Bearings-only tracking of maneuvering targets using abatch-recursive estimator

We present a new batch-recursive estimator for tracking maneuvering targets from bearings-only measurements in clutter (i.e., for low signal-to-noise ratio (SNR) targets), Standard recursive estimators like the extended Kalman Iter (EKF) suffer from poor convergence and erratic behavior due to the lack of initial target range information, On the other hand, batch estimators cannot handle target maneuvers. In order to rectify these shortcomings, we combine the batch maximum likelihood-probabilistic data association (ML-PDA) estimator with the recursive interacting multiple model (IMM) estimator with probabilistic data association (PDA) to result in better track initialization as well as track maintenance results in the presence of clutter. It is also demonstrated how the batch-recursive estimator can be used for adaptive decisions for ownship maneuvers based on the target state estimation to enhance the target observability. The tracking algorithm is shown to be effective for targets with 8 dB SNR     

On Signal and Noise Level Estimation in a Coherent PCM Channel

Joint maximum likelihood estimators are presented for the signal amplitude and noise power density in a coherent PCM channel with white Gaussian noise and a correlation receiver. The estimates are based upon the correlation coefficient outputs of the receiver. From these estimators, an estimator for the quantity (received signal energy)/bit/,(noise power)/(unit bandwidth) upon which the error probabilities depend, is derived. This estimator is shown to be useful as 1) a point estimator for the signal-to-noise ratio for the higher values of this ratio (about 4 dB or greater), and 2) an easily calculated statistic upon which to base data acceptance or rejection criteria. The acceptance or rejection levels are obtained by the use of confidence interval curves in conjunction with word error probability data.     

Spectral Analysis and Subtraction of Noise in Radar Signals

A new method of maximum entropy spectral estimation called the revised maximum entropy method (MEM) is formulated and is applied to the spectral analysis of the echo signals from atmospheric turbulence observed by an incoherent scatter radar. The revised MEM is shown free from many demerits of the other methods for spectral analysis. Further it makes it possible to subtract the white noise usually contained in the data during the processing. Some examples of spectral estimation are shown for the actual radar signals and the simulated data. Another application of the revised MEM is the subtraction of the clutter component which is difficult to do by linear filtering. The method is successfully applied to several data abounding with the clutter to obtain the spectra of the echo signals with less clutter distortion.     

Detection of stochastic signals in the frequency domain

The optimum detector for a random signal, the estimator-correlator, is difficult to implement. If the power spectral density (PSD) of a continuous time signal is known, a locally optimum detector is available. It maximizes the deflection ratio (DR), a measure of the detector output signal-to-noise ratio (SNR). A discrete version of this detector is developed here, called the discrete-MDRD, which takes a weighted sum of the spectral components of the signal data as the detection statistic. Its derivation is applicable to nonwhite noise samples as well. A comparison of this new detector against three other common types, through their DR values and simulation results, reveals that the discrete-MDRD is near optimal at low SNRs. When the PSD of a signal is not known, a common test statistic is the peak of the PSD of the data. To reduce spectral variations, the PSD estimator first divides the data sequence into several segments and then forms the averaged PSD estimate. The segment length affects the DR values; the length that maximizes the DR is approximately the reciprocal of the signal bandwidth. Thus for unknown signal PSD, a detector that approaches the maximum DR is realizable from just the knowledge of the signal bandwidth, which is normally available. Examples and simulation results are provided to illustrate the properties and performance of the new detector     

Probabilistic inference of fatigue damage propagation with limited and partial information

A general method of probabilistic fatigue damage prognostics using limited and partial information is developed.Limited and partial information refers to measurable data that are not enough or cannot directly be used to statistically identify model parameter using traditional regression analysis.In the proposed method, the prior probability distribution of model parameters is derived based on the principle of maximum entropy(Max Ent) using the limited and partial information as constraints.The posterior distribution is formulated using the principle of maximum relative entropy(MRE) to perform probability updating when new information is available and reduces uncertainty in prognosis results.It is shown that the posterior distribution is equivalent to a Bayesian posterior when the new information used for updating is point measurements.A numerical quadrature interpolating method is used to calculate the asymptotic approximation for the prior distribution.Once the prior is obtained, subsequent measurement data are used to perform updating using Markov chain Monte Carlo(MCMC) simulations.Fatigue crack prognosis problems with experimental data are presented for demonstration and validation.     

