Low observable target motion analysis using amplitude information

In conventional passive and active sonar system, target amplitude information (AI) at the output of the signal processor is used only to declare detections and provide measurements. We show that the AI can be used in passive sonar system, with or without frequency measurements, in the estimation process itself to enhance the performance in the presence of clutter where the target-originated measurements cannot be identified with certainty, i.e., for “low observable” or “dim” (low signal-to-noise ratio (SNR)) targets. A probabilistic data association (PDA) based maximum likelihood (ML) estimator for target motion analysis (TMA) that uses amplitude information is derived. A track formation algorithm and the Cramer-Rao lower bound (CRLB) in the presence of false measurements, which is met by the estimator even under low SNR conditions, are also given. The CRLB is met by the proposed estimator even at 6 dB in a cell (which corresponds to 0 dB for 1 Hz bandwidth in the case of a 0.25 Hz frequency cell) whereas the estimator without AI works only down to 9 dB. Results demonstrate improved accuracy and superior global convergence when compared with the estimator without AI. The same methodology can be used for bistatic radar     

基于左矩阵分式模型的模态参数识别方法

提出一种多输入多输出(MIMO)系统的宽频模态参数识别算法。该方法基于频响函数(FRF)的左矩阵分式模型(LMFD),通过最小二乘法在z域内求解模态参数,避免了s域内矩阵的病态问题。针对左矩阵分式模型的特点,给出了一种通过主分量分析(PCA)建立稳定图的方法。指出了传统的频域多参考点(PRFD)方法与基于左矩阵分式模型识别方法之间的关系。最后采用GARTEUR模型仿真算例与飞机模型的实测算例对所提出的方法进行了验证,结果表明该方法具有良好的识别效果。     

一种频域插值变化迭代频率估计方法

针对现有频率估计算法存在的复杂度高、频率估计能力弱、估计结果均方差大等缺点,在固定迭代AM（Aboutanios—Mulgrew）无偏频率估计算法基础上,提出一种频域插值变化迭代频率估计算法,推导了不同迭代参数实现无偏估计的充分条件,证明了有偏估计时本算法的收敛性和偏离度,通过设置不同迭代参数,可以实现无偏或有偏估计。仿真分析表明：当具有较高信噪比时,在整个频率估计范围内,该方法均方误差接近CRLB（Cramer-RaoLowerBound,克拉美一罗下限）;当FFT（FastFourierTransform,快速傅里叶变换）粗估计残余频率接近0．5时,该方法的均方误差优于CRLB,为CRLB的96％。     

Modified fast Fourier transform in FBMC for satellite communications

In this paper,a Doppler scaling fast Fourier transform (Doppler-FFT) algorithm for filter bank multi-carrier (FBMC) is proposed,which can efficiently eliminate the impact of the Doppler scaling in satellite communications.By introducing a Doppler scaling factor into the butterfly structure of the fast Fourier transform (FFT) algorithm,the proposed algorithm eliminates the differences between the Doppler shifts of the received subcarriers,and maintains the same order of computational complexity compared to that of the traditional FFT.In the process of using the new method,the Doppler scaling should be estimated by calculating the orbital data in advance.Thus,the inter-symbol interference (ISI) and the inter-carrier interference (ICI) can be completely eliminated,and the signal to interference and noise ratio (SINR) will not be affected.Simulation results also show that the proposed algorithm can achieve a 0.4 dB performance gain compared to the frequency domain equalization (FDE) algorithm in satellite communications.     

Comparison of various periodograms for sinusoid detection andfrequency estimation

With the advent of the fast Fourier transform (FFT) algorithm, the periodogram and its variants such as the Bartlett's procedure and Welch method, have become very popular for spectral analysis. However, there has not been a thorough comparison of the detection and estimation performances of these methods. Different forms of the periodogram are studied here for single real tone detection and frequency estimation in the presence of white Gaussian noise. The threshold effect in frequency estimation, that is, when the estimation errors become several orders of magnitude greater than the Cramer-Rao lower bound (CRLB), is also investigated. It is shown that the standard periodogram gives the optimum detection performance for a pure tone while the Welch method is the best detector when there is phase instability in the sinusoid. As expected, since the conventional periodogram is a maximum likelihood estimator of frequency, it generally provides the minimum mean square frequency estimation errors     

