Accuracy of source localization using multipath delays

The depth and range of underwater source can be estimated from measurements of propagation delay differences along multiple propagation paths. The accuracy of depth and range estimation using the Cramer-Rao lower bound is studied. The formulas derived can be used in conjunction with a propagation medium (nonconstant velocity profile). Explicit formulas for the bounds are derived for the case of homogeneous medium (constant velocity profile). Numerical examples are presented to illustrate the behavior of these bounds     

Accuracy of angle estimation with monopulse processing using twobeams

Expressions are provided for the accuracy of monopulse angle estimation using two beams. It is shown that, if the signal angle is halfway between the angles of the beams, the Cramer-Rao lower bound (CRLB) for monopulse processing is almost as small as the CRLB obtained if the entire array of sensors is used. The monopulse CRLB is considerably poorer if the angle of the signal is equal to that of one of the two beams. The expressions in this correspondence are for a uniformly weighted linear array of M equally spaced sensors, for which N⩾M beams are formed     

Bounds on Time-Delay Estimation for Monochromatic Signals

Time-delay estimation (TDE) of monochromatic signals,observed by spatially separated sensors, is widely used for sourcelocalization in radar/sonar applications. We use lower bounds tostudy the accuracy of TDE as a function of signal to noise ratio(SNR), frequency, and sensor separation. We show that the Cramer-Rao bound, which is frequently used as a standard ofreference, yields optimistic predictions in many cases.     

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     

Direction finding with a four-element Adcock-Butler matrix antennaarray

The conventional analog Adcock-Butler matrix (ABM) antenna array direction finder suffers from systemic errors, component matching problems, and bandwidth limitations. Three digital bearing estimators are developed as candidates to replace the analog signal processing portion of the ABM. Using the same antenna array, they perform all signal processing in the frequency domain, thereby benefitting from the computational efficiency of the fast Fourier transform (FFT) algorithm. The first estimator requires two analog-to-digital converters (A-D) and three antenna elements. It multiplies the difference between the discrete Fourier transforms (DFTs) of the output signals from two antenna elements with that from a third antenna element. At each frequency component, the phase of this product is a function of the bearing. A weighted least squares (LS) fit through all the phase components then gives a bearing estimate. The second estimator is similar to the first but uses three A-D and all four antenna elements. The output signal from the additional antenna element provides an independent estimate of the weights for the LS fit, giving an improvement in accuracy. The third estimator applies the physical constraint existing between the time-difference-of-arrival (TDOA) of a signal intercepted by two perpendicular sets of antenna elements. This yields a better estimator than simple averaging of the bearing from each set of antenna elements. The simulation studies used sinusoids and broadband signals to corroborate the theoretical treatment and demonstrate the accuracy achievable with these estimators. All three direction finders have superior performance in comparison with the analog ABM     

Localization performance of arrays subject to phase errors

The passive localisation of radiating sources using an array subject to random perturbations in sensor phases is presented. All source signals as well as additive noises observed at the sensors are assumed to be independent identically distributed zero-mean Gaussian random processes. Cramer-Rao bounds are derived for source bearings and ranges for the phase errors at each sensor. It is shown that accurate phase calibration can be achieved when the number of sources exceeds a certain minimum. The locations of the calibrating sources need not be known a priori and need only satisfy mild regularity conditions. A calibration procedure is proposed which uses maximum-likelihood techniques     

DOA estimation using one-bit quantized measurements

The effects 1-bit quantization of the input samples has on the direction-of-arrival (DOA) estimation accuracy are considered. The signal model assumes a single stochastic Gaussian point source that is embedded in white Gaussian noise (WGN). The inherent limitations governed by the extreme clipping of the input data are analyzed using the Cramer-Rao bound (CRB) that is derived for a two-sensor array. In addition, several estimators for the I-bit estimation are discussed. Numerical and analytical analyses of the estimation error reveal weak dependency on signal-to-noise ratio (SNR) with singular behavior of the estimation error in certain DOA angles.     

