CRB: Sinusoid-Sources' Estimation using Collocated Dipoles/Loops

This work derives new asymptotic Cram?r-Rao lower bounds (CRB) for the estimation of multiple pure-tone incident signals' azimuth-elevation arrival-angles, polarization parameters, frequencies, amplitudes, and temporal phases—based on data collected by spatially collocated but orthogonally oriented dipoles and/or loops. The incident sources are pure-tones at distinct, deterministic but unknown frequencies, in contrast to the case of all incident sources at one common known frequency, as has been investigated in the existing research literature on the CRB for diversely-polarized direction-finding. The derived CRBs are closed-form expressions, explicitly in terms of the signal parameters. The new CRBs presented here reveal how a constituent dipole and/or loop's presence and orientation may affect estimation precision, thereby offering guidelines to the system engineer on what dipole(s) and/or loop(s) to include or to omit in constructing the electromagnetic vector-sensor.     

Sparse frequency transmit-and-receive waveform design

A computationally efficient algorithm derives complex digital transmit and receive ultra-wideband radar and communication waveforms with excellent arbitrary frequency band suppression and range sidelobe minimization. The transmit waveform minimizes a scalar function penalizing weighted spectral energy in arbitrary frequency bands. Near constant power results from another penalty function for deviations from constant power, or constant power is enforced by a phase-only formulation. Next, a least squares solution for the receive waveform minimizes a weighted sum of suppressed band spectral energy and range sidelobes (for pulse and continuous wave operation), with a mainlobe response constraint. Both waveforms are calculated by iterative algorithms whose updates require only linear order in memory and computation, permitting quick calculation of long pulses with thousands of samples.     

Phase-only LMS and perturbation adaptive algorithms

The author defines a phase-only gradient-based adaptive algorithm analogous to the least mean square (LMS) algorithm. Two phase-only perturbation algorithms are then defined. It is shown that the gradient for the perturbation algorithms can be obtained by cross-correlating binary perturbation sequences, that are applied to the adaptive phases, with the resulting instantaneous output power or voltage. It is also shown that a single set of phase-only adaptive weights can be used to simultaneously null interference in multiple output beams. Simulation results are presented for all of the new algorithms. The phase-only perturbation techniques eliminate the need for element level receivers and support low cost retrofitting of adaptive nulling on phased arrays by using conventional beamsteering circuits to apply the adaptive weights     

Instantaneous Frequency Estimation Using Adaptive Linear Predictor Weights

A computationally efficient scheme for estimating the digital instantaneous frequencies of narrowband inputs is introduced. The frequency estimates are obtained by searching for minima of the inverse input power spectrum. This spectrum is estimated at each input sample from the weights of an adaptive linear predictor which uses the LMS (least mean square) algorithm to update its weights. The related minima are sought via an iterative search algorithm, referred to as the iterative frequency estimator. This algorithm is computationally more efficient than available methods, and also provides a higher resolution. Simulation results are included; these include tracking of random message sequences in FM signals, and the formant frequency estimation of speech.     

A direct position determination method with combined TDOA and FDOA based on particle filter

The localization of a stationary transmitter using moving receivers is considered. The original Direct Position Determination (DPD) methods, with combined Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA), do not perform well under low Signal-to-Noise Ratio (SNR), and worse still, the computation cost is difficult to accept when the computational capabilities are limited. To get better positioning performance, we present a new DPD algorithm that proves to be more computationally efficient and more precise for weak signals than the conventional approach. The algorithm partitions the signal received with the same receiver into multiple non-overlapping short-time signal segments, and then uses the TDOA, the FDOA and the coherency among the short-time signals to locate the target. The fast maximum likelihood estimation, one iterative method based on particle filter, is designed to solve the problem of high computation load. A secondary but important result is a derivation of closed-form expressions of the Cramer-Rao Lower Bound (CRLB). The simulation results show that the algorithm proposed in this paper outperforms the traditional DPD algorithms with more accurate results and higher computational efficiency, and especially at low SNR, it is more close to the CRLB.     

