Discrete-Time Nonlinear Filtering Algorithms Using Gauss–Hermite Quadrature

In this paper, a new version of the quadrature Kalman filter (QKF) is developed theoretically and tested experimentally. We first derive the new QKF for nonlinear systems with additive Gaussian noise by linearizing the process and measurement functions using statistical linear regression (SLR) through a set of Gauss-Hermite quadrature points that parameterize the Gaussian density. Moreover, we discuss how the new QKF can be extended and modified to take into account specific details of a given application. We then go on to extend the use of the new QKF to discrete-time, nonlinear systems with additive, possibly non-Gaussian noise. A bank of parallel QKFs, called the Gaussian sum-quadrature Kalman filter (GS-QKF) approximates the predicted and posterior densities as a finite number of weighted sums of Gaussian densities. The weights are obtained from the residuals of the QKFs. Three different Gaussian mixture reduction techniques are presented to alleviate the growing number of the Gaussian sum terms inherent to the GS-QKFs. Simulation results exhibit a significant improvement of the GS-QKFs over other nonlinear filtering approaches, namely, the basic bootstrap (particle) filters and Gaussian-sum extended Kalman filters, to solve nonlinear non- Gaussian filtering problems.     

平方根求积分卡尔曼滤波器

 针对具有加性噪声的非线性高斯动态系统的状态估计问题,本文提出一种近似递归的高斯滤波器:平方根求积分卡尔曼滤波器(SRQKF).该滤波器是在求积分卡尔曼滤波器(QKF)基础上的平方根实现形式,使用统计线性回归的方法,通过一套参数化高斯密度的高斯-厄米特积分点来线性化非线性函数的;滤波器采用平方根的实现方法,不仅增强了数值的鲁棒性,确保了状态协方差矩阵的半正定性,而且在一定程度上提高了滤波精度.仿真实验表明,SRQKF的滤波精度比QKF提高约12%,且均高于无味滤波器(UF)和扩展卡尔曼滤波器(EKF),但这二者的计算复杂度均比UF和EKF大.对滤波精度要求比较高的非线性场合,新滤波器是一种很有效的非线性滤波算法.     

Nonlinear diffusion for orientation estimation

This letter presents an image orientation estimation method which is based on a combination of two techniques： quadrature filtering and nonlinear diffusion. The quadrature filters are used to get the orientation tensors for edges, then the orientation tensors are smoothed through nonlinear diffusion. Experimental resuits and analysis show the robustness of the proposed method.     

QPSK, Staggered QPSK, and MSK--A Comparative Evaluation

Bandwidth- and power-efficient quadrature carrier modulation techniques are identified, evaluated, and compared. The modulation techniques include quadrature phase shift keying (QPSK), staggered QPSK (SQPSK), and minimum (frequency) shift keying (MSK). High quality QPSK, SQPSK, and MSK transmitters and receivers were used in the evaluation, along with a computer simulation program which modeled the hardware. Both linear and nonlinear channels were included in the comparative investigation. The agreement between simulated and measured results is shown to be excellent. In the comparison of modulation techniques, the effects of channel filtering (band limiting), nonlinearities, detection techniques, and phase equalization are addressed. The application-oriented results are intended to be an aid in selecting modulation and detection implementations, and in predicting the performance of linear and nonlinear communication systems. For systems with imperfections, data are presented for determination of passive detection filters which can outperform "matched" integrate and dump (I&D) filters.     

Linear Amplification by Sampling Techniques: A New Application for Delta Coders

A new technique for linear amplification of envelopevarying bandpass signals using sampling techniques (LIST) and devices having nonlinear input-output relationships is described. Two component signals are produced by phase-reversal modulating two quadrature carriers with two delta-coded low-pass envelopes derived from the quadrature components of a bandpass signal. The component signals either are produced at a high level or are amplified in nonlinear amplifiers. An amplified replica of the input signal results from passively summing and bandpass filtering these two component signals. A laboratory demonstration shows that a LIST amplifier with spurious 40 dB below desired signals in a two-tone test is easily achieved.     

