boundedness approach. The final part of the paper presents an illustrative example concerning a laboratory multi-tank system. The real data experiments clearly exhibit the performance of the proposed approach.

Adaptive Observer for Simultaneous State and Parameter Estimations for an Output Depending Normal Form

AbstractIn this paper, we investigate the problem of simultaneous state and parameter estimation for a class of nonlinear systems which can be transformed into an output depending normal form. A new and simple adaptive observer for such class of systems is presented. Sufficient condition for the existence of the proposed observer is derived. A concrete application is given in order to highlight the effectiveness of the proposed result.

Multi-body Motion Estimation from Monocular Vehicle-Mounted Cameras

This paper addresses the problem of simultaneous estimation of a vehicle's ego motion and motions of multiple moving objects in the scene–called eoru motions –through a monocular vehicle-mounted camera. Localization of multiple moving objects and estimation of their motions is crucial for autonomous vehicles. Conventional localization and mapping techniques (e.g., visual odometry and simultaneous localization and mapping) can only estimate the ego motion of the vehicle. The capability of a robot localization pipeline to deal with multiple motions has not been widely investigated in the literature. We present a theoretical framework for robust estimation of multiple relative motions in addition to the camera ego motion. First, the framework for general unconstrained motion is introduced and then it is adapted to exploit the vehicle kinematic constraints to increase efficiency. The method is based on projective factorization of the multiple-trajectory matrix . First, the ego motion is segmented and then several hypotheses are generated for the eoru motions . All the hypotheses are evaluated and the one with the smallest reprojection error is selected. The proposed framework does not need any a priori knowledge of the number of motions and is robust to noisy image measurements. The method with a constrained motion model is evaluated on a popular street-level image dataset collected in urban environments (the KITTI dataset), including several relative ego-motion and eoru-motion scenarios. A benchmark dataset ( Hopkins 155 ) is used to evaluate this method with a general motion model. The results are compared with those of the state-of-the-art methods considering a similar problem, referred to as multibody structure from motion in the computer vision community.

Unknown input and state estimation for linear discrete-time systems with missing measurements and correlated noises

This paper is concerned with the problem of simultaneous input and state estimation for a class of linear discrete-time systems with missing measurements and correlated noises. The missing measurements occur in a random way and are governed by a series of mutually independent random variables obeying a certain Bernoulli distribution. The process and measurement noises under consideration are correlated at the same time instant. Our attention is focused on the design of recursive estimators for both input and state such that, for all missing measurements and correlated noises, the estimators are unbiased and the estimation error covariances are minimized. This objective is achieved using direct algebraic operation and the design algorithm for the desired estimators is given. Finally, an illustrative example is presented to demonstrate the effectiveness of the proposed design scheme.

Simultaneous variable selection and de-coarsening in multi-path change-point models

Follow-up studies on a group of units are commonly carried out to explore the possibility that a response distribution has changed at unobservable time points that are different for different units. Often, in practice, there will be many potential covariates, which may not only be associated with the response distribution but also with the distribution of the unobservable change-points. Here, the covariates are allowed to enter the change-point distribution through a proportional odds model whose baseline odds is assumed to be piecewise constant as a function of time. The combination of a large number of putative regression coefficients in the response distributions as well as the change-point distribution, alone leads to a challenging simultaneous variable selection and estimation problem. Moreover, selection and estimation of the parameters that determine the coarseness of the baseline odds function adds a further level of complexity. Using penalized likelihood methods we are able to simultaneously perform variable selection, estimation, and determine the coarseness of the baseline odds function. Our approach is computationally efficient and shown to be consistent in variable selection and parameter estimation. We assess its performance through simulations, and demonstrate its usage in fitting a model for cognitive decline in subjects with Alzheimer’s disease.

Realigning 2D and 3D Object Fragments without Correspondences.

This paper addresses the problem of simultaneous estimation of different linear deformations, resulting in a global non-linear transformation, between an original object and its broken fragments. A general framework is proposed without using correspondences, where the solution of a polynomial system of equations directly provides the parameters of the alignment. We quantitatively evaluate the proposed algorithm on a large synthetic dataset containing 2D and 3D images, where linear (rigid-body and affine) transformations are considered. We also conduct an exhaustive analysis of the robustness against segmentation errors and the numerical stability of the proposed method. Moreover, we present experiments on 2D real images as well as on volumetric medical images.

