Estimating the Angles of Arrival of Multiple Plane Waves

The problem of estimating the angles of arrival of M plane waves incident simultaneously on a line array with L + 1 (L?M) sensors utilizing the special eigenstructure of the covariance matrix C of the signal plus noise at the output of the array is addressed. A polynomial D(z) with special properties is constructed from the eigenvectors of C, the zeros of which give estimates of the angle of arrival. Although the procedure turns out to be essentially the same as that developed by Reddi, the development presented here provides insight into the estimation problem.     

Variance Analysis of the Angle Output Voltage for an Amplitude Monopulse Receiver

The amplitude-comparison monopulse receiver utilizes two overlapping antenna patterns to determine the angle of arrival of an incoming RF signal for use in a direction-finding application. The thermal noise introduced by the receiver distorts the signal, causing an error in determining the exact angle of arrival of the signal. The analysis derives an expression for the deviation of the angle output voltage, or the angular error, due to receiver noise as a function of 1) the angle of arrival and 2) the signal-to-noise ratios of the two channels of the receiver. A receiver using a square-law detector and one using a linear detector are analyzed.     

Detection of Target Multiplicity Using Monopulse Quadrature Angle

The feasibility of using the indicated quadrature angle of arrival of a monopulse radar to discriminate a single target from multiple targets, separated in angle within a radar resolution cell, is investigated. The analysis is performed for steady (fixed) and Rayleigh fluctuating targets which cover a broad range of target characteristics. In both cases, the interfering signals due to noise and clutter in the sum and difference monopulse channels are assumed to be independent, zero-mean Gaussian processes. Detection and false alarm probabilities are evaluated analytically and the receiver operating characteristics are obtained for both fixed and fluctuating target cases. It is shown that multiple targets can be discriminated from a single target condition by integrating the indicated monopulse quadrature angle of arrival from several independent pulses. It is also shown that the probability of detecting multiple targets increases as the fluctuation in the target radar cross section decreases, approaching the fixed amplitude case in the limit.     

Thermal Noise in Amplitude Comparison Monopulse Systems

In this paper we consider the problem of estimation of angle of arrival in an Amplitude Comparison Monopulse antenna arrangement with the explicit inclusion of internally generated thermal, i.e., receiver, noise as an interference to the desired measurement. A pulsed type radar is assumed, and an ideal (i.e., point) radar target is postulated. This latter restriction is made so that consideration of the effects of target scintillation, glint, or other external random phenomena can be excluded from our treatment of the problem. In this context, a maximum likelihood analysis is made to determine the form of the estimate of angle of arrival, and the probability density function (pdf) of this quantity is computed. The form of the estimate is found to be a ratio of Gaussian variables quite like that used in conventional monopulse signal processing. The pdf obtained for the estimate is believed to be new, and it serves to emphasize the bias and indeterminate variance effects associated with this type of nonlinear signal processing. Some useful approximations to the pdf are discussed, and a unit of precision for the estimate is defined.     

Improved Three Subaperture Method for Elevation Angle Estimation

The three subaperture method is a technique for estimating the arrival angles of two targets located in the main beam of a radar. The problem of estimating the arrival angle of a target in the presence of multipath is considered, and it is shown how the accuracy of the three subaperture method can be improved by making use of the information that the amplitude of the direct ray is larger than that of the reflected ray.     

Angle Estimation in Amplitude Comparison Monopulse Systems

The problem of estimation of angle of arrival in amplitude comparison monopulse (ACM) radars in the presence of internally generated thermal noise is considered. A pulse-type radar is assumed and angular noise is postulated to be absent. In the treatment of the problem, explicit inclusion of various simple models for the pulse returns is made to draw a relationship between the a priori statistics of the echo signals and the ability to estimate the angle of arrival in ACM radars. A maximum likelihood analysis is made to determine the form of the estimates of angle of arrival for the various cases and the accuracy of these estimates is evaluated as a function of the signal-to-noise ratio per hit and of the number of hits. Although most of the estimates considered have already received attention, many of the results are believed to be new.     

Analysis of a Signal Processor for an Antenna Array

A signal processor that provides ratio-squared predetection combining, has been investigated for application in an adaptive antenna array. The analysis and experimental data presented here pertain to the signal processing gain when the antenna array is illuminated by a coherent signal source and a partially coherent noise source. For a noise source which is coherent, the processing gain depends on relative strength of the signal and noise, relative directions of arrival, and the usual "array factor." The array exhibits capturing effects much as in an FM receiver. The effective antenna pattern is a superposition of two beams of different magnitudes, one directed to the signal source and the other to the noise source. When the noise is partially coherent, the behavior of the signal processor is quite complex. Analytical prediction and experimental simulation measurement on a four-channel system indicate that the partially coherent noise may be regarded as the source of an incoherent noise component plus a coherent noise component with the magnitude of the latter determined by the coherence coefficient for the noise source.     

