Analysis of Multimodal Systems

The estimation of a multimodal linear system whose mode-to-mode transitions are described by a finite-state Markov chain is described. The problem has application in studying separation standards in an air traffic control environment. An optimal solution is formulated which is computationally infeasible. A suboptimal estimator is then derived which closely approximates the optimal estimator. An example is presented to illustrate the technique.     

Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition

Despite its usefulness, the Kalman-Bucy filter is not perfect. One of its weaknesses is that it needs a Gaussian assumption on the initial data. Recently Yau and Yau introduced a new direct method to solve the estimation problem for linear filtering with non-Gaussian initial data. They factored the problem into two parts: (1) the on-line solution of a finite system of ordinary differential equations (ODEs), and (2) the off-line calculation of the Kolmogorov equation. Here we derive an explicit closed-form solution of the Kolmogorov equation. We also give some properties and conduct a numerical study of the solution.     

Interference between FM Carriers and a Digitally Modulated SCPC Circuit

The interference from the digital single channel per carrier (SCPC) circuits into frequency-modulated carrier systems has been calculated by convolving the desired and the interfering spectra extending the previously published works. Resulting interference noise power in FDM/FM systems covering a wide range of modulation indices and basebands has been presnted. Also plots of interference noise power as a function of the number of SCPC circuits have been presented for various values of carrier power to interference power ratios.     

Satellite fault diagnosis using a bank of interacting Kalman filters

The main objective of this work is development and testing of a detection, isolation, and diagnosis algorithm based on interacting multiple model (IMM) filters for both partial (soft) and total (hard) reaction wheels faults in a spacecraft. This is shown to be accomplished under a number of different faulty mode scenarios for these actuators associated with the attitude control system (ACS) of a satellite. Various operating and faulty conditions due to changes and anomalies in the temperature, the power supply line voltage, and the loss of effectiveness of the torque and the current are considered in each reaction wheel associated with the three axes of the satellite. Once a fault mode is detected and isolated the recovery procedure can subsequently be engaged by invoking appropriate switching control strategies for the ACS. The application of a bank of interacting multiple Kalman filters for detection and diagnosis of anticipated reaction wheel failures in the ACS is described and developed. Compared with other model-based fault detection, diagnosis and isolation(FDDI) strategies developed in the control systems literature, our FDDI strategy is shown, through extensive numerical simulations, to be more accurate and robust with potential for extension to a number of other application areas.     

基于CFD技术的鼻腔输药的流动特性研究

鼻腔输药作为一种新颖的输药方式,具有方便可靠的特点,不仅可以适用于局部而且适用于全身用药,已经受到广泛的重视。但由于人类的呼吸道复杂的立体结构使得鼻腔输药成为生物医药研究的一个长期的挑战。利用CFD(计算流体动力学,Computational Fluid Dynamics)技术对鼻腔输药的流动特性进行研究,对一个基于真实的人类鼻腔解剖的3D模型的输药的流动过程进行了分析,着重研究了不同的药物颗粒的流动和沉淀特性。利用CFD的商用软件FLUENT在层流情况下对不同的密度、直径和流动速率的药物颗粒在鼻腔中流动进行了数值模拟,并对计算结果进行了比较分析。CFD研究的结果为鼻腔输药这种新颖的药物输送方式的优化设计提供了依据。     

Probing the era of galaxy formation via TeV gamma ray absorption by the near infrared extragalactic background

We present models of the extragalactic background light (EBL) based on several scenarios of galaxy formation and evolution. We have treated galaxy formation with the Press-Schecter approximation for both cold dark matter (CDM) and cold+hot dark matter (CHDM) models, representing a moderate (z _f 3) and a late (z _f 1) era of galaxy formation respectively. Galaxy evolution has been treated by considering a variety of stellar types, different initial mass functions and star formation histories, and with an accounting of dust absorption and emission. We find that the dominant factor influencing the EBL is the epoch of galaxy formation. A recently proposed method for observing the EBL utilizing the absorption of 0.1 to 10 TeV gamma-rays from active galactic nuclei (AGN) is shown to be capable of discriminating between different galaxy formation epochs. The one AGN viewed in TeV light, Mrk 421, does show some evidence for a cutoff above 3 TeV; based on the EBL models presented here, we suggest that this is due to extinction in the source. The large absorption predicted at energies > 200 GeV for sources at z > 0.5 indicates that observations of TeV gamma-ray bursts (GRB) would constrain or eliminate models in which the GRB sources lie at cosmological distances.Now at University of Chicago, Dept. of Astronomy & Astrophysics.     

Discrete-time observability and estimability analysis for bearings-only target motion analysis

Observability in the context of bearings-only tracking (BOT) is still the subject of important literature. Different from previous approaches, where continuous-time analysis was considered, our approach relies on discrete-time analysis. It is then shown that this allows us to use directly and efficiently the simple formalisms of linear algebra. Using the direct approach, observability analysis is essentially reduced to basic considerations about subspace dimensions. Even if this approach is conceptually quite direct, it becomes more and more complex as the source-encounter scenario complexity increases. For complex scenarios, the dual approach may present some advantages essentially due to the direct use of multilinear algebra. New results about BOT observability for maneuvering sources are thus obtained. Observability analysis is then extended to unknown instants of source velocity changes. Even if observability analysis provides thorough insights about the algebraic structure of the BOT problem, the optimization of the observer maneuvers is essentially a control problem. Basic algebraic considerations prove that a relevant cost functional for this control problem is the determinant of the Fisher information matrix (FIM). So, a large part of this work is devoted to the analysis of this cost functional. Using multilinear algebra, general approximations of this functional are given. In order to involve only directly estimable parameters, the source bearing-rates are examined. Using these approximations, a general framework for optimizing the observer trajectory is derived which allow us to approximate the optimal sequence of controls. It is worth stressing that our approach does not require the knowledge of the source trajectory parameters and is still valid for a maneuvering source.     

Phase Space Density Analysis of Energy Transport in the Earth’s Magnetotail

Two energetic events in the Earth’s magnetotail detected by Geotail are examined with detailed analysis of three-dimensional velocity phase space density. It is found that the occurrence of multiple ion components is high during these dynamic episodes. Different populations evolve independently of each other, suggesting particles from multiple activity sites contributing to the observed phase space density. The transport properties with consideration of multiple components are evaluated, with the result showing significant differences from those based on a single fluid approach. This comparison indicates that precise evaluation of the energy and magnetic flux transport of energetic events in the magnetotail requires resolving individual populations in the phase space density.     

Instability and unsteadiness of aircraft wake vortices

This paper presents a review of theoretical and experimental results on stability and other unsteady properties of aircraft wakes. The basic mechanisms responsible for the propagation and the amplification of perturbation along vortices, namely the Kelvin waves and the cooperative instabilities, are first detailed. These two generic unsteady mechanisms are described by considering asymptotic linear stability analysis of model flows such as vortex filaments or Lamb–Oseen vortices. Extension of the linear analysis to more representative flows, using a biglobal stability approach, is also described. Experimental results obtained using LDV, hot wire and PIV in wind tunnels are presented and they are commented upon the light of theory.     

PHD filters of higher order in target number

The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of this filter based on propagation of a first-order multitarget moment called the probability hypothesis density (PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which remains first-order in the states of individual targets, but which is higher-order in target number. In this paper we show that this is indeed possible. We derive a closed-form cardinalized PHD (CPHD) filter, which propagates not only the PHD but also the entire probability distribution on target number.