Real and Complex Analysis

Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications, and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book’s practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include MATLAB computations, and the numerous end-of-chapter exercises include computational assignments. MATLAB/GNU Octave source code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods.

贝叶斯滤波与平滑 (Bayesian filtering and smoothing)

WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

Advanced Calculus I

Fundamentals of statistical signal processing: Estimation theory: by Steven M. KAY; Prentice Hall signal processing series; Prentice Hall; Englewood Cliffs, NJ, USA; 1993; xii + 595 pp.; $65; ISBN: 0-13-345711-7

A review on prognostic techniques for non-stationary and non-linear rotating systems

In the work presented here we explore the interest of target localization using multiple-input multiple-output (MIMO) radar systems with widely separated antennas. The time delays between every transmit/receive antenna are an integral part of target localization using MIMO radar systems. We assume that these time delays have already been estimated by a preprocessing algorithm. Accordingly, we propose a target localization algorithm using the least squares estimation which has a closed form without requiring any initial condition. Simulation results evaluate the performance of the proposed method in comparison with the Cramer-Rao lower bound (CRLB) and the best linear unbiased estimator (BLUE) method. The effect of the arrangement and number of transmitters and receivers on the algorithm performance is also investigated.

Target Localization using Least Squares Estimation for MIMO Radars with Widely Separated Antennas

We propose a method that improves the constant false alarm rate (CFAR) detection of targets in a nonhomogenous clutter environment. We assume that the clutter data from neighboring cells may have an edge with unknown location dividing data samples into two parts with different independent and identically distributed (IID) Weibull distributions. We propose automatic clutter edge localization which allows us to eliminate the outlier/misleading data, and thereby improves the CFAR detection performance. We also suggest a CFAR detector (CFARD) which uses this estimator.

A CFAR Detector in a Nonhomogenous Weibull Clutter

Extended Kalman Filter frequency tracker for nonstationary harmonic signals

In this paper, we study some relationships between the detection and estimation theories for a binary composite hypothesis test H0 against H1 and a related estimation problem. We start with a one-dimensional (1D) space for the unknown parameter space and one-sided hypothesis problems and then extend out results into more general cases. For one-sided tests, we show that the uniformly most powerful (UMP) test is achieved by comparing the minimum variance and unbiased estimator (MVUE) of the unknown parameter with a threshold. Thus for the case where the UMP test does not exist, the MVUE of the unknown parameter does not exist either. Therefore for such cases, a good estimator of the unknown parameter is deemed as a good decision statistic for the test. For a more general class of composite testing with multiple unknown parameters, we prove that the MVUE of a separating function (SF) can serve as the optimal decision statistic for the UMP unbiased test where the SF is continuous, differentiable, positive for all parameters under H1 and is negative for the parameters under H0. We then prove that the UMP unbiased statistic is equal to the MVUE of an SF. In many problems with multiple unknown parameters, the UMP test does not exist. For such cases, we show that if one detector between two detectors has a better receiver operating characteristic (ROC) curve, then using its decision statistic we can estimate the SF more e-accurately, in probability. For example, the SF is the signal-to-noise ratio (SNR) in some problems. These results motivate us to introduce new suboptimal SF-estimator tests (SFETs) which are easy to derive for many problems. Finally, we provide some practical examples to study the relationship between the decision statistic of a test and the estimator of its corresponding SF.

Mohammad Reza Taban

Papers

Target Localization using Least Squares Estimation for MIMO Radars with Widely Separated Antennas

A CFAR Detector in a Nonhomogenous Weibull Clutter

Extended Kalman Filter frequency tracker for nonstationary harmonic signals

Separating Function Estimation Tests: A New Perspective on Binary Composite Hypothesis Testing

Weighted order statistic and fuzzy rules CFAR detector for Weibull clutter