Рекурсивное оценивание параметров сварочной цепи с помощью расширенного фильтра Калмана

This paper presents results of welding circuit parameters estimation using Extended Kalman filter. The nonlinear estimation problem is solved during welding process in real-time with uncertainty conditions. In summary, the estimates of inductance and resistance between electrodes are presented. The estimation results are offered with figures and description in the end of the paper

Asymptotically efficient estimators for geometric shape fitting and source localization

Solving the nonlinear estimation problem is known to be a challenging task because of the implicit relationship between the measurement data and the unknown parameters to be estimated. Iterative methods such as the Taylor-series expansion based ML estimator are presented in this thesis to solve the nonlinear estimation problem. However, they might suffer from the initialization and convergence problems. Other than the iterative methods, this thesis aims to provide a computational effective, asymptotically efficient and closed-form solution to the nonlinear estimation problem. Two kinds of classic nonlinear estimation problems are considered: the geometric shape fitting problem and the source localization problem. For the geometric shape fitting, the research in this thesis focuses on the circle and the ellipse fittings. Three iterative methods for the fitting of a single circle: the ML method, the FLS method and the SDP method, are provided and their performances are analyzed. To overcome the limitations of the iterative methods, asymptotically efficient and closed-form solutions for both the circle and ellipse fittings are derived. The good performances of the proposed solutions are supported by simulations using synthetic data as well as experiments on real images. The localization of a source via a group of sensors is another important nonlinear estimation problem studied in this thesis. Based on the TOA measurements, the CRLB and MSE results of a source location when sensor position errors are present are derived and compared to show the estimation performance loss due to the sensor position errors. A closed-formed estimator that takes into account the sensor position errors is then proposed. To further improve the sensor position and the source location estimates, an algebraic solution that jointly estimates the source and sensor positions is provided, which provides better performance in sensor position estimates at higher noise level comparing to the sequential estimation-refinement technique. The TOA based CRLB and MSE studies are further extended to the TDOA and AOA cases. Through the analysis one interesting result has been found: there are situations exist where taking into account the sensor position errors when estimating the source location will not improve the estimation accuracy. In such cases a calibration emitter with known position is needed to limit the estimation damage caused by the sensor position uncertainties. Investigation has been implemented to find out where would be the optimum position to place the calibration emitter. When the optimum calibration source position may be of theoretical interest only, a practical suboptimum criterion is developed which yields a better calibration emitter position than the closest to the unknown source criterion

Identification of Structured LTI MIMO State-Space Models

The identification of structured state-space model has been intensively studied for a long time but still has not been adequately addressed. The main challenge is that the involved estimation problem is a non-convex (or bilinear) optimization problem. This paper is devoted to developing an identification method which aims to find the global optimal solution under mild computational burden. Key to the developed identification algorithm is to transform a bilinear estimation to a rank constrained optimization problem and further a difference of convex programming (DCP) problem. The initial condition for the DCP problem is obtained by solving its convex part of the optimization problem which happens to be a nuclear norm regularized optimization problem. Since the nuclear norm regularized optimization is the closest convex form of the low-rank constrained estimation problem, the obtained initial condition is always of high quality which provides the DCP problem a good starting point. The DCP problem is then solved by the sequential convex programming method. Finally, numerical examples are included to show the effectiveness of the developed identification algorithm.Comment: Accepted to IEEE Conference on Decision and Control (CDC) 201

Non-linear minimum variance estimation for discrete-time multi-channel systems

A nonlinear operator approach to estimation in discrete-time systems is described. It involves inferential estimation of a signal which enters a communications channel involving both nonlinearities and transport delays. The measurements are assumed to be corrupted by a colored noise signal which is correlated with the signal to be estimated. The system model may also include a communications channel involving either static or dynamic nonlinearities. The signal channel is represented in a very general nonlinear operator form. The algorithm is relatively simple to derive and to implement

A SURE Approach for Digital Signal/Image Deconvolution Problems

In this paper, we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white Gaussian noise. The originality of the proposed approach is two-fold. Firstly, we formulate the restoration problem as a nonlinear estimation problem leading to the minimization of a criterion derived from Stein's unbiased quadratic risk estimate. Secondly, the deconvolution procedure is performed using any analysis and synthesis frames that can be overcomplete or not. New theoretical results concerning the calculation of the variance of the Stein's risk estimate are also provided in this work. Simulations carried out on natural images show the good performance of our method w.r.t. conventional wavelet-based restoration methods

Nonlinear projection filter for target tracking using range sensor & optical tracker