Effect of Monopulse Signal Thresholding on Tracking Multiple Targets

The monopulse angle of arrival measured from two targets may wander far beyond the angular separation of the targets. In order to remove large errors, angle of arrival measurements are passed through a threshold detector and the measurements which do not satisfy the threshold are rejected. Thresholding has the tendency to move the mean indicated angle of arrival away from the stronger target and toward the power centroid of the targets, which may be undesirable in some applications. Expressions for the probability density function, the mean, and the variance of the in-phase angle of arrival are developed in this paper as a function of the threshold setting. Background noise and interfering signals are neglected in the analysis.     

Angle measurement in the presence of mainbeam interference

The problem of reducing interference impinging on an antenna array when the sources lie in the main beam is addressed. Adaptive antenna arrays are incorporated to form adapted sum and difference beams in which the interference signals are suppressed. Monopulse error curves are then obtained, providing the necessary distortion correction curves across the entire mainbeam tracking angle region. New Cramer-Rao (C-R) bounds on the angle estimation error are derived with generalized assumptions on the signal amplitude and phase. The bounds previously derived by others are valid under different conditions. With these generalized assumptions on the signal characteristics, a Monte Carlo simulation is performed, based on the estimation procedure presented, to determine the angle estimation error. These errors are compared with the C-R bounds. Good performance is shown for sufficient S/N₀ and angular separation between the target and the interference sources     

Monopulse-radar tracking of swerling III-IV targets using multiple observations

This paper proposes a novel statistical prediction of monopulse errors (Levanon, 1988) for a radar Swerling III-IV target embedded in noise or noise jamming where multiple observations are available. First, the study of the maximum likelihood estimator (MLE) of the complex monopulse ratio for a Swerling III-IV target embedded in spatially white noise allows us to extend the use of the MLE practical approximate form introduced by Mosca (1969) for Swerling 0-I-II cases. Afterward, we derive analytical formulas for both the mean and variance of the MLE in approximate form conditioned by the usual detection step performed on the sum channel of a monopulse antenna. Last, we provide a comparison of target direction of arrival (DOA) estimation performance based on monopulse ratio estimation as a function of the Swerling model in the context of a multifunction radar.     

一种基于三维阵列结构二维波达方向估计的新方法

给出了一种在高斯白噪声环境下对多个窄带信号进行二维波达方向估计的新方法.该方法根据给出的天线阵列结构的特点,首先构造四个相关矩阵,进而构造一个大的矩阵,对其进行一次特征值分解,由ESPRIT原理实现了信号波达方向的准确估计.该方法精度较高,不存在错误估计,有一定的实用性.     

The Effect of Interfering Signals on the Performance of Angle of Arrival Estimates

The performance of angle of arrival estimates using an array in the presence of interfering signals is evaluated using the Cramer-Rao bound. To do this, a model for interference is developed which presents the interference as narrowband, temporally white, but spatially correlated, noise. The bound is evaluated and it is shown to depend upon the ambiguity function of the array and spatial correlation matrix of the noise plus interference. Motivation of the model in the context of air traffic control and sonar surveillance is presented.     

Analysis of an adaptive algorithm for unbiased multipath time delay estimation

The multipath equalization time delay estimator (METDE) provides an adaptive approach for estimating the difference in arrival times of a signal received at spatially separated sensors as well as the multipath channel characteristics. However, the parameter estimates of the METDE are biased in the presence of noise. The METDE algorithm is improved for unbiased parameter estimation via minimizing a modified cost function. Convergence behaviors and variances of the system variables of the amended method are derived. Computer simulations are included to corroborate the theoretical analysis and to evaluate the adaptive multipath delay estimation performance of the proposed algorithm.     

