Comparison of signal estimation using calibrated and uncalibrated arrays

We consider the problem of separating and estimating the waveform of superimposed signals received by an array of sensors. If the array is well calibrated it is possible to first estimate the directions of arrival (DOA) of the signals and then use this information to separate the signals. When the array is not calibrated, but the array elements have the same unknown gain pattern, up to an unknown multiplicative factor and the phases of the elements are arbitrary and unknown, it is possible to estimate the array steering vectors and then use this information for signal estimation. We compare the quality of the estimated signals in the calibrated case with the quality of the estimated signals in the uncalibrated case, in terms of the output signal-to-interference ratio (SIRO) and output signal-to-noise ratio (SNRO).     

Direction finding for two-dimensional incoherently distributed sources with Hadamard shift invariance in non-uniform orthogonal arrays

This paper proposes a novel algorithm for Two-Dimensional (2D) central Direction-of-Arrival (DOA) estimation of incoherently distributed sources. In particular, an orthogonal array structure consisting of two Non-uniform Linear Arrays (NLAs) is considered. Based on first-order Taylor series approximation, the Generalized Array Manifold (GAM) model can first be established to separate the central DOAs from the original array manifold. Then, the Hadamard rotational invariance relationships inside the GAMs of two NLAs are identified. With the aid of such relationships, the central elevation and azimuth DOAs can be estimated through a search-free polynomial rooting method. Additionally, a simple parameter pairing of the estimated 2D angular parameters is also accomplished via the Hadamard rotational invariance relationship inside the GAM of the whole array. A secondary but important result is a derivation of closed-form expressions of the Cramer-Rao lower bound. The simulation results show that the proposed algorithm can achieve a remarkably higher precision at less complexity increment compared with the existing low-complexity methods, which benefits from the larger array aperture of the NLAs. Moreover, it requires no priori information about the angular distributed function.     

Direction of arrival tracking below the ambiguity threshold

We present an algorithm for direction-of-arrival (DOA) tracking that allows operation below the ambiguity threshold of the direction-finding (DF) system. Using multiple target tracking techniques, the algorithm turns the most likely DOAs of each measurement into multiple potential tracks and then selects the true track as that with the maximum cumulative likelihood. The improvement offered by the algorithm, namely the extension of the ambiguity-free signal-to-noise ratio (SNR) domain, is demonstrated in several simulated experiments using several array structures, including a sparse array and a uniform linear array     

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。     

High-resolution multiple target angle tracking

An approach to high-resolution multiple-target-angle tracking that uses the output of an array of sensors is presented. The results of direction-of-arrival estimation by eigenstructure analysis are extended to derive a recursive procedure for tracking moving sources. This procedure involves recursive eigenvalue decomposition and a zero-tracking algorithm, using the coefficient derived from the minimum-norm criterion. The algorithm has superresolution capability in that a pair of closely spaced target angles can be resolved and tracked even though the angular separation between them is less than the reciprocal of the aperture size. Simulation results verify that the algorithm works well in tracking multiple-target sources     

一种基于最小流形长度的高精度线阵设计

 传统上以阵列孔径来比较各种线阵的测向性能,但这一指标没有考虑到阵元数目及阵列几何布局对阵列性能的影响。因子空间类算法需搜索阵列流形来进行测向,所以阵列流形对阵列性能有重要影响。阵列流形又是阵元数、阵列几何布局的函数,可通过阵列流形来研究阵元数、阵列几何布局与阵列测向性能的关系。在分析了线阵流形与线阵测向精度的关系的基础上,提出了一个基于线阵最小流形长度的指标来比较不同线阵的性能,该指标综合考虑了阵元数、阵列几何布局对阵列测向精度的影响。通过对此指标的讨论,给出了提高线阵测向精度的设计思路。对几个不同线阵的仿真证实了该指标的有效性,也验证了该设计思路的可行性。     

Specification and Performance of Passive Sonar Spectral Estimators

The application of existing estimation theory to the problem of specification and performance of passive sonar spectral estimators is considered. The classification function is addressed, so that the signal is assumed to be present, and so that the energy arrival angle is known. The spatial filter considered is a line array of M equally spaced omnidirectional hydrophones. Signal and ambient noise are both zero-mean, wide-sense, stationary Gaussian random processes that differ in their spatial correlation across the face of the array. The signal is a plane wave that can be made totally spacially corrected between array elements by inserting delays between sensors to invert the signal propagation delay. The noise correlation is a function of frequency, bandwidth, element separation, and the relative time delay between sensors. Under these assumptions, the Cramer-Rao lower bound is derived for the class of unbiased estimates of signal power in a narrow frequency band at the hydrophone in the presence of correlated ambient noise of known power. The bound is examined numerically, resulting in a threshold phenomenon with M that constitutes a new design consideration. In addition, there is a striking insensitivity to realistic values of ambient noise correlation, and there are ranges in signal-to-noise ratio for which one gains more by increasing M than by increasing the bandwidth-time product. Specific processors, including a new unbiased estimator when noise power is unknown, are developed.     

