A double-stage piecewise recursive filter for real-time applications

This paper examines the basic problem of estimating the state of a system described by a set of dynamical equations. The state estimation is performed by means of optimal filtering techniques in which the state observation is given by a set of nonlinear equations.The basic issue encountered in most engineering problems is the availability of more observable information than the processor can effectively process in real-time, while performing full optimal filtering on all available observable data. To alleviate this deficiency, an algorithm is developed in which the rate of information processing is kept at a high value, while the system statistics are evaluated at a much slower rate.The method utilizes a combination of fast and slow filtering loops, in which the observable data are processed at a high rate during the fast loop, while the system error covariance, gain computations, and all other system statistics are processed at a lower rate in the slow loop. Methods are provided to resolve any incompatibility in the system statistics resulting from this fast-loop/slow-loop processing combination.Applications describing problems pertaining to aircraft navigation are presented. Specifically, applications to aircraft navigation through a satellite network are studied. Appropriate simulation results from the above studies are shown.This work was performed under contract with the Department of the Air Force, Space and Missile Organization (SAMSO), Los Angeles, California, Contract No. F04-701-75-C-0180.The authors are indebted to Dr. C. Johnson, GPS System Engineer, Mr. G. Consolver, GPS Software Manager, and Mr. W. Riley, Communications/Navigation Department, Texas Instruments for their continuous encouragement in the course of this work. Also, they are indebted to Major M. Birnbaum, SAMSO, for his constructive criticism on the conceptual design of this work, and to Mr. A. Bierman, Aerospace Corporation, for kindly providing simulation data of aircraft trajectories. Finally, the authors would like to express their gratitude to Dr. N. Carlson, Intermetrics, for valuable consultation during the progress of this work.Portions of this paper were presented by the senior author at the GSP Conference, Plan 76, IEEE Position, Location, and Navigation Symposium, San Diego, California, 1976.     

Estimation and filtering on a doubly stochastic poisson process

An explicit formula for the characteristic function of a doubly stochastic Poisson process is derived in this paper by means of the harmonic decomposition of its intensity function that we suppose to be Gaussian. The statistical moments are then obtained, as well as the sample function density of the process. These results are applied to estimate the parameters of several well-known processes. Finally, a linear filtering procedure for the intensity function is developed and the algorithm is implemented by computers.     

基于斑点噪声的拖尾Rayleigh分布的合成孔径雷达图像最大后验概率降噪

为了反映合成孔径雷达图像中斑点噪声尖峰厚尾的统计特征，使用拖尾Rayleigh分布来描述斑点噪声.基于Gamma先验分布和斑点噪声的拖尾Rayleigh分布，推导出了合成孔径雷达图像的最大后验概率滤波方程，并给出了它在特定特征参数时的解析形式.使用Mellin变换从观察图像估计拖尾Rayleigh分布的未知参数.给出了在斑点噪声的拖尾Rayleigh分布下的最大后验概率降噪试验和量化指标.为了消除滑动窗大小和噪声强度对降噪结果的影响，给出了降噪能力随滑动窗大小和噪声方差的动态变化关系.结果表明，拖尾Ray 关键词： 斑点噪声 拖尾Rayleigh分布 最大后验概率降噪 Mellin变换     

基于空间滤波测量气垫导轨上滑块的运行速度

当作为传感器的敏感器件通过一定的敏感体积来检测物体的运行状况时,敏感器件将以其特定的空间权函数对信息进行加权平均,其作用等效于空间低通滤波器.本文介绍了传感器的空间滤波原理,利用空间滤波测量了气垫导轨上滑块的运行速度.该方法不需要触发时间计数装置的开启信号和停止信号,也不需物体在2只传感器之间稳定运动,因而也降低了对运动物体的要求.     

基于小波阈值法和维纳滤波的稀疏孔径光学系统成像的恢复

在研究稀疏孔径理想衍射成像光学系统的基础上，提出基于改进小波阈值法和维纳滤波的稀疏孔径光学系统成像恢复算法。针对存在噪声干扰的稀疏孔径光学成像系统，设计并利用改进的小波阈值去噪算法，较好地去除了成像噪声，最大程度地得到较为理想的成像结果，然后利用维纳滤波方法实现成像恢复。在实验中，利用光学设计软件ZEMAX设计了不同填充因子的稀疏孔径光学系统，并用本算法进行了成像恢复。实验结果表明，该算法的结果优于单独使用维纳滤波方法所获得的结果。     

Extinction ratio enhancement of SOA-based delayed-interference signal converter using detuned filtering

We demonstrate experimentally >3 dB extinction ratio improvement at the output of SOA-based delayed-interference signal converter (DISC) using optical off-centered filtering. Through careful modeling of the carrier and the phase dynamics, we explain in detail the origin of sub-pulses in the wavelength converted output, with an emphasis on the time-resolved frequency chirping of the output signal. Through our simulations we conclude that the sub-pulses and the main-pulses are oppositely chirped, which is also verified experimentally by analyzing the output with a chirp form analyzer. We propose and demonstrate an optical off-center filtering technique which effectively suppresses these sub-pulses. The effects of filter detuning and phase bias adjustment in the delayed-interferometer are experimentally characterized and optimized, leading to a >3 dB extinction ratio enhancement of the output signal.     

A survey of numerical methods for nonlinear filtering problems

The main goal of filtering is to obtain, recursively in time, good estimates of the state of a stochastic dynamical system based on noisy partial observations of the same. In settings where the signal/observation dynamics are significantly nonlinear or the noise intensities are high, an extended Kalman filter (EKF), which is essentially a first order approximation to an infinite dimensional problem, can perform quite poorly: it may require very frequent re-initializations and in some situations may even diverge. The theory of nonlinear filtering addresses these difficulties by considering the evolution of the conditional distribution of the state of the system given all the available observations, in the space of probability measures. We survey a variety of numerical schemes that have been developed in the literature for approximating the conditional distribution described by such stochastic evolution equations; with a special emphasis on an important family of schemes known as the particle filters. A numerical study is presented to illustrate that in settings where the signal/observation dynamics are non linear a suitably chosen nonlinear scheme can drastically outperform the extended Kalman filter.     

Measuring short impulse responses with inverse filtered maximum-length sequences

Most loudspeakers have a non-flat frequency response which produces a long oscillating impulse response. An inverse filtering approach may be used to calculate the driving waveform necessary to equalize the response of the loudspeaker in order to radiate shorter acoustic pulses. When combined with the MLS technique, inverse filtering may be used to pre-emphasize the driving signal so that a shorter impulse response, with a prescribed waveform, is measured. This technique is described and illustrated by applying it to a distributed mode loudspeaker. Originally, this loudspeaker has a rather irregular response in a wide band. When the MLS signal is pre-emphasized with the proper inverse filter, a shorter impulse response is measured with a zero-phase cosine-magnitude spectrum.