Ambiguity properties of quadratic congruential coding

The ambiguity characteristics of multiple access frequency hop codes based on standard quadratic congruences are investigated in the light of results obtained for codes based on Costas arrays and extended quadratic congruences. While the autoambiguity properties are found to be very similar to those of Costa codes, i.e. nearly ideal, the cross-ambiguity properties of quadratic congruential codes are much better. These results are valid across the whole class of code sets considered, but they are obtained at some expense in the pulse compression characteristics of the codes. A uniform upper bound is placed on the entire cross-ambiguity function surface, and bounds are placed on the amplitude of spurious peaks in the autoambiguity function. These bounds depend on the time-bandwidth product and code length exclusively and lead naturally to a discussion of the design tradeoffs for these two parameters. Examples of typical autoambiguity and cross-ambiguity functions are given to illustrate the performance of quadratic congruential coding with respect to Costas coding     

On cross-ambiguity properties of Welch-Costas arrays

We discuss cross-ambiguity properties of a specific family of Costas arrays called Welch-Costas (W-C) arrays. These properties are of interest in multiuser radar and sonar system, especially since Costas arrays are known to possess ideal auto-ambiguity functions. The theory of W-C arrays is reviewed. It is then proved that only pairs of W-C arrays can have at most two hits in their cross-ambiguity function (best possible case). The maximum number of hits in the cross-ambiguity functions of a family of W-C arrays is shown to be a function of the number of W-C arrays in the family. The upper bound on the number of hits in the cross ambiguity functions for a family of W-C arrays is also derived. Specific examples of how reducing the number of W-C arrays improves the cross-ambiguity properties are given for various types of prime numbers     

Time-frequency hop codes based upon extended quadratic congruences

Time-frequency hop codes are developed that can be used for coherent multiuser echolocation and asynchronous spread spectrum communication systems. They represent a compromise between Costas codes, which have nearly ideal autoambiguity but not so good cross-ambiguity properties, and linear congruential codes, which have nearly ideal cross-ambiguity but unattractive autoambiguity properties. Extended quadratic congruential code words are shown to have reasonably good autoambiguity and cross-ambiguity properties across the whole class of code sets considered. A uniform upper bound is placed on the entire cross-ambiguity function surface, and bounds are placed on the position and amplitude of spurious peaks in the autoambiguity function. These bounds depend on the time/bandwidth product and code length exclusively and lead naturally to a discussion of the design tradeoffs for these two parameters. Examples of typical autoambiguity and cross-ambiguity functions are given to illustrate the performance of the new codes     

Time-Frequency HOP Signals Part I: Coding Based upon the Theory of Linear Congruences

Time-frequency hop codes are developed based upon the theory of linear congruences. These codes can be used for multiuser radar and asynchronous spread spectrum communications systems. A uniform upper bound is placed on the cross-correlation function between any two elements of the code set. The upper bound is minimized by choice of time-bandwidth product and is shown to diminish as 2/N, where N is the number of elements in the code set. The size and position of spurious peaks in the autocorrelation functions are discussed. The results are extended to narrowband ambiguity functions.     

鲁棒EKF在脉冲星导航系统中的应用

针对脉冲星导航系统的滤波问题,传统的扩展卡尔曼滤波(EKF)算法存在不能克服系统模型存在不确定性参数以及乘性噪声等缺陷,提出一种鲁棒EKF算法。首先,分析了状态预测误差方程和估计误差方程,利用统计学原理,得到了状态预测方差矩阵和状态估计方差矩阵计算等式。由于系统模型存在不确定性参数,状态预测协方差矩阵和状态估计协方差矩阵无法计算;因此,利用4个重要矩阵不等式,分析并找到预测方差矩阵和状态估计方差矩阵的上界。最后,利用状态估计误差协方差矩阵上界设计状态增益矩阵,使得状态估计协方差矩阵的迹最小。将该算法对脉冲星导航系统进行仿真,仿真结果验证了所提算法的有效性。     

基于扩张状态观测器的舰载机俯仰自适应滑模控制

传统自适应滑模需要系统扰动上界的先验信息和易引发作动器抖振是其不便用于工程实际的主要原因。文章基于扩张状态观测器对传统自适应滑模进行了改进,利用扩张状态观测器(ESO)实时观测外扰并在自适应滑模控制中进行补偿。将改进后的自适应滑模应用于舰载机俯仰姿态控制中,进行仿真计算。计算结果表明,在系统扰动上界未知的情况下,ESO提高了自适应滑模的鲁棒性,消除了抖振。     

Efficient wideband signal parameter estimation using a radon-ambiguity transform slice

A novel efficient technique based on a single slice Radon-ambiguity transform (RAT) for time-delay and time-scale estimation is proposed. The proposed approach combines the narrowband cross-ambiguity function (NBCAF), the wideband cross-ambiguity function (WBCAF), and a single slice RAT to estimate multiple target parameters in noisy environments. The square modulus of Gaussian-enveloped linear frequency modulated (GLFM) signals has high-energy centrality in the ambiguity plane. Its peaks in the NBCAF fall along nearly straight lines whose slopes depend on the Doppler rates of the moving targets. These lines could be effectively detected by computing the entire Radon transform of the NBCAF for all possible angles; however, it is a computationally intensive procedure. It is shown that without calculating the entire RAT, it is possible to estimate target parameters using only a single slice of the RAT, i.e., using an appropriate projection of the NBCAF. It is demonstrated that the proposed method can successfully separate overlapping targets efficiently. The efficiency is achieved due to fast Fourier transform (FFT)-bascd processing, use of a single slice of RAT, and the use of only one-dimensional (1-D) searches.     