Moving scanning emitter tracking by a single observer using time of interception: Observability analysis and algorithm

The target motion analysis (TMA) for a moving scanning emitter with known fixed scan rate by a single observer using the time of interception (TOI) measurements only is investigated in this paper.By transforming the TOI of multiple scan cycles into the direction difference of arrival (DDOA) model,the observability analysis for the TMA problem is performed.Some necessary conditions for uniquely identifying the scanning emitter trajectory are obtained.This paper also proposes a weighted instrumental variable (WIV) estimator for the scanning emitter TMA,which does not require any initial solution guess and is closed-form and computationally attractive.More importantly,simulations show that the proposed algorithm can provide estimation mean square error close to the Cramer-Rao lower bound (CRLB) at moderate noise levels with significantly lower estimation bias than the conventional pseudo-linear least square (PLS) estimator.     

Fault diagnosis based on measurement reconstruction of HPT exit pressure for turbofan engine

Aero-engine gas path health monitoring plays a critical role in Engine Health Management(EHM). To achieve unbiased estimation, traditional filtering methods have strict requirements on measurement parameters which sometimes cannot be measured in engineering. The most typical one is the High-Pressure Turbine(HPT) exit pressure, which is vital to distinguishing failure modes between different turbines. For the case of an abrupt failure occurring in a single turbine component, a model-based sensor measurement reconstruction method is proposed in this paper. First,to estimate the missing measurements, the forward algorithm and the backward algorithm are developed based on corresponding component models according to the failure hypotheses. Then,a new fault diagnosis logic is designed and the traditional nonlinear filter is improved by adding the measurement estimation module and the health parameter correction module, which uses the reconstructed measurement to complete the health parameters estimation. Simulation results show that the proposed method can well restore the desired measurement and the estimated measurement can be used in the turbofan engine gas path diagnosis. Compared with the diagnosis under the condition of missing sensors, this method can distinguish between different failure modes, quantify the variations of health parameters, and achieve good performance at multiple operating points in the flight envelope.     

Variational Bayesian Kalman filter using natural gradient

We propose a technique based on the natural gradient method for variational lower bound maximization for a variational Bayesian Kalman filter. The natural gradient approach is applied to the Kullback-Leibler divergence between the parameterized variational distribution and the posterior density of interest. Using a Gaussian assumption for the parametrized variational distribution, we obtain a closed-form iterative procedure for the Kullback-Leibler divergence minimization, producing estimates of...     

基于空域稀疏性的宽带DOA估计

利用宽带阵列接收信号的空域稀疏性,将宽带信号的波达方向(DOA)估计转化为一个稀疏信号重构的问题,提出了一种新的宽带信号DOA估计算法。该算法将宽带信号分解为多个子带信号,联合利用多个子带信号的空域稀疏性进行重构。它是对用于稀疏重构的标准的稀疏贝叶斯学习算法的推广,可适用于多冗余字典的信号模型。另外,通过对多快拍的阵列接收信号进行奇异值分解(SVD),提取信号子空间作为算法的输入数据,可以在有效减少运算复杂度的同时,提高对噪声的稳健性。与传统的宽带阵列DOA估计方法相比,该算法能够用于低信噪比、快拍有限和信源相关性较高的场合,同时算法的性能对信源个数的估计值不太敏感。仿真实验表明,该算法相对现有的基于子空间类的方法,具有更好的DOA估计性能。     

基于稀疏表示和近似(e)0范数约束的宽带信号DOA估计

针对宽带信号的波达方向(DOA)估计问题,在稀疏框架下提出一种近似(e)0范数约束的宽带信号DOA估计新算法.首先对宽带信号进行预处理,得到同一参考频率点下的接收数据,然后对其协方差矩阵元素进行加和平均运算,得到一个低维的观测向量,并在稀疏框架下进行稀疏表示,最后利用截断(e)1函数设定权值,构造逼近(e)0范数约束的稀疏重构方法,进而重构信号,获得宽带信号的DOA估计.仿真结果表明,相比于传统的宽带信号DOA估计算法,所提算法具有更高的分辨率和估计精度.     