Fast approximate maximum likelihood period estimation from incomplete timing data

 To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid search of the peak of a spectrum, which is equivalent to the periodogram of the periodic point process, thus its performance is found to be sensitive to the chosen grid spacing. This paper derives a novel grid spacing formula, after finding a lower bound of the width of the spectral mainlobe. By employing this formula, the proposed new estimator can determine an appropriate grid spacing adaptively, and is able to yield approximate maximum likelihood estimate (MLE) with a computational complexity of O(n²). Experimental results prove that the proposed estimator can achieve better trade-off between statistical accuracy and complexity, as compared to existing methods. Simulations also show that the derived grid spacing formula is also applicable to other estimators that operate similarly by grid search.     

A Weighted Inner Product Estimator in the Geometric Algebra of Euclidean 3-Space for Source Localization Using an EM Vector-sensor

In this paper, the source localization by utilizing the measurements of a single electromagnetic (EM) vector-sensor is investigated in the framework of the geometric algebra of Euclidean 3-space. In order to describe the orthogonality among the electric and magnetic measurements, two multivectors of the geometric algebra of Euclidean 3-space (G3) are used to model the outputs of a spatially collocated EM vector-sensor. Two estimators for the wave propagation vector estimation are then formulated by the inner product between a vector and a bivector in the G3. Since the information used by the two estimators is different, a weighted inner product estimator is then proposed to fuse the two estimators together in the sense of the minimum mean square error (MMSE). Analytical results show that the statistical performances of the weighted inner product estimator are always better than its traditional cross product counterpart. The efficacy of the weighted inner product estimator and the correctness of the analytical predictions are demonstrated by simulation results.     

Multipath interferometry technique for airborne array calibration

A new technique is developed to compensate multiple-wavelength distortion in airborne antenna arrays. This approach exploits the phase information in microwave reflections from arbitrary terrain. To handle reflections incident over a broad angle, a range-Doppler preprocessor is used in each element channel to resolve wavefronts incident simultaneously from different directions. The phase information for each direction of arrival is compared between elements and processed by optimal estimators to determine the phase corrections needed to compensate the distortion. To develop the estimators, a statistical model of the complex baseband terrain reflections is developed. This is in turn used to generate conditional probability densities involving the range Doppler observations and the parameters to be estimated. These densities are subsequently used to develop minimum variance and maximum likelihood estimators. The new estimators use additional information that has not been exploited by previous techniques and therefore provide enhanced performance     

Bearings-only and Doppler-bearing tracking using instrumentalvariables

In bearings-only tracking (BOT) or Doppler and bearing tracking (DBT), both common passive sonar problems, the measurement equations are nonlinear. To apply the Kalman filter, it is necessary either to linearize the equations or to embed the nonlinearities into the noise terms. The former sometimes leads to filter divergence, while the latter produces biased estimates. A formulation of BOT and DBT which has a constant state vector and simplifies the tracking problem to one of constant parameter estimation is given. The solution is by the instrumental variable method. The instrumental variables are obtained from predictions based on past measurements and are therefore independent of the present noisy measurements. The result is a recursive unbiased estimator. The theoretical developments are verified by simulation, which also shows that the formulation leads to near optimal estimators whose errors are close to the Cramer-Rao lower bound (CRLB)     

基于自适应步长选择的周期格型线搜索估计

稀疏、含噪观测条件下周期点过程的周期估计是一个经典的信号处理问题。针对该问题,提出了一种格型线搜索(LLS)算法,该算法通过数值方式搜索似然函数的最大值,但其性能取决于人为预先选取的搜索步长。推导了一个步长计算公式,并利用该公式改进了LLS算法。改进的LLS算法能够自适应选择搜索步长,其达到的克拉美-罗界(CRLB)的信噪比(SNR)门限与最大似然估计(MLE)算法一致,但计算复杂度比后者低一个多的数量级。性能分析与仿真实验表明,所提算法比已有算法能更好地实现估计精度与复杂度的折中。     

热结构动力优化设计

 考虑温度沿飞行器表面的分布及材料物性系数随温度的变化,按Ｋｕｈｎ－Ｔｕｃｋｅｒ条件建立迭代式,研究具有频率约束、振型节点约束以及变量上、下限约束的热结构动力优化设计。算例讨论了前３阶固有特性及最小目标随温度场的变化规律,证实本方法有效、可行。     

最大熵准则识别材料疲劳寿命分布

疲劳寿命具有很大的分散性,是工程结构设计中必须考虑的因素。为了降低主观不确定性的引入,得到更合理的疲劳寿命分布类型,提出一种用于识别疲劳寿命概率分布类型的一般计算方法。该方法首先根据疲劳试验样本信息确定疲劳寿命的前四阶统计矩;基于统计矩信息,利用最大熵准则确定疲劳寿命的概率分布类型。在基于最大熵准则识别疲劳寿命分布时,利用Lagrange乘子法求解最大熵分布。采用已有的航空铝合金2024-T351板件疲劳裂纹扩展试验数据验证所提计算方法的合理性和有效性。结果表明:所提方法能够高效地识别材料疲劳寿命分布类型,并且不局限于单峰标准分布类型。     