Adaptive pre- and post-compensation of nonlinear distortions for high-level data Modulations

In this letter, we show how different signal processing techniques can be combined to optimize the performance of a typical wideband nonlinear satellite link with spectrally efficient high-level modulation techniques. In particular, we follow two concurrent approaches: on one side, we pursue signal optimization in the form of special amplitude and phase shift keying (APSK) constellations to reduce the effect of nonlinear distortions, while on the other, we analyze the feasibility of adaptive data predistortion (DP) at the transmitter and adaptive nonlinear equalization (NLE) at the receiver. We demonstrate that the use of such optimized constellations relieves the complexity of the nonlinearity compensation techniques, and we also show that by clever adoption of these techniques the sensitivity to nonlinear distortion of both uncoded and turbo coded quadrature amplitude modulation and APSK constellations is greatly reduced.     

On the Spectral Skewness of a Narrow-Band Gaussian Process

This correspondence discusses techniques for estimating the spectral skewness of the baseband spectrum of the complex envelope of a narrow-band Gaussian process from its undistorted and distorted (by memoryless nonlinear devices) in-phase and quadrature components. Some applications of the spectral skewness in communication theory are also mentioned.     

基于统计线性回归的粒子滤波方法

针对非线性、非高斯系统的状态估计问题,该文提出了一种基于统计线性回归的粒子滤波算法。在该算法中,首先对非线性函数基于统计线性回归展开,并利用高斯积分估计回归系数,依此产生重要性密度函数。该密度函数融入了最新的观测信息,扩大了与系统真实后验密度的重叠区域。理论分析和实验结果表明,该算法具有较高的估计精度,与一般的粒子滤波算法相比,有较好的稳定性和较低的计算量。     

A general linear-regression analysis applied to the 3-parameterWeibull distribution

The conventional techniques of linear regression analysis (linear least squares) applied to the 3-parameter Weibull distribution are extended (not modified), and new techniques are developed for the 3-parameter Weibull distribution. The three pragmatic estimation methods in this paper are simple, accurate, flexible, and powerful in dealing with difficult problems such as estimates of the 3 parameters becoming nonpositive. In addition, the inherent disadvantages of the 3-parameter Weibull distribution are revealed; the advantages of a new 3-parameter Weibull-like distribution over the original Weibull distribution are explored; and the potential of a 4-parameter Weibull-like distribution is briefly mentioned. This paper demonstrates how a general linear regression analysis or linear least-squares breaks away from the classical or modern nonlinear regression analysis or nonlinear least-squares. By adding a parameter to the simplest 2-parameter linear regression model (AB-model), two kinds of ABC models (elementary 3-parameter nonlinear regression models) are found, and then a 4-parameter AABC model is built as an example of multi-parameter nonlinear regression models. Although some other techniques are still necessary, additional applications of the ABC models are strongly implied     

Nonlinear signal–noise interactions in dispersion-managed links with various modulation formats

Purpose of this paper is to highlight the principles of the nonlinear signal–noise interaction (NSNI) in dispersion-managed long-haul optical links and provide a quantitative understanding of the system parameters for which NSNI sets the nonlinear performance of the most popular intensity and phase modulation formats, namely on–off keying, differential binary and quadrature phase-shift keying and coherent quadrature phase-shift keying.     

A root of less evil [digital signal processing]

This work discusses several methods for estimating the square root of a number, with particular focus on high-speed techniques for approximating the square root of a single value as well as the square root of a sum of squares for quadrature (I/Q) vector magnitude estimation. The paper presents the Newton-Raphson inverse method and the nonlinear IIR filter method for estimating the square root of a single value using iterative methods. It also presents the binary-shift magnitude estimation method and the equiripple-error magnitude estimation method for estimating the magnitude of a complex number.     