A novel multistage estimation of signal parameters

A multistage estimation scheme is presented for estimating the parameters of a received carrier signal possibly phase-modulated by unknown data and experiencing very high Doppler, Doppler rate, etc. Such a situation arises, for example, in the case of the Global Positioning Systems (GPS). In the proposed scheme, the first-stage estimator operates as a coarse estimator of the frequency and its derivatives, resulting in higher RMS estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency (an event termed cycle slip). The second stage of the estimator operates on the error signal available from the first stage, refining the overall estimates, and in the process also reduces the number of cycle slips. The first-stage algorithm is a modified least-squares algorithm operating on the differential signal model and referred to as differential least squares (DLS). The second-stage algorithm is an extended Kalman filter, which yields the estimate of the phase as well as refining the frequency estimate. A major advantage of the proposed algorithm is a reduction in the threshold for the received carrier power-to-noise power spectral density ratio (CNR) as compared with the threshold achievable by either of the algorithms alone     

Radar power multiplier for acquisition of low observables using anESA radar

In this paper the acquisition of a low observable (LO) incoming tactical ballistic missile using the measurements from a surface based electronically scanned array (ESA) radar is presented. We present a batch maximum likelihood (ML) estimator to acquire the missile while it is exo-atmospheric. The proposed estimator, which combines ML estimation with the probabilistic data association (PDA) approach resulting in the ML-PDA algorithm to handle false alarms, also uses target features. The use of features facilitates target acquisition under low signal-to-noise ratio (SNR) conditions. Typically, ESA radars operate at 13-20 dB, whereas the new estimator is shown to be effective even at 4 dB SNR (in a resolution cell, at the end of the signal processing chain) for a Swerling III fluctuating target, which represents a significant counter-stealth capability. That is, this algorithm acts as an effective “power multiplier” for the radar by about an order of magnitude. An approximate Cramer-Rao lower bound (CRLB), quantifying the attainable estimation accuracies and shown to be met by the proposed estimator, is derived as well     

Passive ranging of a low observable ballistic missile in agravitational field

In this paper we present an estimation algorithm for tracking the motion of a low-observable target in a gravitational field, for example, an incoming ballistic missile (BM), using angle-only measurements. The measurements, which are obtained from a single stationary sensor, are available only for a short time. Also, the low target detection probability and high false alarm density present a difficult low-observable environment. The algorithm uses the probabilistic data association (PDA) algorithm in conjunction with maximum likelihood (ML) estimation to handle the false alarms and the less-than-unity target detection probability. The Cramer-Rao lower bound (CRLB) in clutter, which quantifies the best achievable estimator accuracy for this problem in the presence of false alarms and nonunity detection probability, is also presented. The proposed estimator is shown to be efficient, that is, it meets the CRLB, even for low-observable fluctuating targets with 6 dB average signal-to-noise ratio (SNR). For a BM in free flight with 0.6 single-scan detection probability, one can achieve a track detection probability of 0.99 with a negligible probability of false track acceptance     

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     

GPS软件接收机的捕获与跟踪算法

研究了GPS软件接收机的捕获与跟踪算法。分析了时域串行滑动相关捕获算法和频域基于FFT的并行相关捕获算法,设计了适合GPS软件接收机的并行算法,实现了对空中可见卫星的捕获。针对GPS信号的特点,设计了基于DLL与PLL相结合方法的GPS跟踪算法。利用实测中频信号对上述捕获与跟踪算法进行了验证分析,测试结果表明,基于FFT的并行相关捕获算法能够有效增强软件接收机的捕获能力,采用DLL与PLL相结合的方法能够实现对GPS信号的有效跟踪。     

基于自适应陷波滤波器的伺服系统谐振频率估计及抑制

在使用陷波滤波器抑制伺服系统机械谐振时,需要获取准确的机械谐振频率。为了快速检测出谐振频率,提出了一种基于自适应陷波滤波器(ANF)的机械谐振频率估计算法,通过速度误差信号分析,实现谐振频率在线快速辨识。首先,建立柔性连接伺服系统模型;然后,对ANF频率估计算法进行分析,并且与常用的快速傅里叶变换(FFT)频率检测算法的分析精度和计算速度进行对比。数值比较和仿真验证表明,ANF频率估计算法可以更快地实现谐振频率的精确检测。最后搭建试验平台,以ANF频率估计的结果作为陷波器的中心频率,成功实现了电机转速振荡的抑制,验证了该方法的有效性。     

A Linear-correction Least-squares Approach for Geolocation Using FDOA Measurements Only