General direction-of-arrival estimation: a signal subspace approach

A high-resolution algorithm is presented for resolving multiple incoherent and coherent plane waves that are incident on an array of sensors. The incident sources can be a mixture of narrowband and broadband sources, and, the geometry of the array is unrestricted. The algorithm makes use of a fundamental property possessed by those eigenvectors of the array spectral density matrix that are associated with eigenvalues that are larger than the sensor noise level. Specifically, it is shown that these eigenvectors can each be represented as linear combinations of the steering vectors identifying the incident plane waves. This property is then used to solve the important special cases of incoherent sources incident on a general array and coherent sources incident on an equispaced linear array. Simulation results are presented to illustrate the high-resolution performance achieved with this approach relative to that obtained with MUSIC and spatial smoothed MUSIC in which the coherent-signal-subspace focusing method is used     

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。     

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.     

Array shape estimation tracking using active sonar reverberation

This paper concerns the problem of array shape estimation and tracking for towed active sonar arrays, using received reverberation returns from a single transmitted CW pulse. Uniform linear arrays (ULAs) deviate from their nominal geometry while being towed due to ship maneuvers as well as ocean currents. In such scenarios, conventional beamforming performed under the assumption of a ULA can sometimes lead to unacceptably high spatial sidelobes. The reverberation leaking through the sidelobes can potentially mask weak targets in Doppler, especially when the target Doppler is close to that of the mainlobe reverberation and the reverberation-to-target ratio (RTR) is very high. Although heading sensors located along the array can be used to provide shape estimates, they may not be sufficiently available or accurate to provide the required sidelobe levels. We propose an array shape calibration algorithm using multipath reverberation returns from each ping as a distributed source of opportunity. More specifically, a maximum likelihood (ML) array shape calibration algorithm is developed, which exploits a deterministic relationship between the reverberation spatial and Doppler frequencies causing it to be low rank in the space-time vector space formed across a single coherent processing interval (CPI). In this application, a sequence of overlapped CPI length snapshots of duration less than the CW pulse is used. The ML estimates obtained for each snapshot are tracked using a Kalman filter with a state equation corresponding to the water pulley model for array dynamics. Simulations performed using real heading sensor data in conjunction with simulated reverberation suggest that 8-10 dB improvement in sidelobe level may be possible using the proposed array shape tracking algorithm versus an algorithm that uses only the available heading information.     

Efficient multisensor fusion using multidimensional dataassociation

We present the development of a multisensor fusion algorithm using multidimensional data association for multitarget tracking. The work is motivated by a large scale surveillance problem, where observations from multiple asynchronous sensors with time-varying sampling intervals (electronically scanned array (ESA) radars) are used for centralized fusion. The combination of multisensor fusion with multidimensional assignment is done so as to maximize the “time-depth” in addition to “sensor-width” for the number S of lists handled by the assignment algorithm. The standard procedure, which associates measurements from the most recently arrived S-1 frames to established tracks, can have, in the case of S sensors, a time-depth of zero. A new technique, which guarantees maximum effectiveness for an S-dimensional data association (S⩾3), i.e., maximum time-depth (S-1) for each sensor without sacrificing the fusion across sensors, is presented. Using a sliding window technique (of length S), the estimates are updated after each frame of measurements. The algorithm provides a systematic approach to automatic track formation, maintenance, and termination for multitarget tracking using multisensor fusion with multidimensional assignment for data association. Estimation results are presented for simulated data for a large scale air-to-ground target tracking problem     

Analysis of Min-Norm and MUSIC with arbitrary array geometry

A nonasymptotic performance comparison is presented between the Min-Norm and MUSIC algorithms for estimating the directions of arrival of narrowband plane waves impinging on an array of sensors. The analysis is based on a finite amount of sensor data. The analysis makes the assumption of high signal-to-noise ratio (SNR), and it applies to arrays of arbitrary geometry. It is shown that Min-Norm can be expressed as a certain data-dependent weighted MUSIC algorithm, and that this relationship allows a unified performance comparison. It is also shown that the variances of the estimated directions-of-arrival from the MUSIC algorithm are always smaller than those of the Min-Norm algorithm at high SNR when both algorithms employ a numerical search procedure to obtain the estimates     

An intelligent algorithm for coherent sound source localization based on a strong tracking filter

Background noise is inevitable when sensor arrays are used for aeroacoustic measurements in wind tunnels. The direct removal of background noise, however, would affect the measurement accuracy. In particular, the existing array signal processing algorithms are either invalid or inefficient for removing the noise that is coherent with the signal of interest. In this paper, an intelligent algorithm is developed to localize the coherent sound sources and background noise in real time by iteratively checking the collected data from the array. The proposed method can automatically adjust the suboptimal fading factor to extract useful information as much as possible in residual sequence. This algorithm is tested in simulations and then demonstrated in an experiment.Compared to the two existing methods, the results indicate that the new method has a good phase-shift tracking ability and rapid estimation-error convergence speed, and can achieve an acceptable performance even for low-cost acoustic sensors. Overall, the proposed method should assist array beamforming and hence benefit aeroacoustic measurement.     

