On Conopulse Radar Theoretical Angle Tracking Accuracy

The Cramer-Rao analysis method is applied to a conopulse radar to determine a lower bound on the variance of angle tracking error. The analysis allows the calculation of the variance independent of the form of the signal processor attached to the antenna. Under reasonable assumptions it is found that angle error variance is larger than that of a similar monopulse system by a factor of 2.     

Some properties of retrodirective beam of multiple sidelobecanceler

The retrodirective or perturbation beam concept is often used to aid in explaining the nulling of interference sources. The classical explanation for cancellation of a single-zero-bandwidth source is that of a perturbation beam steered to and peaking at that interferer angle. The subtraction of this perturbation beam from the main beam causes the nulling. It is shown that, for discrete point main and auxiliary antennas, this explanation can be generalized to non-zero bandwidth sources. It is demonstrated that if the main and auxiliary antennas are spatial points, then the retrodirective beam is nonuniformly weighted, steered to the interference source, and peaks at the interferer angle. For the more realistic assumption of a nonpoint main antenna, the retrodirective beam does not peak at the interferer angle for any bandwidth     

Dimension reduction for array processing with robust interference cancellation

We present a robust solution for data reduction in array processing. The purpose is to reduce the computation and improve the performance of applied signal processing algorithms by mapping the data into a lower dimension beamspace (BS) through a transformation. Nulls steering to interference are incorporated into a transformation using the subspace projection technique, and the BS spatial spectrum estimation accuracy is evaluated and maximized with a measure. The derived transformation tries to preserve the full-dimension Cramer-Rao bounds (CRBs) for the parameters of interest while rejecting undesired signals effectively. When compared with an optimal method and an adaptive approach, simulation results show that significant improvements are obtained in terms of BS direction-of-arrival (DOA) estimation root-mean-squared error (RMSE), bias, and resolution probability.     

Effect of bias on bearing-only target location

The influence of angle measurement bias on passive target location estimation is investigated. First the conditions for target observability are found and generalized to the non-zero-mean measurement noise case. Then the Cramer-Rao lower bound on the estimation error is derived. Numerical examples are included, illustrating the target location uncertainty in the presence of measurement bias     

基于最优误差动力学的时间角度控制制导律

针对带有攻击时间和终端攻击角度约束的导弹制导问题,设计了一种基于最优误差动力学的时间角度控制制导律,并给出了明确的性能指标。推导广义最优角度控制制导律作用下的剩余飞行时间估算表达式,在广义最优角度控制制导律的基础上增加攻击时间误差反馈项,将攻击时间误差看做跟踪误差,设计的制导律使跟踪误差以最优模式在有限时间内收敛到零,最终实现攻击时间和终端攻击角度的共同控制。对不同参数下的情况进行仿真,验证了所提制导律的有效性。     

Multicomponent receiver architectures for GPS interference suppression

The global positioning system (GPS) is a one-way satellite-based navigation system employing spread-spectrum techniques that is widely used for commercial and military applications. Although the very low signal-to-noise ratio (SNR) is handled by the large spreading gain, GPS is susceptible to high-power interference signals and various types of jammers. We propose multicomponent receiver architectures for GPS interference suppression. A conventional antenna system is first considered which utilizes a minimum-variance distortionless-response (MVDR) beam former and assumes that the GPS signal angle of arrival (AOA) and the antenna model are known at the receiver. However, this receiver is sensitive to AOA estimation errors and can have a high computational complexity. This sensitivity problem is eliminated by a multicomponent system based on a multistage matched filter (MF). Since this MF receiver also has a high computational complexity because the jammer AOAs must be estimated, we introduce a blind interference canceler based on the constant modulus (CM) array that is insensitive to AOA estimation errors and has a low computational complexity. Computer simulations are provided to illustrate the performance of the various systems for interference suppression in example signal scenarios.     

Instrumental variable adaptive array processing

An instrumental variable (IV) approach is presented for estimating the weights of an adaptive antenna array. Theoretical analysis of the IV method shows that the antenna gain weights are independent of finitely correlated noise, so that unbiased estimation of signal arrival angles is possible. Only matrix inversions are required to compute the weight estimates. In this sense, the IV method provides performance comparable with eigenvector techniques but with lower computational burden. Both minimal and overdetermined IV estimators are derived. The overdetermined estimators give the same theoretical array weights as minimal estimators, but yield more accurate weight estimates in real data situations. Simulation results are presented to compare these IV methods with one another and with conventional matrix inversion weight estimators. In these examples it is seen that IV methods are able to resolve closely spaced interference sources when conventional matrix inversion techniques cannot. It is also shown that overdetermined methods are capable of providing weight estimates with lower variances than those of minimal methods     