高效亚音轴流压气机级几何参数最佳选择

将亚音速轴流压气机级的设计问题表述为气动力学损失和重量为极小化、压气机喘振边界极大化的多目标非线性数学规划问题。求优中考虑了多种气动与机械约束条件。介绍了压气机级性能估算的模型, 给出了最大效率、最小重量、最大喘振边界以及效率、重量、喘振边界三者权衡最优条件下的算例。此方法可拓广用于多级轴流压气机中。      

Emitter localization using clustering-based bearing association

A closed-form emitter location estimator using time difference of arrival (TDOA) measurements is developed based on triangulation of hyperbolic asymptotes. The problem of associating the asymptotes with the emitter is solved by clustering the bearing angles of the linear asymptotes using a kernel density estimate. A closed-form estimate of the emitter location is obtained from triangulation of the clustered bearings using a weighted version of the pseudolinear estimator. By way of simulation examples, the proposed closed-form estimator is shown to outperform the computationally demanding and divergence-prone maximum likelihood (ML) estimator at moderate TDOA noise levels.     

小样本下分位数函数的Bootstrap置信区间估计

航空产品试验一般为小样本试验,为了分析小样本情况下的试验数据,结合以概率加权矩为约束条件的最大熵法和求解置信区间及置信带的Bootstrap方法,提出了一种估计小样本试验件母体分位数函数置信区间的方法。最大熵法在矩约束下能够估计样本的密度函数,而以概率加权矩为约束条件的最大熵法能够针对小样本直接给出分位数的无偏估计,无需由密度函数积分得到累积分布函数,再进行转化得到分位数函数。Bootstrap方法求解置信区间具有不依赖于数据分布的优点,具有广泛的应用范围。     

On Attitude Estimation Schemes for Fine-Pointing Control

This paper studies single-axis equations of motion that are applicable to a spacecraft or to a space experiment pointing assembly whose motion has been perfectly isolated from the carrier vehicle. It considers four state estimators for implementation in the control loop for a stellar observation experiment. The first three estimators are very general and do not make use of input torque in their prediction models, while the proposed fourth estimator utilizes this information, It is shown via closed-loop covariance analysis that the best achievable pointing performance with the best of the first three estimators is limited to about 0.125 are-sec (rms) with the given rate-gyro and star-tracker inaccuracies. It is also shown that the fourth estimator has the capability of achieving a pointing performance far superior to the performance achievable using the first three estimators. The fourth estimator relies on the ability to accurately generate the desired control torque (i.e., low input noise).     

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     

Multiple-model estimation with variable structure. V. Likely-modelset algorithm

For pt. IV see ibid., vol. 35, no. 1, p. 242-254 (1999). A multiple-model (MM) estimator with a variable structure, called likely-model set (LMS) algorithm, is presented, which is generally applicable to most hybrid estimation problems and is easily implementable. It uses a set of models that are not unlikely to match the system mode in effect at any given time. Different versions of the algorithm are discussed. The model set is made adaptive in the simplest version by deleting all unlikely models and activating all models to which a principal model may jump so as to anticipate the possible system mode transitions. The generality, simplicity, and ease in the design and implementation of the LMS estimator are illustrated via an example of tracking a maneuvering target and an example of fault detection and identification. Comparison of its cost-effectiveness with other fixed- and variable-structure MM estimators is given     

Passive localization of moving emitters using out-of-planemultipath

The purpose of this work is to establish how a moving emitter, such as a jammer, can be localized by a passive receiver through the use of out-of-plane multipath signals reflected by the terrain. This is a novel localization technique that assumes no a priori knowledge of the localization of the multipath sources. The emitter parameters of range, heading, velocity, and altitude are estimated by exploiting the correlation between the direct-path signal and the delayed and Doppler modulated signals. Two basis assumptions about the scattering properties of the terrain lead to different maximum likelihood estimators (MLEs). The Cramer-Rao lower bounds (CRLB) are used to study estimator performance versus emitter velocity for each case. The proposed estimators are successfully demonstrated using field data collected at White Sands Missile Range (WSMR) during the DARPA/Navy Mountaintop program     

振动诊断的理论基础

本文是“整机振动规范及信号分析技术研究”、“发动机台架振动监视预研”两个课题的总结。本文着重分析振动诊断的理论基础,从理论上总结研究中的经验。