基于模糊自适应卡尔曼滤波的大气数据辅助姿态算法

 针对中低精度航姿参考系统(AHRS)在机体机动时不能利用加速度计修正水平姿态,以及噪声统计特性随实际工作情况变化的问题,提出了一种基于模糊自适应卡尔曼滤波的大气数据辅助姿态解算的方法。首先,考虑大气数据系统和航姿参考系统的优势,利用真空速、攻角和侧滑角等大气数据信息对非重力加速度进行补偿,以辅助水平姿态解算;其次,基于模糊自适应卡尔曼滤波原理,对观测模型的参数进行估计和修正,以实现水平姿态的最优估计;最后,选取某型飞机的试飞数据进行仿真验证。仿真结果表明,该方法可使飞机的水平姿态估计精度达到1.3°,且在偏差较大时有明显的纠偏作用。因此,相对于无机动加速度补偿和常规卡尔曼滤波来说,该方法能够更好地进行姿态估计,具有一定的实用价值。     

基于改进TLS-ESPRIT算法的相干定位信号波达方向空间平滑

针对室内角度定位,在定位信号相干条件下无法实现准确估计波达方向(DOA)的问题,提出了一种基于TLS-ESPRIT算法的双向空间平滑方法。该算法先对定位相干信号进行双向空间平滑处理,然后用TLS-ESPRIT算法进行DOA的精确估计,使其最大限度地利用信号子空间的信息,从而解决了算法计算过程中输出信号的协方差矩阵秩亏损情况。该算法能够准确实现定位信号相干条件下DOA估计,与传统的空间平滑结合其他改进ESPRIT算法相比,具有更好的平稳性及抗干扰能力。最后通过仿真实验验证了算法的有效性和稳定性。     

Tracking the Frequency Translation of a Sum of Orthogonal Sinusoids

The maximum likelihood approach is used to derive a method for estimating and tracking the frequency translation of a signal consisting of a sum of orthogonal sinusoids corrupted by additive white noise. The likelihood function is reduced to an equivalent statistic expressed in terms of the squared magnitude of the finite Fourier transform of the received signal. A function that generates an error signal for a frequency translation tracking loop is derived, and a method of generating the error signal using the discrete Fourier transform (DFT) of the received signal weighted by a linear ramp is suggested. Two noise-free examples are presented.     

Estimating the number of signals using reference noise samples

Criteria for estimating the number of signals in the case of small-sample populations are considered. The criteria introduced by M. Wax and T. Kailath (1985) do not work well in this case. Two new criteria based on information theoretic and eigenmode composition-based criteria are proposed, assuming a known noise covariance. Simulation results show a significant improvement in the performance of estimating the number of signals in the small-sample case, by the use of the new criteria combined with an estimate of the noise covariance obtained from reference noise samples     

Control-Loop Noise in Adaptive Array Antennas

Adaptive array receiving antennas can be designed to sense the external noise field and to optimize the array illumination function. A substantial improvement in signal-to-noise ratio can be obtained with adaptive arrays when the external noise field is nonuniformly distributed in angle. The external noise process may be time varying and contain both discrete sources and continuously distributed sources. Two adaptive array implementations which maximize the signal-to-noise ratio are described in this paper. Expressions are derived for control-loop noise, i.e., the variance of the array element weights, and for the additional noise in the array output due to this element weight noise. It is shown that both the element weight noise and the array convergence rate are determined by the eigenvalues of the noise covariance matrix.     

谱估计测向的MUSIC算法研究

由天线阵对被测信号的响应矩阵的特征值,可得到对应于信号和噪声的特征向量,以此扩展成信号子空间和噪声子空间。利用信号子空间与噪声子空间的正交关系,即可求得信号方位角的估计值。这种空间谱估计测向的MUSIC算法,用于圆形天线阵对非相干信号进行测向,可以克服一般干涉仪测向体制中测向模糊和测向盲区的问题。     

Least squares range difference location

An array of n sensors at known locations receives the signal from an emitter whose location is desired. By measuring the time differences of arrival (TDOAs) between pairs of sensors, the range differences (RDs) are available and it becomes possible to compute the emitter location. Traditionally geometric solutions have been based on intersections of hyperbolic lines of position (LOPs). Each measured TDOA provides one hyperbolic LOP. In the absence of measurement noise, the RDs taken around any closed circuit of sensors add to zero. A bivector is introduced from exterior algebra such that when noise is present, the measured bivector of RDs is generally infeasible in that there does not correspond any actual emitter position exhibiting them. A circuital sum trivector is also introduced to represent the infeasibility; a null trivector implies a feasible RD bivector. A 2-step RD Emitter Location algorithm is proposed which exploits this implicit structure. Given the observed noisy RD bivector Δ, (1) calculate the nearest feasible RD bivector Δˆ, and (2) calculate the nearest point to the ( ₃ⁿ) planes of position, one for each of the triads of elements of Δˆ. Both algorithmic steps are least squares (LS) and finite. Numerical comparisons in simulation show a substantial improvement in location error variances