Radio source parameter estimation by maximum likelihood processing of variable baseline correlation interferometer data

The accurate joint determination of the direction and strength of a point noise source when the mutual coherence function of its radiated field is spatially sampled atMbaselines by a correlation interferometer is considered. The measurements are corrupted by the combined effects of a) the additive background and receiver noises at the interferometer antennas and b) the finite integration time of a practical correlator. The problem is approached from a statistical point of view (as contrasted with beam forming techniques). First the probability density function of the measurements is derived. The source's two parameters (direction and strength) are then jointly estimated using the maximum likelihood (ML) method. Investigation of the estimates' properties shows that they are virtually unbiased with variances that effectively attain the standard Cramer-Rao (C-R) lower bound when the number of measurements exceeds a "threshold" which is a decreasing function of the measurements' signal-to-noise ratio (SNR). The empirically observed fact that such a threshold is quite small, even at low SNR's, as well as the unbiasedness of the estimates, makes the performance of these (ML) estimates optimum for most practical applications.     

Maximum-likelihood bearing estimation with partly calibrated arraysin spatially correlated noise fields

The problem of using a partly calibrated array for maximum likelihood (ML) bearing estimation of possibly coherent signals buried in unknown correlated noise fields is shown to admit a neat solution under fairly general conditions. More exactly, this paper assumes that the array contains some calibrated sensors, whose number is only required to be larger than the number of signals impinging on the array, and also that the noise in the calibrated sensors is uncorrelated with the noise in the other sensors. These two noise vectors, however, may have arbitrary spatial autocovariance matrices. Under these assumptions the many nuisance parameters (viz., the elements of the signal and noise covariance matrices and the transfer and location characteristics of the uncalibrated sensors) can be eliminated from the likelihood function, leaving a significantly simplified concentrated likelihood whose maximum yields the ML bearing estimates. The ML estimator introduced in this paper, and referred to as MLE, is shown to be asymptotically equivalent to a recently proposed subspace-based bearing estimator called UNCLE and rederived herein by a much simpler approach than in the original work. A statistical analysis derives the asymptotic distribution of the MLE and UNCLE estimates, and proves that they are asymptotically equivalent and statistically efficient. In a simulation study, the MLE and UNCLE methods are found to possess very similar finite-sample properties as well. As UNCLE is computationally more efficient, it may be the preferred technique in a given application     

Robust maximum likelihood bearing estimation in contaminatedGaussian noise

A robust maximum likelihood (ML) direction-of-arrival (DOA) estimation method that is insensitive to outliers and distributional uncertainties in Gaussian noise is presented. The algorithm has been shown to perform much better than the Gaussian ML algorithm when the underlying noise distribution deviates even slightly from Gaussian while still performing almost as well in pure Gaussian noise. As with the Gaussian ML estimation, it is still capable of handling correlated signals as well as single snapshot cases. Performance of the algorithm is analyzed using the unique resolution test procedure which determines whether a DOA estimation algorithm, at a given confidence level, can resolve two dominant sources with very close DOAs     

Rake Reception With Channel Estimation Error

Several digital cellular systems employ coherent RAKE reception, wherein channel estimates are used to combine despread values. In this paper, a maximum likelihood (ML) approach to RAKE combining that accounts for channel estimation error, including error correlation across despread values, is examined. Fading and noise correlation are also considered. The performance of the ML approach is compared to traditional RAKE combining as well as approximate ML-based approaches. Results show that when the channel estimation error and noise are of the same order, ML-based approaches can provide gains on the order of 1 dB over traditional RAKE reception     

Joint maximum likelihood symbol and slot synchronization foroptical OPPM channels

A jointly optimum slot and symbol clock recovery scheme for a direct-detection optical communication system with overlapping pulse position modulation (OPPM) is proposed. To arrive at the suggested optimum synchronizer, the maximum likelihood (ML) estimation technique is used when the observed process is a Poisson point process (i.e., shot noise limited receiver). Two suboptimal synchronizer models computationally superior to the ML model are also proposed     