Ergodic sum rate for uplink NOMA transmission in satellite-aerial-ground integrated networks

The application of Non-Orthogonal Multiple Access (NOMA) technology into satellite-aerial-ground integrated networks can meet the requirements of ultra-high rate and massive connectivity for the Sixth-Generation (6G) communication systems. We consider an uplink NOMA scenario for such a satellite-aerial-ground integrated network where multiple users communicate with satellite under the help of an Unmanned Aerial Vehicle (UAV) as an aerial relay equipped with a phased array. Supposing that buffer-aided decode-and-forward protocol is adopted at the UAV relay, we first formulate an optimization problem to maximize Ergodic Sum Rate (ESR) of the considered system subject to individual power constraint and quality-of-service constraint of each user. Then, with known imperfect channel state information of each user, we propose a joint power allocation and robust Beam Forming (BF) iterative algorithm to maximize ESR for the user-to-UAV link. Besides, to take the advantages of Free-Space Optical (FSO) and millimeter Wave (mmWave) communications, we present a switch-based hybrid FSO/mmWave scheme and a robust BF algorithm for the UAV-to-satellite link to achieve higher rate. Moreover, a closed-form ESR expression is derived. Finally, the effectiveness and correctness of the proposed solutions are verified by numerical simulations, and the performance evaluation results show that the proposed solutions not only achieve performance enhancement and robustness, but also outperform the orthogonal multiple access significantly.     

Synchronous chirp mode extraction: A promising tool for fault diagnosis of rolling element bearings under varying speed conditions

As critical components in modern aerospace productions, rolling element bearings(REBs) generally work under varying speed conditions, which brings great challenges to their operating health monitoring. Some novel time–frequency decomposition(TFD) algorithms are established recently to extract nonlinear features from the non-stationary signals effectively, which are promising for realizing fault diagnosis of REBs under varying speed conditions. However, numerous personal experiences must be incor...     

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。     

Iterative Optimal Orthogonalization of the Strapdown Matrix

This paper treats the problem of finding an orthogonal matrix which is the closest, in the Forbenius norm, to a given nonorthogonal matrix. This nonorthogonal matrix is the result of a fast but rather inaccurate computation of the well-known direction cosine matrix (DCM) of a strapdown inertial navigation system. The known closed-form solution to this problem is rederived using the directional derivative method, and the conditions for minimum distance are derived and discussed. A new iterative technique for solving this problem is derived as a result of the application of the gradient projection technique and the directional derivative method. The practical computational problems involved in this technique are discussed. The new technique is demonstrated by three examples. Although particular attention is given to the 3 X 3 direction cosine matrix, the conclusions are nonetheless valid higher order matries.     

A Gaussian Mixture PHD Filter for Jump Markov System Models

The probability hypothesis density (PHD) filter is an attractive approach to tracking an unknown and time-varying number of targets in the presence of data association uncertainty, clutter, noise, and detection uncertainty. The PHD filter admits a closed-form solution for a linear Gaussian multi-target model. However, this model is not general enough to accommodate maneuvering targets that switch between several models. In this paper, we generalize the notion of linear jump Markov systems to the multiple target case to accommodate births, deaths, and switching dynamics. We then derive a closed-form solution to the PHD recursion for the proposed linear Gaussian jump Markov multi-target model. Based on this an efficient method for tracking multiple maneuvering targets that switch between a set of linear Gaussian models is developed. An analytic implementation of the PHD filter using statistical linear regression technique is also proposed for targets that switch between a set of nonlinear models. We demonstrate through simulations that the proposed PHD filters are effective in tracking multiple maneuvering targets.     

Tracking a Maneuvering Target Using Input Estimation

The conventional Kalman tracking filter incurs mean tracking errors in the presence of a pilot-induced target maneuver. Chan,Hu, and Plant proposed a solution to this problem which used themean deviations of the residual innovation sequence to make corrections to the Kalman filter. This algorithm is further developedhere for the case of a one-dimensional Kalman filter, for which an Implementable closed-form recursive relation exists. Simulation results show that the Chan, Hu, and Plant method can accurately detect and correct an acceleration discontinuity under a variety of maneuver models and radar parameters. Also, the inclusion of thislogic into a multiple hypothesis tracking system is briefly outlined.     