Theoretical analysis of the sequential lobing technique

A theoretical analysis of the sequential lobing technique for target angle tracking is presented. The signal power received by each antenna beam is assumed to pass through a logarithmic amplifier. A rigorous statistical approach is adopted in the analysis for both non-fluctuating and fluctuating targets. Closed form expressions are derived for the normalized mean error and rms error of the angle estimate for Swerling 0, I, II, and III targets. Results are compared with those obtained using a simplified approach for the non-fluctuating target     

深空探测多天线组阵的增益损失研究

为定量分析上行天线组阵增益损失的影响因素,提出一种通过建立数学模型分析合成损耗的估计方法.首先基于天线原理和电磁波传输理论建立了天线组阵上行链路信号的数学模型,以统计学理论对数学模型进行分析,得到了影响上行链路信号的若干因素.通过分析得出,深空探测信号在远距离传输中因大气相位扰动引起的误差是造成天线组阵增益损失的最主要因素.再通过对大气相位扰动误差的进一步分析,构建S频段和X频段下大气相位扰动的空间自相关模型和时间自相关模型,得到组阵基线长度和工作仰角同合成损耗的关系.经过对各误差源的分析可知,在目前的技术水平下,能够满足上行天线组阵工程应用的精度要求.     

CRB: Sinusoid-Sources' Estimation using Collocated Dipoles/Loops

This work derives new asymptotic Cram?r-Rao lower bounds (CRB) for the estimation of multiple pure-tone incident signals' azimuth-elevation arrival-angles, polarization parameters, frequencies, amplitudes, and temporal phases—based on data collected by spatially collocated but orthogonally oriented dipoles and/or loops. The incident sources are pure-tones at distinct, deterministic but unknown frequencies, in contrast to the case of all incident sources at one common known frequency, as has been investigated in the existing research literature on the CRB for diversely-polarized direction-finding. The derived CRBs are closed-form expressions, explicitly in terms of the signal parameters. The new CRBs presented here reveal how a constituent dipole and/or loop's presence and orientation may affect estimation precision, thereby offering guidelines to the system engineer on what dipole(s) and/or loop(s) to include or to omit in constructing the electromagnetic vector-sensor.     

Phase Monopulse Error Due to Nonuniform Noise Background

A phase monopulse antenna system can be used for the high accuracy tracking of active or passive objects in space or on earth. Far-field noise sources that are present in the background of the object being tracked will introduce an offset or bias error in the determination of the angle of incidence of the coherent sinusoidal wave received from the source. The dependency of this bias error upon the nonuniformity of the noise background or equivalently upon the asymmetry of the antenna patterns about the direction to the signal being tracked is determined. Although the variance in the measurement of the sinusoidal source direction can be reduced by increasing the post detection integration time, it is shown that the bias or offset error is unaffected by this change. In order to decrease the offset or bias error the predetection bandwidth must be reduced.     

嵌套阵列最大似然估计测向算法

针对在辐射源个数未知的条件下嵌套阵列难以估计多个辐射源角度的问题,提出了基于最大似然估计(MLE)的嵌套阵列角度估计算法。算法在嵌套阵列模型的基础上,首先通过推导阵列截获多辐射源信号的最大似然函数及其梯度,利用最速下降法估计出空域中所有潜在辐射源的角度;然后,通过多元假设检验,利用最大似然比与门限进行比较,确定出空域中所有潜在辐射源中某一时刻发射信号的活跃辐射源角度,排除其余噪声形成的虚假辐射源角度,解决了在辐射源个数未知条件下嵌套阵列对多个辐射源角度估计问题。仿真结果表明:与传统多重信号分类(MUSIC)算法相比,该算法在辐射源数目未知、存在相干信号、低信噪比(SNR)、低快拍数条件下,均具有较好的角度估计精度,并且算法形成的虚拟阵列自由度是空间平滑MUSIC算法的2倍;多元假设检验法比传统信源数目估计算法在低信噪比条件下和处理相干信号方面具有明显优势。     

Bounds on the Probability of Error in Digitial Communications

A class of upper bounds and lower bounds on the probability of error in digital communications are derived. Several degrading factors like intersymbol interference, cochannel interference, inaccurate carrier synchronization, and incoherent detection can be considered in obtaining the bounds. Several examples are given and it is shown that many situations not considered so far can be put into the conceptual framework developed here.     

Application of the Volterra Series to the Analysis and Design of an Angle Track Loop

A typical function of an angle tracking loop is to keep a radar antenna pointed at a target. The error in pointing is directly related to successful operation of the tracking device; therefore, its behavior is of interest. For a tracker with a general polynomial nonlinearity, an arbitrary initial pointing error, and a bounded deterministic input, a method is developed for finding upper bounds on the magnitude of the tracking error using Volterra series techniques. Convergence regions of the Volterra series are also obtained. Applications of these results are made to a second-order tracking device.     