阵列宽带Lamb波在结构损伤检测中的应用

阵列信号处理中的空间谱估计可以对信号源进行辨别和定位,于是通过采集在结构上布置的阵列传感器Lamb波信号用来检测损伤发生的位置。通常,大多数空间谱估计方法均以窄带信号为假定,在很多基于Lamb波的结构损伤检测中,为了减小频散特性的影响,大多数研究以Lamb波为窄带信号进行分析,但无限窄的激励信号是物理不可实现的。因此,其在多数情况下Lamb波信号并不符合窄带信号假定,更应被认为是一种宽带信号来进行处理。进而利用空间谱估计中宽带信号非相干子空间处理方法（Incoherent Signal Subspace Method,ISM）中阵列接收的宽带Lamb波信号进行处理,检测出结构发生单一损伤时的损伤位置。随后,当结构损伤与边界反射波有叠加时会引起损伤信号相干,采用宽带信号相干子空间方法（Coherent Signal Subspace Method,CSM）对损伤位置进行检测,得到了较好的结果。     

Optimum Active Array Processing Structure and Space-Time Factorability

An active array processor is concerned with the problem of detecting a signal echo, reflected from a target, in the presence of reverberation (clutter). The processor can also be used to estimate target range and bearing. It is a priori not evident whether the optimum (likelihood ratio) detector can be factored into spatial and temporal operations, thus resulting in a simpler processor implementation. This paper studies this problem for a linear continuous array in a reverberation-limited environment. Conditions on signal, reverberation, and array parameters are derived under which the optimum detector is factorable. The validity of using factorability as a criterion of signal design is briefly examined. Finally, the relationship between space-time factorability and range-bearing estimates is pointed out.     

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。     

Joint TDOA,FDOA and differential Doppler rate estimation: Method and its performance analysis

Considering the estimation accuracy reduction of Frequency Difference of Arrival(FDOA) caused by relative Doppler companding, a joint Time Difference of Arrival(TDOA),FDOA and differential Doppler rate estimation method is proposed and its Cramer-Rao low bound is derived in this paper.Firstly, second-order ambiguity function is utilized to reduce the dimensionality and estimate initial TDOA and differential Doppler rate.Secondly, the TDOA estimation is updated and FDOA is obtained using cross ambiguity function, in which relative Doppler companding is compensated by the existing differential Doppler rate.Thirdly, differential Doppler rate estimation is updated using cross estimator.Theoretical analysis on estimation variance and Cramer-Rao low bound shows that the final estimation of TDOA, FDOA and differential Doppler rate performs well at both low and high signal–noise ratio, although the initial estimation accuracy of TDOA and differential Doppler rate is relatively poor under low signal–noise ratio conditions.Simulation results finally verify the theoretical analysis and show that the proposed method can overcome relative Doppler companding problem and performs well for all TDOA, FDOA and differential Doppler rate estimation.     

一种针对恒模信号的运动单站直接定位算法

相比于常规的"测向+位置估计"两步定位模式,以Weiss等提出的目标直接位置确定(DPD)算法具有估计精度高、分辨能力强和无需数据关联等诸多优点。基于该类定位算法的基本理念,提出了一种利用单个运动天线阵列对恒模(即相位调制)信号的DPD算法。首先,依据最大似然(ML)准则以及恒模信号的恒包络特征,建立了相应的直接定位优化模型;接着,根据优化函数的代数特征提出了一种有效的多参量交替迭代算法,用以获得ML估计器的最优数值解;此外,推导了针对恒模信源的位置直接估计方差的克拉美罗界(CRB),从而为新算法的定位精度提供定量的理论下界。仿真实验表明:相比于已有的基于单个运动天线阵列的直接定位算法以及传统的两步定位算法,通过利用恒模信号的恒包络特征可以明显提高目标直接定位的估计精度。     

Systems Capabilities of Arrays of Large-Aperture Antennas

The array approach to increasing space-communication capability is analyzed and discussed. The problem of signal acquisition is given particular attention. A lower range bound of array operation is defined by assuming a system which employs independent acquisition by each antenna circuit; an upper bound is defined by assuming a prefocused array. It is believed that systems can be implemented which have capabilities well in excess of that achievable by the former system and not greatly less than that achievable by the latter system.     

Acoustic node calibration using a moving source

Acoustic nodes, each containing an array of microphones, can track targets in x-y space from their received acoustic signals, if the node positions and orientations are known exactly. However, it is not always possible to deploy the nodes precisely, so a calibration phase is needed to estimate the position and the orientation of each node before doing any tracking or localization. An acoustic node can be calibrated from sources of opportunity such as beacons or a moving source. We derive and compare several calibration methods for the case where the node can hear a moving source whose position can be reported back to the node. Since calibration from a moving source is, in effect, the dual of a tracking problem; methods derived for acoustic target trackers are used to obtain robust and high resolution acoustic calibration processes. For example, two direction-of-arrival-based calibration methods can be formulated based on combining angle estimates, geometry, and the motion dynamics of the moving source. In addition, a maximum likelihood (ML) solution is presented using a narrowband acoustic observation model, along with a Newton-based search algorithm that speeds up the calculation the likelihood surface. The Cramer-Rao lower bound (CRLB) on the node position estimates is also derived to show that the effect of position errors for the moving source on the estimated node position is much less severe than the variance in angle estimates from the microphone array. The performance of the calibration algorithms is demonstrated on synthetic and field data.     

