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。     

增益幅度不同时信号二维方向角和多普勒频率的盲估计

 在各阵元增益幅度不一致的条件下,提出了一种起伏目标的二维方向角和多普勒频率盲估计的新方法。此方法在各阵元增益幅度不一致的条件下,仍可获得很好的估计性能,并能应用于各个信号的频率相同的场合。且具有对噪声不敏感,不需进行谱峰搜索,适用范围广等特点。仿真结果表明了此算法的有效性。     

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.     

DOA estimation and mutual coupling calibration with the SAGE algorithm

In this paper, a novel algorithm is presented for direction of arrival（DOA） estimation and array self-calibration in the presence of unknown mutual coupling. In order to highlight the relationship between the array output and mutual coupling coefficients, we present a novel model of the array output with the unknown mutual coupling coefficients. Based on this model, we use the space alternating generalized expectation-maximization（SAGE） algorithm to jointly estimate the DOA parameters and the mutual coupling coefficients. Unlike many existing counterparts, our method requires neither calibration sources nor initial calibration information. At the same time,our proposed method inherits the characteristics of good convergence and high estimation precision of the SAGE algorithm. By numerical experiments we demonstrate that our proposed method outperforms the existing method for DOA estimation and mutual coupling calibration.     

Adaptive Arrays Can Be Used to Separate Communication Signals

Using eigentheory, it is shown how up to n unknown independent narrowband signals arriving from different directions at an array of n antenna elements can be separated into n channels where each channel contains primarily one signal. An expression for the signal-to-interference ratio (SIR) on eachoutput channel is determined analytically and evaluated for many illustrative cases. The results show that in most cases the SIR is + 10 dB or greater; only when two signals arrive within a few degrees of each other does the SIR fall substantially below 0 dB.     

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     

Equivalent transformation for a partially adaptive array

A partially adaptive array is one in which elements of a phased array are controlled or adaptively weighted in groups or in which certain elements, called auxiliary elements, are made controllable. Mathematically, this type of array is formed by transforming all of the elements of an array by a nonsquare matrix such that the resulting output vector has a length less than the number of array elements. It is shown that there is an equivalent matrix transform that can effectively be utilized in analyzing the partially adaptive array's performance when a small number of external jammers are present. Processor implementation and convergence rate considerations lead to the desirability of reducing the dimensionality of the cancellation processor while maintaining good sidelobe interference protection. A meaningful measure of canceller performance is to compute the optimal output signal-to-noise ratio. This expression is a function of the jammer, direction-of-arrival vectors (DOAVs), jammer powers, the array steering vector, and internal noise. It is shown that if this expression is computed for the fully adaptive array then it is easily computed for the partially adaptive array by transforming the jammer DOAVs and the steering vector by the orthogonal projection matrix defined by the rows of the subarray transformation matrix and substituting these vectors back into the original expression for the fully adaptive 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。     

Application of Adaptive Arrays to Suppress Strong Jammers in the Presence of Weak Signals

The purpose of this paper is to demonstrate that an adaptive array can be used to acquire weak signals, whose direction and timing are unknown, in an environment of stronger jammers. Specifically, it is shown that in an environment of one weak signal and one strong jammer, the adaptive array output suppresses the strong jammer below the weak signal by roughly the same amount that the jammer exceeded the signal before adaptation.     

Doppler and direction-of-arrival (DDOA) radar for multiple-mover sensing

A low-cost two-element receiving array concept is investigated for detecting multiple moving targets in indoor surveillance applications. Conventional direction-of-arrival (DOA) detection requires the use of an antenna array with multiple elements. Here we investigate the use of only two elements in the receiver array. The concept entails resolving the Doppler frequencies of the returned signals from the moving targets, and then measuring the phase difference at each Doppler frequency component to calculate the DOA of the targets. Simulations are performed to demonstrate the concept and to asses the DOA errors for multiple movers. An experimental system is designed and constructed to test the concept. The system consists of a two-element receiver array operating at 2.4 GHz. Measurement results of human subjects in indoor environments are presented, including through-wall scenarios.     