Generalized Response of a Linear FM Pulse Compression Matched Filter

A pulse compression matched filter is analyzed so that the response may be computed when the pulse width, FM rate, and center frequency simultaneously differ from design conditions. Unilateral and bilateral time domain amplitude weighting for sidelobe reduction is included. A general cross-ambiguity function is defined to include these effects and some basic computed results are presented for the peak envelope response with various degrees of Hamming weighting. Computer evaluation of this cross-ambiguity function allows one to choose a combination of mismatches for signal design trade-off between resolution and detection performance. Since no restrictions are placed upon the mismatch parameters, this analysis may also be used to evaluate the filter discrimination against various interfering signals.     

Comments on "on Probability of Error in Decision Feedback Equalizer"

The above-mentioned paper [1] derives bounds on the error probability of a decision feedback equalizer (DFE) which are claimed to be significantly tighter than the earlier upper bound of [2]. Unfortunately, [1] makes an unsupportable assumption which reddars the conclusions incorrect. We show that valid bounds can be obtained by the methods of [1], but that for the numerical example of [2] , the resulting upper bound is never tighter than, and sometimes significantly weaker than, that derived in [2]. Similarly, a lower bound derived by the method of [1] is shown for the same numerical example to be very close to the error-free past lower bound previously known.     

Frequency hop multiple access codes based upon the theory of cubiccongruences

The need for families of frequency-hop codes which have mutually small auto-ambiguity and cross-ambiguity functions is discussed. Current coding methods are reviewed. A new family of frequency-hop codes based upon the number-theoretic concept of cubic congruences is introduced. It is shown that for about 50% of the prime numbers, families of full codes exist which have at most two coincidences for any time-frequency shift in their auto-ambiguity functions and at most three coincidences in the set of mutual cross-ambiguity functions     

一类中立型高维周期微分系统的周期解

文中利用指数型二分法,结合不动点定理考虑如下形式的中立型高维周期系统: 苦d/dt[x(t)+cx1]=A(t,x(t))x(t)+f(t,x1),得到其T-周期解存在的充分性条件,所得结论改进或推广了早先文献中周期解存在的相应结论。     

Periodic ambiguity function of CW signals with perfect periodicautocorrelation

A periodic ambiguity function (PAF) is discussed which describes the response of a correlation receiver to a CW signal modulated by a periodic waveform, when the reference signal in the receiver is constructed from an integral number N, of periods T, of the transmitted signal. The PAF is a generalization of the periodic autocorrelation function, to the case of non-zero Doppler shift. It is shown that the PAF of N periods is obtained by multiplying the PAF of a single period by the universal function sin(Nπν T)/N sin(πνT), where ν is the Doppler shift, to phase-modulated signals which exhibit perfect periodic autocorrelation when there is no Doppler shift. The PAF of these signals exhibits universal cuts along the delay and Doppler axes. These cuts are functions only of t, N and the number M, the modulation bits in one period     

Ambiguity Functions for Quadratic Phase-Coded Pulse Trains

The matched filter ambiguity function is presented for a burst waveform composed of repeated subbursts, each one of which consists of N pulses in which the phase is varied quadratically from pulse to pulse. The resulting ambiguity function exhibits small residual ambiguities along the delay axis separated by the reciprocal of the pulse repetition frequency (PRF). A cross-ambiguity function is derived which reduces these ambiguities to zero amplitude. A third cross-ambiguity function is presented for a receiver matched to a generalized Hamming weighted repeated quadratic burst. The location in the delay/Doppler plane of the waveform ambiguities for these waveforms is compared with that of an uncoded pulse burst.     

Grid-Adaptive Computations of Magnetized Jets

We present grid-adaptive numerical simulations of magnetized plasma jets, modeled by means of the compressible magnetohydrodynamic equations. The Adaptive Mesh Refinement strategy makes it possible to investigate long-term jet dynamics where both large-scale and small-scale effects are at play. We extend recent findings for uniformly magnetized, periodic shear layers to planar and fully 3D extended jet segments. The jet lengths cover multiple, typically 10, axial wavelengths of the fastest growing Kelvin–Helmholtz (KH) like modes. The dominant linear MHD instabilities of the jet flows are quantified by means of MHD spectroscopic analysis. In cases characterized by sonic Mach numbers about unity and large plasma beta values, both single and double shear layers (planar jets) manifest self-organizing trends to large scales, e.g. by continuous pairing/merging between co-rotating vortices, simultaneously with the introduction of small-scale features by magnetic reconnection events. The vortices form as a result of KH unstable shear-flow layers, and their coalescence arises from the growth of subharmonic modes at multiple wavelengths of the fastest growing KH instability. In extended two-dimensional jet segments, we investigate how varying jet width alters this coalescence process occurring at both edges, e.g. by introducing Batchelor-like coupling between counter-rotating vortices formed at opposing weakly magnetized, close shear layers. Finally, periodic segments of supersonic magnetized jets are simulated in two- and three-dimensional cases, which are characterized by violent shock-dominated transients.     