数字闭环光纤陀螺的调制串扰误差

 通过分析数字闭环光纤陀螺的阶梯波调制信号与输出死区、周期噪声干扰及小角速度漂移的关系,提出了调制串扰误差的概念。指出调制信号与探测器输出信号之间的电交叉耦合及调制信号产生的调制误差是产生调制串扰误差的干扰源。将调制串扰通道模型简化为比例环节和部分积分环节,并和光纤陀螺理想模型结合,建立了光纤陀螺调制串扰误差模型,利用该模型推导出了产生死区的条件及周期噪声干扰和小角速度漂移造成的输出偏差表达式,并对周期噪声的幅值、频率与陀螺输出量级、带宽之间的关系进行了定量分析。调制串扰误差的仿真和实验结果与理论分析结果基本一致,验证了调制串扰误差模型的正确性。     

An Application of Radiometric Techniques to Precision Angle Tracking Radar Systems

A new technique is described which provides for precision angle tracking of celestial radio sources with a conventional monopulse antenna receiving system. It is shown that this technique is readily adapted to angle tracking radars. The features of conventional monopulse operation are preserved while permitting precise angle tracking of noise sources when signal to noise ratios are much less than unity. Measurements, using a four-horn monopulse feed with a 28-foot parabolic reflector and a "monopulse radiometer" produced the characteristic monopulse angle detection functions when using the sun, the moon, and Cassiopeia A as boresight reference sources. Precision measurements were made to 8 arc second under varying weather conditions using 28-foot radio astronomy antennas. The accuracy of the measurements were limited by the antenna angle encoders, consequently no conclusions are drawn with regard to the absolute accuracy of the measurements. The celestial coordinates of four discrete radio sources and the equations for coordinate transformation to local elevation and azimuth are contained in the Appendixes.     

Bounds on Elevation Error Estimates of a Target in Multipath

The Cramer-Rao bound for an unbiased estimate of the elevation angle of a target in the presence of multipath is calculated for the symmetric (target and image symmetric about the elevation symmetry plane of antenna) and nonsymmetric cases for an antenna consisting of 21 elements. These bounds are compared to the maximum likelihood estimates and it is found that the rms error of the maximum likelihood estimate (which has a bias) is below the Cramer-Rao bound for unbiased estimates.     

基于超短基线声传感器阵的高速目标轨迹估计

针对低空高速飞行目标跟踪问题,首先研究了某典型目标噪声信号的时频特性,发现其信号呈现宽带低频特征,难以从频域对目标轨迹进行估计。在此基础上,从各路接收信号的到达时延量入手,考虑到声基阵只能布设于有限空间内的制约,提出了一种基于超短基线阵时延估计的目标跟踪方法。该方法利用各个超短基线阵接收声强极值点分别估计目标运动轨迹垂线方向,计算多个垂线的叉乘向量实现对目标运动方向的估计,再利用多面交汇的方式获估计得到目标运动轨迹。分别对目标俯仰角、方位角及运动轨迹估计的理论误差进行了推导,根据理论估计误差,为能够实现对目标运动轨迹的估计,各个超短基线阵应尽量保证与目标运动轨迹不在同一平面上。根据仿真结果,在采用4个传感器基阵时,角度估计平均误差在4°以内,位置估计相对误差在5%左右。仿真结果验证了该方法的有效性。     

Interferometer Design for Elevation Angle Estimation

Radars that are developed for the purpose of monitoring aircraft landings in the terminal air traffic control system can be designed to exploit the relatively high signal-to-noise ratio that characterizes the power budgets calculated for such a link. An interferometer using a pair of low gain antennas can be used to obtain passive coverage over a targe azimuth and elevation sector. A large baseline can be used to obtain the desired elevation angle estimation accuracy. In this paper an optimal tradeoff between the width of the subarray aperture and the width of the interferometer baseline is performed that achieves a specified elevation angle estimation error while minimizing the overall height of the interferometer configuration. The algorithm searches through the class of antenna patterns that can be synthesized from so-called finite impulse response, linear phase digital filters. For the specific problem of designing an elevation sensor for monitoring landing aircraft on final approach, the elevation angle can be estimated with no more than 1-mrad rms error when the aircraft is within ± 60° azimuth, 2.5° to 40° elevation, using two 7-wavelength subarray antennas spaced 8 wave-lengths apart. The design of a separate sensor for resolving the interferometer ambiguities is formulated as a hypothesis testing problem and solved using statistical decision theory. A bound on the probability of an ambiguity error is derived that accounts for the effects of ground reflection multipath and receiver noise.     

Tracking Performance of a Monopulse Radar in the Presence of Multiple Targets

The equations derived by A. J. Rainal for the probability density function of the angle error output of a monopulse radar excited by a Gaussian signal and Gaussian thermal noise are generalized to include the presence of multiple targets. The examples given demonstrate the radar's behavior for various combinations of target and noise parameters.