Simultaneous Pose and Correspondence Estimation Based on Genetic Algorithm

Although several algorithms have been presented to solve the simultaneous pose and correspondence estimation problem, the correct solution may not be reached to with the traditional random-start initialization method. In this paper, we derive a novel method which estimates the initial value based on genetic algorithm, considering the influences of different initial guesses comprehensively. First, a set of random initial guesses is generated as candidate solutions. Second, the assignment matrix and the perspective projection error are computed for each candidate solution. And then each individual is modified (selection, crossover, and mutation) in current iterative process. Finally, the fittest individual is stochastically selected from the final population. With the presented initialization method, the proper initial guess could be first calculated and then the simultaneous pose and correspondence estimation problem could be solved easily. Simulation results with synthetic data and experiments on real images prove the effectiveness and robustness of our proposed method.

Batch nonlinear continuous-time trajectory estimation as exactly sparse Gaussian process regression

In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent variable. Our continuous-time prior can be defined by any nonlinear, time-varying stochastic differential equation driven by white noise; this allows the possibility of smoothing our trajectory estimates using a variety of vehicle dynamics models (e.g. ‘constant-velocity’). We show that this class of prior results in an inverse kernel matrix (i.e., covariance matrix between all pairs of measurement times) that is exactly sparse (block-tridiagonal) and that this can be exploited to carry out GP regression (and interpolation) very efficiently. When the prior is based on a linear, time-varying stochastic differential equation and the measurement model is also linear, this GP approach is equivalent to classical, discrete-time smoothing (at the measurement times); when a nonlinearity is present, we iterate over the whole trajectory to maximize accuracy. We test the approach experimentally on a simultaneous trajectory estimation and mapping problem using a mobile robot dataset.

Global stability analysis of switched nonlinear observers

This paper considers the problem of simultaneous estimation of the system states and the strategy of commutation for a larger class of nonlinear switched systems. First, a hybrid high gain observer is considered to get the exact estimation of the continuous states where the strategy of switching is previously known. Then, an extension to a larger class of nonlinear hybrid systems with arbitrary switching is made. Stability analysis is widely discussed for the two cases to provide a finite-time convergence of the estimation errors. The effectiveness of the proposed hybrid high gain observer has been proved by applying it to a quadruple tank process.

Integrated state/disturbance observers for two‐dimensional linear systems

In this study, the problem of simultaneous estimation of system states and disturbances is addressed for two-dimensional (2D) linear systems. The considered 2D systems can be described as Fornasini–Marchesini second local state–space model coupled with unknown disturbances in the measurement equation. Asymptotically stable and uniformly ultimately bounded integrated state/disturbance observers are proposed as solutions to the simultaneous estimation problem under different system conditions. For the asymptotically stable integrated state/disturbance observer, a necessary and sufficient condition for its existence is presented and proved. For the uniformly ultimately bounded integrated state/disturbance observer, a sufficient condition for its existence is given and proved, and it can be designed such that its estimation error has arbitrarily small upper bound. Moreover, some constructive design methods are given for the proposed integrated state/disturbance observers. Finally, a thermal process plant and another numerical example are provided to illustrate the effectiveness of the proposed methods.

Simultaneous State and Parameter Estimation Based Actuator Fault Detection and Diagnosis for an Unmanned Helicopter

Abstract Simultaneous state and parameter estimation based actuator fault detection and diagnosis (FDD) for single-rotor unmanned helicopters (UHs) is investigated in this paper. A literature review of actuator FDD for UHs is given firstly. Based on actuator healthy coefficients (AHCs), which are introduced to represent actuator faults, a combined dynamic model is established with the augmented state containing both the flight state and AHCs. Then the actuator fault detection and diagnosis problem is transformed into a general nonlinear estimation one: given control inputs and the measured flight state contaminated by measurement noises, estimate both the flight state and AHCs recursively in each time-step, which is also known as the simultaneous state and parameter estimation problem. The estimated AHCs can further be used for fault tolerant control (FTC). Based on the existing widely used nonlinear estimation methods such as the unscented Kalman filter (UKF) and the extended set-membership filter (ESMF), three kinds of adaptive schemes (KF-UKF, MIT-UKF and MIT-ESMF) are proposed by our team to improve the actuator FDD performance. A comprehensive comparative study on these different estimation methods is given in detail to illustrate their advantages and disadvantages when applied to unmanned helicopter actuator FDD.

Simultaneous state and input estimation with partial information on the inputs

This paper investigates the problem of simultaneous state and input estimation (SSIE) for discrete-time linear stochastic systems when the information on the inputs is partially available. To incorporate the partial information on the inputs, matrix manipulation is used to obtain an equivalent system with reduced-order inputs. Then Bayesian inference is drawn to obtain a recursive filter for both state and input variables. The proposed filter is an extension of the recently developed state filter with partially observed inputs to the case where the input filter is also of interest, and an extension of the SSIE to the case where the information on the inputs is partially available. A numerical example is given to illustrate the proposed method. It is shown that, due to the additional information on the inputs being incorporated in the filter design, the performances of both state and input estimation are substantially improved in comparison with the conventional SSIE without partial input information.