The influence of electromagnetic environment on operation of activearray antennas: analysis and simulation techniques

This paper presents an overview of active array antennas, system-level nonlinear effects in such antennas, and their modeling and simulation techniques. Advantages of active array antennas, in comparison with passive array antennas, are discussed. The influence of nonlinear distortions and interference in active antennas on the overall system performance is considered. Modeling and simulation techniques that can be applied to active array antennas are substantially different from those used for circuits and systems. Analytical and numerical techniques are used for the analysis of active antennas, with the prevailing use of numerical techniques at the present time. Electromagnetic-level and circuit-level simulation techniques are discussed. System-level simulation techniques are considered in detail, with special emphasis on their application to active array antennas. The “instantaneous” quadrature technique is proposed as an effective tool for numerical simulation of active arrays over wide frequency and dynamic ranges in a computationally-effective way     

一种目标特性辅助的积分粒子滤波新方法

针对非均匀稀疏采样环境下目标跟踪中的非线性滤波问题,提出了一种基于Gauss-Hermite积分和目标特性辅助的积分粒子滤波新方法(AQPF).在该方法中,构建了基于Gauss-Hermite积分的积分点概率密度函数作为重要性密度函数,同时,在时间更新阶段引入目标观测、目标观测的有效时间间隔、目标速度等目标特性,综合改善滤波器中预测粒子和预测协方差估计的准确性和粒子的多样性,有效提高目标状态的估计性能.实验结果表明,提出方法的估计性能要明显好于无迹kalman滤波(UKF)、积分kalman滤波(QKF)、粒子滤波(PF)、辅助粒子滤波(APF)和高斯粒子滤波(GPF),能够有效对目标状态进行估计.     

Characterizing the effects of nonlinear amplifiers on linearmodulation for digital portable radio communications

The design and performance of linear modulation techniques and RF power amplifiers are discussed. Various types of power amplifier are used in the comparison, using simulation, of out-of-band radiation and power efficiency. The designs focus on high-frequency silicon bipolar power amplifiers suitable for low-power portable radio applications. Two different 4-QAM (4-level quadrature amplitude modulation) schemes are compared. Power efficiency as high as 40% can be achieved using a dynamically biased amplifier operating near saturation. The effects of nonlinear distortions from power amplifiers on adjacent channel interference as well as bit and block error rate performance are also investigated     

Performance analysis of AF OFDM system using multiple relay in presence of nonlinear‐PA over inid Nakagami‐m fading

In this paper, performance of an orthogonal frequency division multiplexing–based variable‐gain amplify and forward cooperative system using multiple relay with relay selection is analyzed over independent but not necessarily identically distributed frequency selective Nakagami‐m fading channels. For the analysis, nonlinear power amplifier is considered at the relay, and selection combining is adopted at destination node. Closed‐form expressions of the outage probability for various threshold signal‐to‐noise ratio (SNR) values and average symbol error rate for M‐ary quadrature amplitude modulation techniques are derived for the considered system. Further, the outage probability analysis is performed in high SNR regime to obtain the diversity order. Furthermore, impact of different fading parameters, multiple relay, and nonlinear power amplifier is highlighted on the outage probability and asymptotic outage probability for various threshold SNRs and on the average symbol error rate for various quadrature amplitude modulation constellations. The derived analytical expressions are generalized for various fading environments while considering the integer‐valued fading parameters. Finally, all the analytical results are verified through the Monte Carlo simulations for various SNR levels and system configurations.     

稀疏网格平方根求积分非线性滤波器

针对具有加性噪声的非线性高斯动态系统的状态估计问题,本文提出一种新的基于稀疏网格法的平方根求积分滤波器(SSRQF),该滤波器通过稀疏网格取点来近似计算多维积分并进行平方根滤波.与常规QF的积分点数随着维数呈指数增长相比,该方法的积分点数随着维数呈多项式增长,减少了计算量;理论分析表明,无味卡尔曼滤波器(UKF)只是稀疏网格求积分滤波器(SQF)的一个特例,因此SSRQF在精度和取点上比UKF更为灵活.仿真实验表明,SSRQF的滤波精度均高于UKF和扩展卡尔曼滤波器(EKF),是一种效率较高的高精度非线性滤波算法.     

