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.     

Multiple radar targets estimation by exploiting induced amplitude modulation

This work deals with the problem of estimating complex amplitudes, Doppler frequencies, and directions of arrival (DOA) of multiple targets present in the same range-azimuth resolution cell of a surveillance radar. The maximum likelihood (ML) and the asymptotic (large sample size) ML (AML) estimators are derived. To reduce the computational complexity of the maximization of the nonlinear two-dimensional criterion function of the AML estimator, we propose a computationally efficient algorithm based on the RELAXation method. It allows decoupling the problem of jointly estimating the parameters of the signal components into a sequence of simpler problems, where the parameters of each component are separately and iteratively estimated. The proposed method overcomes the resolution limitation of the classical monopulse technique and resolves multiple targets exhibiting an arbitrarily small difference in azimuth as long as their Doppler frequencies differ at least by the inverse of the number of integrated pulses, provided that enough signal-to-noise ratio (SNR) per pulse is available. The performance of the proposed AML-RELAX estimator is numerically investigated through Monte Carlo simulation and Cramer-Rao lower bound (CRLB) calculation.     

Angle Estimation with Adaptive Arrays in External Noise Fields

A method of estimating the angle of arrival of a signal at an array of sensors in an external noise environment is outlined. The development is based on a maximum likelihood estimator and leads naturally to adaptive sum and difference beams which null the external noise sources. An algorithm for estimating angle of arrival, based on the outputs of adaptively distorted sum and differnce beams, is shown to perform well in the presence of sidelobe and/or main beam interference.     

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。     

由飞行试验数据求取直升机气动导数的最佳方法研究

本文主要介绍利用频率法、卡尔曼滤波和最大似然法求取气动导数的方法。方法的特点是,通过频率法使旋翼高频成份的影响减至最小,同时求取试验数据的测量噪声和过程噪声,然后通过卡尔曼滤波使试验数据包含的随机噪声减小,最后使用最大似然法使试验数据包含的随机噪声进一步减小,并求取最终的气动导数。计算结果表明,该方法可使试验数据中包含的噪声减至最小,复合相关系数提高到0.95以上,特征根更接近真值,其准确度优于最小二乘法、频率法、卡尔曼滤波方法和最大似然法,它保留了使用低通滤波数据的卡尔曼滤波方法的优点,克服了原方法振荡模态频率偏低的缺点,适合于各种直升机的导数识别。     

Maximum Likelihood DOA Estimation in Unknown Colored Noise Fields

Direction-of-arrival (DOA) estimation in unknown noise environments is an important but challenging problem. Several methods based on maximum likelihood (ML) criteria and parameterization of signals or noise covariances have been established. Generally, to obtain the exact ML (EML) solutions, the DOAs must be jointly estimated along with other noise or signal parameters by optimizing a complicated nonlinear function over a high-dimensional problem space. Although the computation complexity can be reduced via derivation of suboptimal approximate ML (AML) functions using large sample assumption or least square criteria, nevertheless the AML estimators still require multi-dimensional search and the accuracy is lost to some extent. A particle swarm optimization (PSO) based solution is proposed here to compute the EML functions and explore the potential superior performances. A key characteristic of PSO is that the algorithm itself is highly robust yet remarkably simple to implement, while processing similar capabilities as other evolutionary algorithms such as the genetic algorithm (GA). Simulation results confirm the advantage of paring PSO with EML, and the PSO-EML estimator is shown to significantly outperform AML-based techniques in various scenarios at less computational costs.     

动态系统时延参数估计的重构输入法

首先指出了过去在进行时延系统参数估计时所用的近似处理方法的弊端，然后就动态系统未知时延参数的估计问题提出了重构系统输入的估计方法，并以极大似然估计迭代算法为基础给出了一套估计动态系统时延参数的算法，最后，应用所提出的方法进行了仿真计算，仿真结果表明，参数估计的精度极高，这说明该方法是可靠且可行的。     

On Processing Optical Images Propagated Through the Atmosphere

The problem of how to process optical images that have propagated through a turbulent atmosphere is considered. It is assumed that either the object or its (free-space) scattered field at the receiving aperture is known, except for unknown parameters that are to be estimated. Isotropic and homogeneous turbulence as discussed by Tatarski and Chernov is assumed. It is assumed that a very short (in time) reception is made, that the turbulence-induced complex phase errors are either small or have a correlation distance short relative to the receiving aperture extent, and that the object is within an isoplanatic region. The method of maximum likelihood (ML) is used as a criterion; its applicability is discussed. The ML image-processing structure is found and is nonlinear. Asymptotic cases are examined; among other conclusions, it is shown that the ML processing of independent receptions is more complex than an ML processing of the sum of the receptions. A coherent optical system that realizes the ML image processor is described; it includes the capability to generate the scattered field. Simplifications are pointed out.     