  A linear-correction least-squares(LCLS) estimation procedure is proposed for geolocation using frequency difference of arrival (FDOA) measurements only. We first analyze the measurements of FDOA, and further derive the Cram閞-Rao lower bound (CRLB) of geolocation using FDOA measurements. For the localization model is a nonlinear least squares(LS) estimator with a nonlinear constrained, a linearizing method is used to convert the model to a linear least squares estimator with a nonlinear constrained. The Gauss-Newton iteration method is developed to conquer the source localization problem. From the analysis of solving Lagrange multiplier, the algorithm is a generalization of linear-correction least squares estimation procedure under the condition of geolocation using FDOA measurements only. The algorithm is compared with common least squares estimation. Comparisons of their estimation accuracy and the CRLB are made, and the proposed method attains the CRLB. Simulation results are included to corroborate the theoretical development.     

Constrained bandwidth waveforms with minimal dilation sensitivity

Bandpass waveforms which have envelopes which are insensitive to this velocity-induced time dilation can be efficiently processed by narrowband receivers in which envelope correlation is fixed and Doppler tested using fast Fourier transform (FFT) processing. The peak level of the waveform ambiguity function (AF) can be used to gauge the distortion of the waveform induced by dilation. The degree of AF attenuation is shown to be proportional to the dilation parameter or velocity, waveform traveling wave (TW) product, and a sensitivity parameter which depends on the envelope function utilized. Classes of symmetric, constrained bandwidth, phase modulated envelope functions which are minimally dilation sensitive (Doppler tolerant) are derived. When the resulting waveforms are used with a simple correlation receiver structure and the echo data is derived from slowly fluctuating point scattering in white Gaussian noise, the receiver becomes an uncoupled joint estimator of delay and dilation (Doppler). In the case of the bandpass waveforms, only odd symmetry of the phase modulation (PM) yields an uncoupled estimator     

An efficient SAR parallel processor

A parallel architecture especially designed for a synthetic-aperture-radar (SAR) processing algorithm based on an appropriate two-dimensional fast Fourier transform (FFT) code is presented. The algorithm is briefly summarized, and the FFT code is given for the one-dimensional case, although all results can be immediately generalized to the double FFT. The computer architecture, which consists of a toroidal net with transputers on each node, is described. Parametric expressions for the computational time of the net versus the number of nodes are derived. The architecture allows drastic reduction of the processing time, preserving elaboration accuracy and flexibility     

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     

基于旋转滤波矩阵束的异步电机转子断条故障诊断

现有异步电机故障诊断技术存在短时数据分辨率低、硬件开销大等缺点。针对这一问题,提出一种基于短时数据的旋转滤波矩阵束的异步电机转子断条故障诊断新方法。利用矩阵束算法抗噪性能强的优点,准确求出定子电流基频成分,并通过逆、正同步旋转变换,剔除了定子电流中的基频成分。利用矩阵束算法准确估算定子电流故障信号的频率和幅值,突破传统基于快速傅里叶变换(FFT)分析算法分辨率不足的限制。仿真和电机试验共同表明:旋转滤波矩阵束算法可以在短时数据的基础上准确辨识转子断条故障。     

具有（N-1）/2次乘法的快速傅里叶变换

 本文提出递归傅里叶变换的一种快速实现方法。对于一个质数长度的离散傅里叶变换,仅需用一个复数系数就可以递归算出全部N个（N=P）频率分量。恰当地选用这个系数,使其为2^-m形式,就可以用（m-1）次移位代替乘法,免去了递归结构内部的乘法,大大提高运算速度。这种方法结构简单,总共需用（N-1）/2次实数常数乘法,尤其适于硬件实现。文中给出快速运算的系数表、硬件实现的方案及乘法次数的比较,讨论了系数误差的影响,并提出了高精度实现的方案。     

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.     

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.     

运行模态分析的频域空间域分解法及其应用

提出了一种基于频域空间域分解(Frequency and Spatial Domain Decomposition, FSDD)的运行模态分析方法。该法将同时具有输入和输出的试验模态分析的经典方法——复模态指示因子(Complex Mode Indicator Function, CMIF)法拓展到了仅有输出响应的运行状态模态分析。FSDD法采用奇异值分解将信号空间和噪声空间分离开来,把奇异值曲线作为模态指示的依据,以奇异值向量作为加权函数得到每一阶模态的增强功率谱(Power Spectrum Density, PSD),进而在频域内对增强PSD曲线进行最小二乘拟合以得到准确的模态频率和阻尼参数。采用了一个二层楼仿真算例和在欧洲广为人知的瑞士Z24公路大桥实测算例来验证FSDD算法。