Array signal Processing in the known waveform and steering vector case

The amplitude estimation of a signal that is known only up to an unknown scaling factor, with interference and noise present, is of interest in several applications, including using the emerging quadrupole resonance (QR) technology for explosive detection. In such applications, a sensor array is often deployed for interference suppression. This paper considers the complex amplitude estimation of a known waveform signal whose array response is also known a priori. Two approaches, viz., the Capon and the maximum likelihood (ML) methods, are considered for the signal amplitude estimation in the presence of temporally white but spatially colored interference and noise. We derive closed-form expressions for the expected values and mean-squared errors (MSEs) of the two estimators. A comparative study shows that the ML estimate is unbiased, whereas the Capon estimate is biased downwards for finite data sample lengths. We show that both methods are asymptotically statistically efficient when the number of data samples is large but not when the signal-to-noise ratio (SNR) is high. Furthermore, we consider a more general scenario where the interference and noise are both spatially and temporally correlated. We model the interference and noise vector as a multichannel autoregressive (AR) random process. An alternating least squares (ALS) method for parameter estimation is presented. We show that in most cases, the ALS method is superior to the model-mismatched ML (M/sup 3/L) method, which ignores the temporal correlation of the interference and noise.     

基于空间平滑和盖尔圆准则的信源数目估计方法

基于空间平滑理论和盖尔圆准则，提出了一种能够在色噪声环境下估计相干源结构和数目的方法。该方法首先借助空间平滑技术去除信源的相干性，然后利用盖尔圆准则估计去相干后的信号子空间的维数，经多次平滑和估计得到阵列协方差矩阵的平滑秩图，从而确定信源的相干结构和数目。仿真实验证明了该方法的有效性。     

On the robustness of parameter estimation of superimposed signalsby dynamic programming

We analyze a recently proposed dynamic programming algorithm (REDP) for maximum likelihood (ML) parameter estimation of superimposed signals in noise. We show that it degrades gracefully with deviations from the key assumption of a limited interaction signal model (LISMO), providing exact estimates when the LISMO assumption holds exactly. In particular, we show that the deviations of the REDP estimates from the exact ML are continuous in the deviation of the signal model from the LISMO assumption. These deviations of the REDP estimates from the MLE are further quantified by a comparison to an ML algorithm with an exhaustive multidimensional search on a lattice in parameter space. We derive an explicit expression for the lattice spacing for which the two algorithms have equivalent optimization performance, which can be used to assess the robustness of REDP to deviations from the LISMO assumption. The values of this equivalent lattice spacing are found to be small for a classical example of superimposed complex exponentials in noise, confirming the robustness of REDP for this application     

Bounds on maximum likelihood ratio-part I: application to antenna array detection-estimation with perfect wavefront coherence

The multiple hypothesis testing problem of the detection-estimation of an unknown number of independent Gaussian point sources is adequately addressed by likelihood ratio (LR) maximization over the set of admissible covariance matrix models. We introduce nonasymptotic lower and upper bounds for the maximum LR. Since LR optimization is generally a nonconvex multiextremal problem, any practical solution could now be tested against these bounds, enabling a high probability of recognizing nonoptimal solutions. We demonstrate that in many applications, the lower bound is quite tight, with approximate maximum likelihood (ML) techniques often unable to approach this bound. The introduced lower bound analysis is shown to be very efficient in determining whether or not performance breakdown has occurred for subspace-based direction-of-arrival (DOA) estimation techniques. We also demonstrate that by proper LR maximization, we can extend the range of signal-to-noise ratio (SNR) values and/or number of data samples wherein accurate parameter estimates are produced. Yet, when the SNR and/or sample size falls below a certain limit for a given scenario, we show that ML estimation suffers from a discontinuity in the parameter estimates: a phenomenon that cannot be eliminated within the ML paradigm.     