On the development of a multifunction millimeter-wave sensor for displacement sensing and low-velocity measurement

A new multifunction millimeter-wave sensor operating at 35.6 GHz has been developed and demonstrated for measurement of displacement and low velocity. The sensor was realized using microwave integrated circuits and monolithic microwave integrated circuits. Measured displacement results show unprecedented resolution of only 10 /spl mu/m, which is approximately equivalent to /spl lambda//sub 0//840 in terms of free-space wavelength /spl lambda//sub 0/, and maximum error of only 27 /spl mu/m. A polynomial curve-fitting method was also developed for correcting the error. Results indicate that multiple reflections dominate the displacement measurement error. The sensor was able to measure speed as low as 27.7 mm/s, corresponding to 6.6 Hz in Doppler frequency, with an estimated velocity resolution of 2.7 mm/s. A digital quadrature mixer (DQM) was configured as a phase-detecting processor, employing a quadrature sampling signal-processing technique, to overcome the nonlinear phase response problem of a conventional analog quadrature mixer. The DQM also enables low Doppler frequency to be measured with high resolution. The Doppler frequency was determined by applying linear regression on the phase sampled within only fractions of the period of the Doppler frequency. Short-term stability of the microwave signal source was also considered to predict its effect on measurement accuracy.     

光PM-DQPSK调制格式性能研究

对偏振复用-33%归零-差分正交相移键控(PM-33%RZ-DQPSK)和偏振复用-抑制载波归零-差分正交相移键控(PM-CSRZ-DQPSK)调制格式进行了传输性能仿真,在仿真过程中,分别考虑了光纤系统中的偏振模色散(PMD)、色散(CD)和非线性效应(SPM)三种限制因素。仿真结果表明偏振复用系统比非偏振复用系统更易受到PMD、CD和非线性效应的影响。整体来看,PM-CSRZ-DQPSK调制格式的传输性能比PM-33%RZ-DQPSK更为优秀。     

An adaptive digital method of imbalances cancellation in LINC transmitters

The linear amplification using nonlinear components (LINC) technique is a well-known power amplifier linearization method to reduce adjacent channel interference in a nonconstant envelope modulation system. Its major drawback is the inherent sensitivity to gain and phase imbalances between the two amplifier branches. In this paper, a novel full-digital base band method is described which corrects any gain and phase imbalances in LINC transmitters mainly due to the unmatching of the two amplifier paths. Amplifiers are characterized by a level-dependent complex gain using a memoryless model. The method uses adaptive signal processing techniques to obtain the optimal complex coefficient to adjust gain and phase imbalances. Its main advantage is the ability to track the input signal variations and adapt to the changes of amplifier nonlinear characteristics. Other effects are included in the analysis such as quadrature modulator and demodulator imbalances and loop delay. A computer simulation has been carried out to verify the method functionality.     

The Effects of Transponder Nonlinearity on Binary CPSK Signal Transmission

An analytical approach is developed to investigate the performance of coherent phase-shift keying (CPSK) systems transmitted through a nonlinear satellite transponder. A novel quadrature model of the satellite nonlinearity is introduced, and is found to yield an excellent fit to the actual traveling wave tube (TWT) characteristics as commonly used in a satellite transponder, with the advantage of requiring the choosing of only a few parameter values. Based on this quadrature model an expression for the bit error rate is derived in the form of an infinite series where the leading term corresponds to the error-rate for a linear channel and the remaining terms are correction terms accounting for nonlinear effects. The performance of a binary PSK system is computed and presented as a function of the up-link and down-link carrier-to-noise-power ratios (CNR) and a bandwidth spread factor.