Radar measurement extraction in the presence of sea-surface multipath

In the presence of sea-surface multipath monopulse radar signals from a low elevation target have three alternative paths in addition to the direct (radar-to-target) path due to reflections from the sea surface. The specular reflection causes significant signal fading. The diffuse reflection causes an approximately constant bias to the in-phase component of the monopulse ratio, which is the standard extractor of the direction of arrival (DOA) in the monopulse processing. The diffuse reflection also causes higher standard deviation to the in-phase component of the monopulse ratio. We propose a maximum likelihood (ML) angle extraction technique for low elevation targets of known average signal strength having a Rayleigh fluctuation. The results show that this method reduces the error of the estimated angle compared with the conventional monopulse ratio estimator. Subsequently, the ML angle extractor is modified for the unknown average signal strength case. This modified angle extractor has only a small performance degradation compared with the known average signal strength case, but it performs much better than the monopulse ratio based estimator. An algorithm to calculate the accuracy of the estimated angle (or height) is also presented. This angle extractor reduces the root-mean-square error (RMSE) by more than 50% in the signal processing stage when used in a low flying target tracking scenario. The same algorithm can be used to track sea skimmers.     

Optimum detection and location estimation of target lines in the range-time space of a search radar

The average likelihood ratio detector is derived as the optimum detector for detecting a target line with unknown normal parameters in the range-time data space of a search radar, which is corrupted by Gaussian noise. The receiver operation characteristics of this optimum detector is derived to evaluate its performance improvement in comparison with the Hough detector, which uses the return signal of several successive scans to achieve a non-coherent integration improvement and get a better performance than the conventional detector. This comparison, which is done through analytic derivations and also through simulation results, shows that the average likelihood ratio detector has a better performance for different SNR values. This result is justified by showing the disadvantages of the Hough method, which are eliminated by the optimum detector. To have an estimate for the location of the detected target line in the optimum detection method as the Hough method, which detects and localizes the target lines simultaneously, we present the maximum a posteriori probability estimator. The estimation performance of the two methods is then compared and it is shown that the maximum a posteriori probability estimator localizes the detected target lines with a better performance in comparison with the Hough method.     

Maximum likelihood angle extractor for two closely spaced targets

In a scenario of closely spaced targets special attention has to be paid to radar signal processing. We present an advanced processing technique, which uses the maximum likelihood (ML) criterion to extract from a monopulse radar separate angle measurements for unresolved targets. This processing results in a significant improvement, in terms of measurement error standard deviations, over angle estimators using the monopulse ratio. Algorithms are developed for Swerling I as well as Swerling III models of radar cross section (RCS) fluctuations. The accuracy of the results is compared with the Cramer Rao lower bound (CRLB) and also to the monopulse ratio technique. A novel technique to detect the presence of two unresolved targets is also discussed. The performance of the ML estimator was evaluated in a benchmark scenario of closely spaced targets - closer than half power beamwidth of a monopulse radar. The interacting multiple model probabilistic data association (IMMPDA) track estimator was used in conjunction with the ML angle extractor     

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.     

Markov随机跳变系统的传感器系统误差估计

 针对Markov随机跳变系统的系统误差估计问题,提出一种基于马尔可夫链蒙特卡罗(MCMC)和最大似然估计相结合的在线系统误差估计方法。利用最大似然估计给出系统误差等效后验概率分布函数,采用Metropolis-Hastings抽样方法从该概率分布函数中进行抽样;利用系统误差估计和状态估计互为因果的关系,采用期望极大化(EM)方法迭代估计出最优的系统误差;分别对时变和时不变系统误差场景进行仿真分析,结果表明,在考虑系统误差统计特性的同时,所提方法对解决目标运动模型难以建立情况下的系统误差估计问题具有可行性和有效性。     

Maximum Likelihood Energy Detection of Mary Orthogonal Signals

The literature on energy detection is extended by applying it to the processing of M'ary orthogonal communication signals of arbitrary time-bandwidth product. Guassian noise channel transition probabilities are derived for maximum likelihood energy detection, modified to the extent of including an erasure threshold. Relations and computational techniques are described for determining the symbol erasure and error probabilities for general signal alphabet sizes (M) and time-bandwidth products. When time of arrival is known exactly and Doppler is negligible, gible, it is determined that energy detection is inferior to noncoherent matched filter detection. For time-bandwidth products of the order of 100 and error probabilities around 10 3, a loss of about 5 dB occurs which is attributable to a lack of knowledge of the detail signal structure. However, for problems where time of arrival and/ or Doppler are unknown, energy detection will perform nearly as well as matched filter detection of, for example, spread spectrum signals, and is also simpler to implement. General energy detection performance curves are given in terms of required signal energy for specific error and erasure probabilities, as a function of M'ary and time-bandwidth product.     