A two-step weighted least-squares method for joint estimation of source and sensor locations: A general framework

It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for joint estimation of multiple disjoint sources and sensor locations in this paper. Unlike some existing works, the presented method is based on more general measurement model, and therefore it can be applied to many different localization scenarios.Besides, it does not have the initialization and local convergence problem. The closed-form expression for the covariance matrix of the proposed TWLS estimator is also derived by exploiting the first-order perturbation analysis. Moreover, the estimation accuracy of the TWLS method is shown analytically to achieve the Cramér-Rao Bound(CRB) before the threshold effect takes place. The theoretical analysis is also performed in a common mathematical framework, rather than aiming at some specific signal metrics. Finally, two numerical experiments are performed to support the theoretical development in this paper.     

一种基于多普勒频率的恒模信号直接定位方法

相比于传统的差分多普勒(DD)两步定位方法,以Amar和Weiss提出的基于多普勒频率的单步直接定位方法在低信噪比和小样本条件下具有更高的定位精度。在该类新型定位体制的基础上,提出了一种基于多普勒频率的恒模信号直接定位方法。首先,依据最大似然(ML)准则以及恒模信号的恒包络特征,建立相应的直接定位优化模型。然后,根据目标函数的代数特征将全部未知参量分成两组,并提出一种有效的多参量交替迭代算法,用以获得该优化问题的最优数值解。新算法包含了针对这两组未知参量的Newton型迭代公式,用以避免网格搜索,并能实现多维参数的"解耦合"估计。最后,推导出针对恒模信号的目标位置直接估计方差的克拉美罗界(CRB)。数值实验验证了新方法的优越性。     

Accurate closed-form eigensolutions of three-dimensional panel flutter with arbitrary homogeneous boundary conditions

Highly accurate closed-form eigensolutions for flutter of three-dimensional (3D) panel with arbitrary combinations of simply supported (S), glide (G), clamped (C) and free (F) boundary conditions (BCs), such as cantilever panels, are achieved according to the linear thin plate theory and the first-order piston theory as well as the complex modal analysis, and all solutions are in a simple and explicit form. The iterative Separation-of-Variable (iSOV) method proposed by the present authors is employed to obtain the highly accurate eigensolutions. The flutter mechanism is studied with the benefit of eigenvalue properties from mathematical senses. The effects of boundary conditions, chord-thickness ratios, aerodynamic damping, aspect ratios and in-plane loads on flutter properties are examined. The results are compared with those of Kantorovich method and Galerkin method, and also coincide well with analytical solutions in literature, verifying the accuracy of the present closed-form results. It is revealed that, (A) the flutter characteristics are dominated by the cross section properties of panels in the direction of stream flow; (B) two types of flutter, called coupled-mode flutter and zero-frequency flutter which includes zero-frequency single-mode flutter and buckling, are observed; (C) boundary conditions and in-plane loads can affect both flutter boundary and flutter type; (D) the flutter behavior of 3D panel is similar to that of the two-dimensional (2D) panel if the aspect ratio is up to a certain value; (E) four to six modes should be used in the Galerkin method for accurate eigensolutions, and the results converge to that of Kantorovich method which uses the same mode functions in the direction perpendicular to the stream flow. The present analysis method can be used as a reference for other stability issues characterized by complex eigenvalues, and the highly closed-form solutions are useful in parameter designs and can also be taken as benchmarks for the validation of numerical methods.     

A Closed-Form Solution for Doppler Satellite Navigation

Doppler satellite navigation relies on an initial position estimate with an iterative solution. A closed-form solution of this problem, which forms the basis of a complete analytic treatment, is presented. The solution is exact for arbitrary satellite orbits with an ellipsoid Earth model.