压气机旋转不稳定性的周向模态特性及其分解方法

基于实验和数值模拟的方法,研究压气机叶顶区域不稳定压力波的周向模态特性。使用基于空间傅里叶变换的周向模态分解方法对实验和数值计算结果进行了分析,给出了实验和数值计算结果的频谱模态分解结果,得到了压气机连续周向模态特征频谱峰值。对压气机叶顶区域各模态幅值和相位的时变特性做了详细分析,得到了叶顶旋转不稳定性周向模态传播速度和传播方向。结果表明:旋转不稳定性的主模态具有稳定的周向传播结构,而其他模态波的幅值和相位存在较大波动。利用多组有限测点组合方式消除了模态混叠现象影响,将可以分析的模态上限提高数倍,取决于测点数的选择;基于该方法可以用有限测点捕捉高阶模态,大大减少了实验所需的传感器数目。      

航天用反作用飞轮旋转变压器位置检测算法

目前,航天用反作用飞轮大多采用霍尔传感器或光电码盘进行测速。但是,霍尔传感器在反作用飞轮低速运行时精度相对较低,光电编码器的环境适应性相对较弱。基于此,提出了一种使用旋转变压器检测反作用飞轮转子位置的方法。但如果在现有飞轮控制电路中额外使用旋转变压器专用解码芯片,会导致成本大大提高,故提出了使用控制电路中的FPGA进行解码的方法。首先,介绍了旋转变压器的工作原理,通过求解反三角函数获得转子位置。其次,介绍了传统坐标旋转数字计算机(Coordinate Rotation Digital Computer,CORDIC)算法。最后,针对传统CORDIC算法无法求解完整平面角度值问题,提出了一种改进型CORDIC算法求解转子位置,并给出了一种能够减少硬件使用资源的全流水线CORDIC阵列结构。通过Modelsim仿真,证明了所提出的方法具有占用资源较少、延迟低、测量精度较高等优点,在反作用飞轮测速应用中具有良好前景。     

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     

面向雷达天线平台的容错纠错策略及其FPGA实现

 针对雷达天线平台可能出现的传感器故障,提出了一种容错纠错策略。如果雷达天线平台周围的3条驱动腿中的某一个传感器发生故障,则可根据空间闭链机构约束,由其他正常工作驱动腿的传感器和中间从动腿的冗余传感器的测量值计算出故障传感器的应测值。推导了对应的位移传感器故障的容错重构算法,研究了基于现场可编程门阵列（FPGA）的上述容错策略的硬件实现方法。通过引入坐标旋转数字计算（CORDIC）算法使得FPGA运算中只需进行基本的移位和加/减操作;设计了基于FPGA的循环高速流水线处理器结构,使得重构算法的在线计算速度大大提高。仿真模拟了突变型传感器故障,结果表明,所提容错纠错方案能有效地保证雷达天线平台运行的安全性和可靠性。     

常规闭口风洞相阵列气动声学试验

传统气动声学研究观点认为,精确的声学测量要求风洞背景噪声和洞壁反射足够低,传声器测量结果有足够高的信噪比,这是大多数风洞无法达到的要求。近些年,基于声纳和雷达技术发展起来的麦克风相阵列技术可以通过增加阵列的传声器数目从而大幅提高声学测量的信噪比,具有噪声源研究和定位能力,并被成功地应用于非声学固壁风洞噪声源测量和噪声物理机制研究。作者基于相阵列波束生成频域算法研制出常规闭口风洞相阵列系统及相关技术,在FD-09风洞尝试进行了相阵列校准试验和某民机噪声测量试验。结果表明：相阵列技术能够准确捕捉到真实的校准声源,并从技术上验证了相阵列系统在常规闭口风洞测量气动噪声是有效的。     

Performance analysis of wavefront curvature methods for rangeestimation of a moving source

In numerous practical situations a large array of sensors is required, especially for improving the system ability to detect and track moving sources. However, the array performance is strongly affected by the lack of stationarity of the impinging signals. The use of a large array of sensors allow us to perform the source localization by using the wavefront curvature. The analysis of the range estimates based on the wavefront curvature have been thoroughly performed by various authors but, to our knowledge, is restricted to the case of fixed sources. The study of the effects of source motion for range estimation (Section III) and source detection (Section V) constitutes an important part of this work. This study reveals that the array performance can be far from the expected values, especially for large array. Therefore, the robustness of a direct processing of the whole sensor array is very questionable. The computational burden constitutes another serious drawback of this (direct) approach. The use of partitioned processings (Sections IV and VI) seems thus quite promising even if (and perhaps because) it is not optimal so as to fulfil the computation cost and robustness requirements. The performance of such processings for estimating the range of moving sources is presented