Adaptive Maximum Likelihood Receiver for Direct-Ranging Applications

Recent interest in direct-ranging navigation methods has prompted new research into practical receiver structures which provide improved signal processing. Maximum likelihood receivers are compared with conventional phase-locked receivers by theoretical and simulation methods as phase estimators based on signal measurements only. Signal-to-noise ratio (SNR) enhancement is examined and filter recommendations made. An adaptive maximum likelihood receiver is then developed which uses both signal measurements and a priori data to improve phase estimation accuracy. Simulation results indicate a 33.3 dB processing gain yielding a ranging error standard deviation of ±15 feet for zero dB received SNR. Nonadaptive and adaptive receivers are fabricated, flight tested, and experimental results reported.     

Quickest detection for sequential decentralized decision systems

Quickest detection procedures are techniques used to detect sudden or abrupt changes (also called disorders) in the statistics of a random process. The goal is to determine as soon as possible that the change occurred, while at the same time minimizing the chance of falsely signaling the occurrence of a disorder before the change. In this work the distributed quickest detection problem when the disorder occurs at an unknown time is considered. The distributed local detectors utilize a simple summing device and threshold comparator, with a binary decision at the output. At the fusion center, the optimal maximum likelihood (ML) procedure is analyzed and compared with the more practical Page procedure for quickest detection. It is shown that the two procedures have practically equivalent performance. For the important case of unknown disorder magnitudes, a version of the Hinkley procedure is also examined. Next, a simple method for choosing the thresholds of the local detectors based on an asymptotic performance measure is presented. The problem of selecting the local thresholds usually requires optimizing a constrained set of nonlinear equations; our method admits a separable problem, leading to straightforward calculations. A sensitivity analysis reveals that the resulting threshold settings are optimal for practical purposes. The issue of which sample size to use for the local detectors is investigated, and the tradeoff between decision delay and communication cost is evaluated. For strong signals, it is shown that the relative performance deteriorates as the sample size increases, that is, as the system cost decreases. Surprisingly, for the weak signal case, lowering the system cost (increasing the sample size) does not necessarily result in a degradation of performance     

Bayesian Detection of Targets of Unknown Location

In this paper the array detection problem for certain deterministic signals in spatially uncorrelated Gaussian noise is formulated in Bayesian terms and the required likelihood ratios and resulting performance characteristics are obtained. Primary emphasis is on detection of targets of unknown spatial location using a likelihood ratio approach, with the target location treated as a random parameter, rather than an estimator-correlator approach. The tradeoff among array parameters and signal parameters is demonstrated. It is shown that the dominant uncertainty affecting detection performance seems to be that of location when compared with uncertainty on energy and/or phase.     

系统识别与飞机颤振

本文在简要综述了系统识别技术在飞机颤振研究中的应用后,介绍了三种系统识别方法。重点讨论了其算法要点及理论基础。对有关数据处理问题也作了适当说明。基于复模态分析和优化技术的传递函数法可以精确识别出全部模态参数,并在带外挂机翼颤振模型试验中获得成功,该法可推广到仅有响应数据的风洞与飞行试验情况。脉冲响应和自回归滑动平均模型法采用了相关和最小二乘技术,可以在较强干扰情况下得到精确结果,后者还可求出估计值与真值的协方差。两种时域方法皆可无需专用信号分析设备而直接利用测量采样数据进行系统识别。     

Frequency estimation techniques for high dynamic trajectories

A comparison is presented of four different estimation techniques applied to the problem of continuously estimating the rapidly varying parameters of a sinusoidal signal, observed in the presence of additive noise. Frequency estimates are emphasized, although phase and/or frequency rate are also estimated by some of the algorithms. These parameters are related to the velocity, position, and acceleration of the maneuvering receiver or transmitter. Estimated performance at low carrier-to-noise ratios and high dynamics is investigated for the purpose of determining the useful operating range of an approximate maximum likelihood estimator, an extended Kalman filter, a cross-product automatic frequency loop and a phase-locked loop. Numerical simulations are used to evaluate performance while tracking a common trajectory exhibiting high dynamics     

Localization of step changes in multitemporal SAR images

Deals with multitemporal sequences of synthetic aperture radar (SAR) images with regions possibly affected by step reflectivity patterns of change. Specifically, it addresses the problems of detecting a temporal step pattern with small reflectivity change against a constant pattern and of estimating the transition instant for the step. The statistically optimized signal processing techniques proposed in this work are most appropriate for the new generation of SAR systems with high revisit time that are currently under development. We propose two different techniques, based on the maximum likelihood (ML) approach, that make different use of prior knowledge on the radar cross section (RCS) levels of the searched pattern. They process the whole sequence to achieve optimal discrimination capability between regions affected and not affected by a step change and optimal estimation accuracy for the step transition instant. The first technique (known step pattern (KSP)-detector) assumes complete knowledge of the RCS levels of the searched pattern of change, while the second one (USP-detector) is based on the assumption of totally unknown step pattern.