RFNN control for PMLSM drive via backstepping technique

A robust fuzzy neural network (RFNN) control system is proposed in this study to control the position of the mover of a permanent magnet linear synchronous motor (PMLSM) drive system to track periodic reference trajectories. First, an ideal feedback linearization control law is designed based on the backstepping technique. Then, a fuzzy neural network (FNN) controller is designed to be the main tracking controller of the proposed RFNN control system to mimic an ideal feedback linearization control law, and a robust controller is proposed to confront the shortcoming of the FNN controller. Moreover, to relax the requirement for the bound of uncertainty term, which comprises a minimum approximation error, optimal parameter vectors and higher order terms in Taylor series, an adaptive bound estimation is investigated where a simple adaptive algorithm is utilized to estimate the bound of uncertainty. Furthermore, the simulated and experimental results due to periodic reference trajectories demonstrate that the dynamic behaviors of the proposed control systems are robust with regard to uncertainties.     

Comments on "Bounds on Probability of Error in Decision Feedback Equalizers"

In the above paper1 a technique was proposed to derive an upper bound on the error probability of a decision feedback equalizer. It involves decomposition of the probability density function of residual intersymbol interference and derivation of Chebyshev-type bounds on the error functionals over the decomposed functions. In this correspondence, we demonstrate that the technique is not applicable in general. The result is not a bound in many cases.     

Coordinate Conversion and Tracking for Very Long Range Radars

The problem of tracking with very long range radars is studied in this paper. First, the measurement conversion from a radar's r-u-v coordinate system to the Cartesian coordinate system is discussed. Although the nonlinearity of this coordinate transformation appears insignificant based on the evaluation of the bias of the converted measurements, it is shown that this nonlinearity can cause significant covariance inconsistency in the conventionally converted measurements (CM1). Since data association depends critically on filter consistency, this issue is very important. Following this, it is shown that a suitably corrected conversion (CM2) eliminates the inconsistency. Then, initialized with the converted measurements (using CM2), four Cartesian filters are evaluated. It is shown that, among these filters, the converted measurement Kalman filter with second order Taylor expansion (CM2KF) is the only one that is consistent for very long range tracking scenarios. Another two approaches, the range-direction-cosine extended Kalman filter (ruvEKF) and the unscented Kalman filter (UKF) are also evaluated and shown to suffer from consistency problems. However, the CM2KF has the disadvantage of reduced accuracy in the range direction. To fix this problem, a consistency-based modification for the standard extended Kalman filter (E1KF) is proposed. This leads to a new filtering approach, designated as measurement covariance adaptive extended Kalman filter (MCAEKF). For very long range tracking scenarios, the MCAEKF is shown to produce consistent filtering results and be able to avoid the loss of accuracy in the range direction. It is also shown that the MCAEKF meets the posterior Carmer-Rao lower bound for the scenarios considered.     

Cochannel Interference Analysis between Spaceborne and Terrestrial Radars

An analysis of cochannel interference between spaceborne and terrestrial radars is presented. A generic modeling methodology is applied, which, it is felt, will represent the worst-case situation. In order to account for Doppler shifts, auto-and cross-ambiguity functions ions have been developed for determining matched filter outputs. The results support the ability of such radar systems to coexist relatively harmoniously utilizing currently accepted assignment procedures.     

IMA双层调度算法中的任务可调度性分析方法

任务可调度性分析是综合模块化航电(IMA)系统双层调度算法研究中的一个关键问题。针对这个问题,首先剖析了单分区调度系统中任务精确响应时间计算方法所具有的计算复杂度高以及计算函数不连续等局限性;然后提出了一种计算任务响应时间上限的快速方法,分析该计算方法的推导过程,得到了双层调度情况下任务响应时间上限的计算方法,并由此推演出任务可调度性分析方法和分区参数设计方法;最后通过计算机仿真实验,分别使用定量的响应时间上限相对误差法以及定性的资源放大分析法考察了系统任务数量以及系统利用率对文中提出的响应时间上限计算方法精度的影响程度,并得到了该方法取得较高应用精度的可行性条件。     

变薄拉深的上限法分析

根据上限法原理建立了一种适用于分析变薄拉深的上限模型,包括两个用于优化上限解的独立参数。通过优化计算,变薄拉深力理论值与实验值吻合良好;用该模型研究了变薄拉深系数、凹模半锥角、原始筒形件内外径比、定径带相对长度以及内外摩擦因子等主要工艺参数对变薄拉深力的影响规律。