一种稀疏阵列下的二维DOA估计方法

研究了稀疏阵列下二维波达方向（DOA）的估计问题,提出一种基于不动点迭代的空间谱估计（FPC-MUSIC）算法。首先建立基于矩阵填充的DOA估计信号模型,并验证该信号模型满足零空间性质（NSP）,其次通过不动点迭代算法将稀疏阵列信号恢复为完整信号,最后利用恢复信号估计二维DOA。该算法可在稀疏阵列下大幅度降低谱估计平均副瓣,在大幅度降低阵元数的同时具有较高的估计精度。计算机仿真表明：FPC-MUSIC算法可在稀疏阵列下准确估计二维DOA,验证了该算法的有效性和优越性。     

An operational system implementation of the ESPIRIT DF algorithm

The practical implementation of the ESPRIT algorithm into direction-finding system architecture is considered. In particular, the problems of phase ambiguity resolution for extended array separations and multidimensional azimuth/elevation estimation are addressed. Generalized solutions for these problems are proposed, and a bearing quality indicator that provides a measure of credibility associated with each angle-of-arrival estimate is developed. Plots of computer simulated performance are presented in order to assess the probability of detection, of failure to alarm, and of false alarm as a function of azimuthal separation and period of signal observation     

Beamspace ML bearing estimation incorporating low-angle geometry

A problem in low-angle radar tracking, namely, bearing estimation in the presence of a strong specular multipath component that arrives within the beamwidth of the direct path signal, is studied. Three-dimensional beamspace domain maximum likelihood (3D-BDML) is a computationally simple ML bearing estimation algorithm applicable in this scenario which operates in a 3-D beamspace. A variation of 3D-BDML incorporating the multipath geometry as a priori information is presented. In symmetric 3D-BDML the pointing angle of the center beam is equal to the bisector angle between the direct path ray and the image ray, which may be estimated a priori given only the radar height and the target range. The effect of the inclusion of a priori information on the performance of 3D-BDML is analyzed in terms of the dependence on the relative phase difference between the direct and specular path signals, the sensitivity to error in the bisector angle estimate, and the results of operation when no specular multipath component is present in the data. In addition, computationally simple schemes for coherently incorporating multifrequency data into 3D-BDML are investigated     

Model-based multifrequency array signal processing for low-angletracking

Tracking low-altitude targets over the sea is problematic because of interference between the direct and reflected signal. Standard monopulse trackers can experience large errors because of multipath maximum likelihood estimation (MLE) has been used to more accurately estimate the target height in the presence of multipath MLE is a model-fitting technique where the model parameters are chosen to maximize the likelihood function. It is shown that the type of observation model has a large effect on performance. Tracking performance is compared using three different observation models employing varying amounts of a priori information. Results are presented for different array sizes: eight and 32-element arrays and two-element subarrays typical of phase monopulse. Performance is compared with that of standard techniques such as Fourier beamforming and phase monopulse     

聚焦变换在MIMO阵列方位估计中的应用

MIMO阵列是近年来信号处理领域提出的一种新体制阵列技术,可有效避免常规阵列中的相干源问题。为解决多载波造成的方位模糊,提出了一种基于聚焦变换的MIMO阵列目标方位估计方法。该方法将MIMO阵列接收信号分解为多个频率分量的信号,并通过聚焦算法将多个频率信号聚焦到同一信号子空间,然后对聚焦后的信号进行方位估计。仿真结果表明:与直接对MIMO阵列接收信号进行方位估计相比,该方法利用了MIMO阵列的回波不相干性和宽带信号能量,具有更好的分辨能力和更高的方位估计精度。     

Angle-of-Arrival Estimation Using an Adaptive Antenna Array

A direction-finding technique is presented that is capable of simultaneously estimating the arrival angles of multiple signals. Pulsed as well as continuous signals can be handled with the signal form only approximately specified. An adaptive antenna array is used as a processing device in the estimation technique. The effect of input signal and feedback loop parameters upon estimate bias is discussed.