Performance of a Square Law Pseudonoise Ranging Time-of-Arrival Estimator

The performance of a square law time-of-arrival (TOA) estimator that has been proposed for use in ASTRO-DABS, part of a possible satellite-based fourth generation air traffic control system is considered. The transmitted message consists of a pulse amplitude modulated (PAM) ranging sequence that, due to transmitter characteristics, is corrupted by an unknown frequency offset. The optimum TOA estimator, for the case of no frequency uncertainty, is first presented, together with a lower bound on the variance of the estimate generated. This is followed by the consideration of a suboptimum TOA estimator for which a high signal-to-noise ratio (SNR) performance analysis is carried out; here, the effects of frequency uncertainty are included. Next, the zero-crossing properties of the derivative of the (suboptimum) estimation statistic are presented and the results used to derive an upper bound to the TOA estimate variance that is valid for all SNR values. This latter result is significant because it displays the system threshold effect and complements performance lower bounds that may be derived via other methods. In addition, the method presented here may be applied to other optimum and suboptimum systems where a discrete set of parameters is to be estimated.     

Noise subspace techniques in non-gaussian noise using cumulants

We consider noise subspace methods for narrowband direction-of-arrival or harmonic retrieval in colored linear non-gaussian noise of unknown covariance and unknown distribution. The non-gaussian noise covariance is estimated via higher order cumulants and combined with correlation information to solve a generalized eigenvalue problem. The estimated eigenvectors are used in a variety of noise subspace methods such as multiple signal classification (MUSIC), MVDR and eigenvector. The noise covariance estimates are obtained in the presence of the harmonic signals, obviating the need for noise-only training records. The covariance estimates may be obtained nonparametrically via cumulant projections, or parametrically using autoregressive moving average (ARMA) models. An information theoretic criterion using higher order cumulants is presented which may be used to simultaneously estimate the ARMA model order and parameters. Third- and fourth-order cumulants are employed for asymmetric and symmetric probability density function (pdf) cases, respectively. Simulation results show considerable improvement over conventional methods with no prewhitening. The effects of prewhitening are particularly evident in the dominant eigenvalues, as revealed by singular value decomposition (SVD) analysis     

DOA and steering vector estimation using a partially calibratedarray

We consider the problem of estimating directions of arrival (DOAs) using an array of sensors, where some of the sensors are perfectly calibrated, while others are uncalibrated. We identify a cost function whose minimizer is a statistically consistent and efficient estimator of the unknown parameters-the DOAs and the gains and phases of the uncalibrated sensors. Next we present an iterative algorithm for finding the minimum of that cost function The proposed algorithm is guaranteed to converge. The performance of the estimation algorithm is compared with the Cramer Rao bound (CRB). The derivation of the bound is also included. It is shown that DOA accuracy can be improved by adding uncalibrated sensors to a precisely calibrated array. Moreover, the number of sources that can be resolved may be larger than the number that can be resolved by the calibrated portion of the array     

Performance of a Modified Applebaum Adaptive Array

The performance of a modified Applebaum adaptive array is studied. The new array is obtained by removing the desired signal component from the output signal fed back to the correlator of an Applebaum type adaptive array. Various signal scenarios, including single desired signals or multiple simultaneous desired signals are examined. The new array is less sensitive to beam pointing errors and does not cause power inversion of desired signals. In the case of multiple simultaneous desired signals, the new array does not degrade the SNRs of strong desired signals.     

