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.     

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.     

A New Mathematical Formulation for Strapdown Inertial Navigation

A differential equation is developed for the orientation vector relating the body frame to a chosen reference frame. The time derivative of this vector is the sum of the inertially measurable angular velocity vector and of the inertially nonmeasurable noncommutativity rate vector. It is precisely this noncommutativity rate vector that causes the computational problems when numerically integrating the direction cosine matrix. The orientation vector formulation allows the noncommutativity contribution to be isolated and, therefore, treated separately and advantageously. An orientation vector mechanization is presented for a strap down inertial system. Further, an example is given of the applica tion of this formulation to a typical rigid body rotation problem.     

Specification and Performance of Passive Sonar Spectral Estimators

The application of existing estimation theory to the problem of specification and performance of passive sonar spectral estimators is considered. The classification function is addressed, so that the signal is assumed to be present, and so that the energy arrival angle is known. The spatial filter considered is a line array of M equally spaced omnidirectional hydrophones. Signal and ambient noise are both zero-mean, wide-sense, stationary Gaussian random processes that differ in their spatial correlation across the face of the array. The signal is a plane wave that can be made totally spacially corrected between array elements by inserting delays between sensors to invert the signal propagation delay. The noise correlation is a function of frequency, bandwidth, element separation, and the relative time delay between sensors. Under these assumptions, the Cramer-Rao lower bound is derived for the class of unbiased estimates of signal power in a narrow frequency band at the hydrophone in the presence of correlated ambient noise of known power. The bound is examined numerically, resulting in a threshold phenomenon with M that constitutes a new design consideration. In addition, there is a striking insensitivity to realistic values of ambient noise correlation, and there are ranges in signal-to-noise ratio for which one gains more by increasing M than by increasing the bandwidth-time product. Specific processors, including a new unbiased estimator when noise power is unknown, are developed.     

Radar Performance with Multipath Using the Complex Angle

The complex angle (CA) method for resolving a low angle target from its multipath signal is evaluated in the presence of system noise. It is shown that standard deviation improvements of around 3-to-1 can be achieved at a 20-dB signal-to-noise power ratio relative to a normal monopulse system without the CA. It is also shown that the CA method is unbiased, giving bias improvements of as much as 100 times relative to normal monopulse. Evaluation of the assumptions in the technique shows very little sensitivity to knowledge of the reflecting surface's conductivity or dielectric constant. However, the method is somewhat sensitive to knowledge of surface roughness.