Target tracking filters have a variety of applications in various areas. Typically, a radar provides the range measurement and an optical sensor measures the orientation of a target. The measurements provided by the sensors have very strong nonlinearities with the states of the target given in the Cartesian coordinates while its dynamics is linear parameter time-varying. The time-varying component exists because of the unknown acceleration input in the target. Nonlinear projection filter provides a solution to the nonlinear estimation problem by approximating the solution as a linear combination of orthogonal basis functions. The analytic expression for propagating the joint probability density function is derived for the target tacking problem and this reduces large amount of computation times, where the filter equations are normally obtained numerically. The effectiveness of the filter is demonstrated by a numerical simulation

Time series forecasting by principal covariate regression.

This paper is concerned with time series forecasting in the presence of a large numberof predictors. The results are of interest, for instance, in macroeconomic and financialforecasting where often many potential predictor variables are available. Most of thecurrent forecast methods with many predictors consist of two steps, where the largeset of predictors is first summarized by means of a limited number of factors -forinstance, principal components- and, in a second step, these factors and their lags areused for forecasting. A possible disadvantage of these methods is that the constructionof the components in the first step is not directly related to their use in forecasting inthe second step. This motivates an alternative method, principal covariate regression(PCovR), where the two steps are combined in a single criterion. This method hasbeen analyzed before within the framework of multivariate regression models. Moti-vated by the needs of macroeconomic time series forecasting, this paper discusses twoadjustments of standard PCovR that are necessary to allow for lagged factors and forpreferential predictors. The resulting nonlinear estimation problem is solved by meansof a method based on iterative majorization. The paper discusses some numericalaspects and analyzes the method by means of simulations. Further, the empirical per-formance of PCovR is compared with that of the two-step principal component methodby applying both methods to forecast four US macroeconomic time series from a set of132 predictors, using the data set of Stock and Watson (2005).distributed lags;dynamic factor models;economic forecasting;iterative majorization;principal components;principal covariate regression

Recursive Motion Estimation on the Essential Manifold

Visual motion estimation can be regarded as estimation of the state of a system of difference equations with unknown inputs defined on a manifold. Such a system happens to be "linear", but it is defined on a space (the so called "Essential manifold") which is not a linear (vector) space. In this paper we will introduce a novel perspective for viewing the motion estimation problem which results in three original schemes for solving it. The first consists in "flattening the space" and solving a nonlinear estimation problem on the flat (euclidean) space. The second approach consists in viewing the system as embedded in a larger euclidean space (the smallest of the embedding spaces), and solving at each step a linear estimation problem on a linear space, followed by a "projection" on the manifold (see fig. 5). A third "algebraic" formulation of motion estimation is inspired by the structure of the problem in local coordinates (flattened space), and consists in a double iteration for solving an "adaptive fixed-point" problem (see fig. 6). Each one of these three schemes outputs motion estimates together with the joint second order statistics of the estimation error, which can be used by any structure from motion module which incorporates motion error [20, 23] in order to estimate 3D scene structure. The original contribution of this paper involves both the problem formulation, which gives new insight into the differential geometric structure of visual motion estimation, and the ideas generating the three schemes. These are viewed within a unified framework. All the schemes have a strong theoretical motivation and exhibit accuracy, speed of convergence, real time operation and flexibility which are superior to other existing schemes [1, 20, 23]. Simulations are presented for real and synthetic image sequences to compare the three schemes against each other and highlight the peculiarities of each one

Nonlinear projection filter with parallel algorithm and parallel sensors

Over the past few decades, the computational power has been increasing rapidly. With advances of the parallel computation architectures it provides new opportu- nities for solving the optimal estimation problem in real- time. In addition, sensor miniaturization technology enables us to acquire multiple measurements at low cost. Kolmogorov’s forward equation is the governing equation of the nonlinear estimation problem. The nonlinear projection filter presented in the late 90’s is an almost exact solution of the nonlinear estimation problem, which solves the governing equation us- ing Galerkin’s method. The filter requires high-dimensional integration in several steps and the complexity of the filter increases exponentially with the dimension of systems. The current parallel computation speed with the usage of many sensors at the same time make it feasible to implement the filter efficiently for practical systems with some mild dimension sizes. On-line or off-line multi-dimensional integration is to be performed over the parallel computation using the Monte- Carlo integration method and random samples for the state update are obtained more efficiently based on the multiple sensor measurements. A few simplifications of the filter are also derived to reduce the computational cost. The methods are verified with two numerical examples and one experimental example