Decision fusion rules in multi-hop wireless sensor networks

The decision fusion problem for a wireless sensor network (WSN) operating in a fading environment is considered. In particular, we develop channel-aware decision fusion rules for resource-constrained WSNs where binary decisions from local sensors may need to be relayed through multi-hop transmission in order to reach a fusion center. Each relay node employs a binary relay scheme whereby the relay output is inferred from the channel impaired observation received from its source node. This estimated binary decision is subsequently transmitted to the next node until it reaches the fusion center. Under a flat fading channel model, we derive the optimum fusion rules at the fusion center for two cases. In the first case, we assume that the fusion center has knowledge of the fading channel gains at all hops. In the second case, we assume a Rayleigh fading model, and derive fusion rules utilizing only the fading channel statistics. We show that likelihood ratio (LR) based optimum decision fusion statistics for both cases reduce to respective simple linear test statistics in the low channel signal-to-noise ratio (SNR) regime. These suboptimum detectors are easy to implement and require little a priori information. Performance evaluation, including a study of the robustness of the fusion statistics with respect to unknown system parameters, is conducted through simulations.     

Error Analysis of the Optimal Antenna Array Processors

The optimal weights of an antenna array processor, which maximizes the output signal-to-noise ratio (SNR) in the absence of errors, are computed using the noise-alone matrix inverse (NAMI) and the steering vector in the look direction or the signal-plus-noise matrix inverse (SPNMI) and the steering vector. In practice the estimated steering vector as well as the estimated optimal weights are corrupted by random errors. This paper has analyzed the effects of these errors on the performance of the NAMI processor and the SPNMI processor by deriving analytic expressions for the output signal power, output noise power, output SNR, and the array gain as a function of the error variance. The treatment is for a general array configuration and no assumption about a particular array geometry is made.     

Separation of SSR Signals by Array Processing in Multilateration Systems

Location and identification of cooperating aircraft in the airport area (and beyond) may be implemented by multilateration (MLAT) systems using the secondary surveillance radar (SSR) mode S signals. Most of these signals, spontaneously emitted from on-board mode S transponders at a fixed carrier frequency, arrive randomly at the receiving station, as well as many mode A/C replies from legacy transponders still in use. Several SSR signals are, then, overlapped in multiple aircraft situations. Therefore, the aim of this work is the separation of overlapped SSR signals, i.e., signals superimposed in time at receiving stations. We improve the MLAT receiving station by replacing the single antenna by an array of m elements and using array signal processing techniques. In the literature, several algorithms address the general source separation problem, but a very few of them are specifically designed for a mixture of overlapping SSR replies. Unfortunately, all of them have either some shortcomings, or an expensive computational cost, or no simple practical implementation. In this paper, we use the time sparsity property of the sources to propose more reliable, simpler, and more effective algorithms based on projection techniques to separate multiple SSR signals. Real recorded signals in a live environment are used to demonstrate the effectiveness of our method.     

Algorithms for Spatial Laser Beacon Acquisition

The pointing system for optical data transmission over unguided channels uses a return beacon from the receiver back to the transmitter to aid the reciprocal alignment of the two stations. We concentrate on CW or pulsed-beacon acquisition with array detectors in the presence of extended clutter in addition to background and receiver noises. Acquisition in the presence of a single interferer (jammer) is also considered. A maximum likelihood (ML) approach is used when preliminary scene information is available. In the case of unknown scenario, a picture-picture subtraction algorithm is considered for the pulsed laser. Performance is evaluated in terms of probability of an acquisition error for Poisson statistics of the photodetector output.     

Steered Beam and LMS Interference Canceler Comparison

The performance of two kinds of interference cancelers is compared, namely, a constrained steered beam interference canceler (CSBIC) and a least mean square interference canceler (LMSIC). For simplicity, this is done for a two-element array. In our comparison we use the array output desired signal-to-interference power ratio (SIR) and the desired signal-to-noise ratio (SNR). These power ratios are obtained for the CSBIC and LMSIC under two sets of conditions: 1) The error in the assumed angle of incidence for the CSBIC is small, and the LMSIC operates in a codetracking mode. 2) The error in the assumed angle of incidence for the CSBIC is large, and the LMSIC operates in a code-acquisition mode. Comparison of the corresponding power ratios obtained under these two sets of conditions then establishes the condition under which it is more desirable to use a CBSIC as compared with an LMSIC.