Sequential Joint Detection and Estimation

We consider the problem of simultaneous detection and estimation under a sequential framework. In particular, we are interested in sequential tests that distinguish between the null and the alternative hypothesis, and every time the decision is in favor of the alternative they provide an estimate of a random parameter. As we demonstrate with our analysis, treating the two subproblems separately with the corresponding optimal strategies does not result in the best possible performance. To enjoy optimality one needs to take into account the optimum estimator during the hypothesis testing phase.

A unified approach to decision-theoretic properties of the MLEs for the mean directions of several Langevin distributions

The two-parameter Langevin distribution has been widely used for analyzing directional data. We address the problem of estimating the mean direction in its Cartesian and angular forms. The equivariant point estimation is introduced under different transformation groups. The maximum likelihood estimator (MLE) is shown to satisfy many decision theoretic properties such as admissibility, minimaxity, the best equivariance and risk-unbiasedness under various loss functions. Moreover, it is shown to be unique minimax when the concentration parameter is assumed to be known. These results extend and unify earlier results on the optimality of the MLE. These findings are also established for the problem of simultaneous estimation of mean directions of several independent Langevin populations. Further, estimation of a common mean direction of several independent Langevin populations is studied. A simulation study is carried out to analyze numerically the risk function of the MLE.

Bayes minimax estimation of the multivariate normal mean vector under balanced loss function

We investigate the problem of simultaneous estimation of multivariate normal mean vector using Zellner (1994)’s balance loss function when common variance σ2 is unknown. We first find a class of minimax estimators for this problem which extends a class given by Chung et al. (1999). This result is then used to obtain a large class of Bayes minimax estimators for mean vector.

Spatial-differential principles for solving the degenerate navigation problem

The procedure of applying the spatial-differential principles to solving the degenerate navigation problem for the objects belonging to one-dimensional spatial manifolds is discussed. The problem is shown to belong to the class of problems of simultaneous discrimination and estimation. An approximate spatial-differential procedure for generating navigation information is obtained. An example is given.

Robust variable selection for nonlinear models with diverging number of parameters

Abstract We focus on the problem of simultaneous variable selection and estimation for nonlinear models based on modal regression (MR), when the number of coefficients diverges with sample size. With appropriate selection of the tuning parameters, the resulting estimator is shown to be consistent and to enjoy the oracle properties.

A Distributed Classification/Estimation Algorithm for Sensor Networks

In this paper, we address the problem of simultaneous classification and estimation of hidden parameters in a sensor network with communications constraints. In particular, we consider a network of noisy sensors which measure a common scalar unknown parameter. We assume that a fraction of the nodes represent faulty sensors, whose measurements are poorly reliable. The goal for each node is to simultaneously identify its class (faulty or nonfaulty) and estimate the common parameter. We propose a novel cooperative iterative algorithm which copes with the communication constraints imposed by the network and shows remarkable performance. Our main result is a rigorous proof of the convergence of the algorithm, under a fixed communication graph, and a characterization of the limit behavior as the network size goes to infinity. In particular, we prove that, in the limit when the number of sensors goes to infinity, the common unknown parameter is estimated with arbitrary small error, while the classification error converges to that of the optimal centralized maximum likelihood estimator. We also show numerical results that validate the theoretical analysis and support their possible generalization. We compare our strategy with the expectation-maximization algorithm and we discuss trade-offs in terms of robustness, speed of convergence, and implementation simplicity.

Estimation of State and Parameters of Dynamic System with the Use of Ellipsoids at the Lack of a Priori Information on Estimated Quantities

We consider the problem of the state estimation of linear dynamic system and the problem of simultaneous estimation of states and parameters of the SISO linear dynamic system in a framework of the set-theoretic approach. The modified method of ellipsoids, proposed and analyzed by the author earlier while solving the problem of the linear regression parameters estimation, was used for the estimation. Properties of the proposed estimation algorithms are illustrated by numerical examples.

Filtering and Parameter Estimation for a Class of Hidden Markov Models with Application to Bubble-Counting in Microfluidics

Motivated by a practical problem, in this work we investigate the problem of simultaneous estimation of state and parameters of an Hidden Markov Model with a particular structure. The motivating application is the problem of automatic counting of bubbles or droplets flowing into a microfluidic channel, where the noisy output of a photodiode has to be processed in order to detect the transit of bubbles. The goal is achieved through the recursive computation of a pseudo-max-likelihood estimate.