On Optimum and Suboptimum Coherent Detection of Continuous Phase Modulation on a Two-Ray Multipath Fading Channel

In this paper, the performance of continuous phase modulation (CPM) transmitted on a two-ray fading channel and received in white Gaussian noise is studied. The optimum coherent maximum likelihood (ML) detector and approximations thereof and their performance are studied by means of minimum Euclidean distance and simulated symbol error probability. A linear detector optimum at large signal-to-noise ratios is also studied and the performance is given by means of error probability. It is assumed that measurements on the channel provide information about the channel parameters. It is found that the loss in signal power due to the channel is small when an ML detector or an approximation thereof is used for binary schemes with modulation indexh =1/2. The loss for these schemes with a linear detector becomes significantly larger, especially when MSK is transmitted. The performance for this linear detector can, however, be improved significantly by using decision feedback, but still, the performance of the ML detector is superior.     

Efficient dipole parameter estimation in EEG systems with near-ML performance

Source signals that have strong temporal correlation can pose a challenge for high-resolution EEG source localization algorithms. In this paper, we present two methods that are able to accurately locate highly correlated sources in situations where other high-resolution methods such as multiple signal classification and linearly constrained minimum variance beamforming fail. These methods are based on approximations to the optimal maximum likelihood (ML) approach, but offer significant computational advantages over ML when estimates of the equivalent EEG dipole orientation and moment are required in addition to the source location. The first method uses a two-stage approach in which localization is performed assuming an unstructured dipole moment model, and then the dipole orientation is obtained by using these estimates in a second step. The second method is based on the use of the noise subspace fitting concept, and has been shown to provide performance that is asymptotically equivalent to the direct ML method. Both techniques lead to a considerably simpler optimization than ML since the estimation of the source locations and dipole moments is decoupled. Examples using data from simulations and auditory experiments are presented to illustrate the performance of the algorithms.     

基于四阶累积量的最大似然测向方法研究

论述了最大似然（ML）算法测向以及四阶累积量阵列扩展的基本原理，在此基础上给出了一种基于最大似然算法和四阶累积量的DOA估计新方法。与普通的基于二阶矩的最大似然算法相比，本方法具有对阵列进行四阶扩展的能力，可以解决信号源数大于阵元数时的测向问题，并且由于四阶累积量自身的盲高斯性，还可以有效抑制高斯色噪声。     

Stopping Rule for the MLE Algorithm Based on Statistical Hypothesis Testing

It is known that when the maximum likelihood estimator (MLE) algorithm passes a certain point, it produces images that begin to deteriorate. We propose a quantitative criterion with a simple probabilistic interpretation that allows the user to stop the algorithm just before this effect begins. The MLE algorithm searches for the image that has the maximum probability to generate the projection data. The underlying assumption of the algorithm is a Poisson distribution of the data. Therefore, the best image, according to the MLE algorithm, is the one that results in projection means which are as close to the data as possible. It is shown that this goal conflicts with the assumption that the data are Poisson-distributed. We test a statistical hypothesis whereby the projection data could have been generated by the image produced after each iteration. The acceptance or rejection of the hypothesis is based on a parameter that decreases as the images improve and increases as they deteriorate. We show that the best MLE images, which pass the test, result in somewhat lower noise in regions of high activity than the filtered back-projection results and much improved images in low activity regions. The applicability of the proposed stopping rule to other iterative schemes is discussed.     

利用改进遗传算法的DOA估计

用极大似然估计（ＭＬＥ）得到到达信号的方向（ＤＯＡ）,在统计性能方面要比其它一些理论优越,但是由于该方法为种多维参数估计,采用常规搜索方法,精度受到网格限制,不能任意逼近最优解,并且容易收敛到局部最优。而遗传算法是一种有导向的随机搜索方法,它具有适用条件宽松,有较大的概率收敛到全局最优等优点。在此通过改进的遗传算法（ＩＧＡ）,较好地解决了一般搜索算法存在的不足,计算机模拟实验证明可行。     

宽带信号源相干结构估计方法

基于平滑秩图和改进的最小描述长度准则,提出了一种估计宽带信号源相干结构和数目的方法。该方法不需对宽带信号进行聚焦变换,而是对阵列在各个频率点的相关矩阵进行平滑去相关,再利用平滑秩图来估计相干结构和信号源数目。计算机仿真实验证明了该方法的有效性。     

Near-field multiple source localization by passive sensor array

The localization of multiple near-field sources in a spatially white Gaussian noise environment is studied. A modified two-dimensional (2-D) version of the multiple signal classification (MUSIC) algorithm is used to localize the signal sources; range and bearing. A global-optimum maximum likelihood searching approach to localize these sources is discussed. It is shown that in the single source situation, the covariances of both the 2-D MUSIC estimator and the maximum likelihood estimator (MLE) approach the Cramer-Rao lower bound as the number of snapshots increases to infinity. In the multiple source situation, it is observed that for a high signal-to-noise ratio (SNR) and a large number of snapshots, the root mean square errors (RMSEs) of both localization techniques are relatively small. However, for low SNR and/or small number of snapshots, the performance of the MLE is much superior that of the modified 2-D MUSIC     

Maximum likelihood parameter estimation of F-ARIMA processes using the genetic algorithm in the frequency domain

This work aims to treat the parameter estimation problem for fractional-integrated autoregressive moving average (F-ARIMA) processes under external noise. Unlike the conventional approaches from the perspective of the time domain, a maximum likelihood (ML) method is developed in the frequency domain since the power spectrum of an F-ARIMA process is in a very explicit and more simple form. However, maximization of the likelihood function is a highly nonlinear estimation problem. Conventional searching algorithms are likely to converge to local maxima under this situation. Since the genetic algorithm (GA) tends to find the globally optimal solution without being trapped at local maxima, an estimation scheme based on the GA is therefore developed to solve the ML parameter estimation problem for F-ARIMA processes from the frequency domain perspective. In the parameter estimation procedure, stability of the F-ARIMA model is ensured, and convergence to the global optimum of the likelihood function is also guaranteed. Finally, several simulation examples are presented to illustrate the proposed estimation algorithm and exhibit its performance.     

Maximum likelihood estimation and MUSIC in array localization signal processing: A review

Algorithms to treat the maximum likelihood (ML) estimation problem in array localization signal processing are reviewed, including the alternating projection method, the iterative quadratic maximum likelihood method and the expectation-maximization method. The relationship of ML estimators and the MUSIC algorithm is presented. The Cramer-Rao bounds for the deterministic and stochastic models in array localization are summarized. Finally, the problem of the estimation of the number of sources is discussed.     

Direction of Arrival Estimation in the Presence of Noise Coupling in Antenna Arrays

The direction of arrival (DOA) estimation problem in the presence of signal and noise coupling in antenna arrays is addressed. In many applications, such as smart antenna, radar and navigation systems, the noise coupling between different antenna array elements is often neglected in the antenna modeling and thus, may significantly degrade the system performance. Utilizing the exact noise covariance matrix enables to achieve high-performance source localization by taking into account the colored properties of the array noise. The noise covariance matrix of the antenna array consists of both the external noise sources from sky, ground and interference, and the internal noise sources from amplifiers and loads. Computation of the internal noise covariance matrix is implemented using the theory of noisy linear networks combined with the method of moments (MoM). Based on this noise statistical analysis, a new four-port antenna element consisting of two orthogonal loops is proposed with enhanced source localization performance. The maximum likelihood (ML) estimator and the Cramer-Rao lower bound (CRLB) for DOA estimation in the presence of noise coupling is derived. Simulation results show that the noise coupling in antenna arrays may substantially alter the source localization performance. The performance of a mismatched ML estimator based on a model which ignores the noise coupling shows significant performance degradation due to noise coupling. These results demonstrate the importance of the noise coupling modeling in the DOA estimation algorithms.