Robust detection of small stochastic signals

We consider the problem of detecting a stochastic signal in white not-necessarily-Gaussian noise, using vector valued observations. The locally optimal detector is presented and its performance evaluated. The least-favorable signal spectrum and noise density (over specified classes) are found, and it is shown that the detector using these least-favorable assumptions is minimax robust. The class of spectra is that of any stochastic signal of specified power whose spectrum can be bounded from above and from below by two given positive functions. The class of densities is the ε-contamination model. We present examples of the performance achievable with the robust detector in one of these the spectral uncertainty class corresponds to the unknown Doppler shift of a radar return signal. It is demonstrated that the standard matched-filter's performance degradation with increasing Doppler shift can be avoided almost entirely through use of the robust processor     

Performance of a Two-Sample Mann-Whitney Nonparametric Detector in a Radar Application

The detection of signals in an unknown, typically non-Gaussian noise environment, while attempting to maintain a constant false-alarm rate, is a common problem in radar and sonar. The raw receiver data is commonly processed initially by a bank of frequency filters. The further processing of the outputs from the filter bank by a two-sample Mann-Whitney detector is considered. When the noise statistics in all filters are identical, the Mann-Whitney detector is distribution free, i. e., the false-alarm probability may be prescribed in advance regardless of the precise form of the noise statistics. The primary purpose of this paper is to demonstrate the potential advantage of nonparametric detectors over conventional detectors. The signal detection performance of the Mann-Whitney detector is compared to that of an ordinary linear envelope detector plus integrator in the presence of Gaussian and several hypothetical forms of non-Gaussian noise. This comparison is made for both uniform and nonuniform distributions of noise power across the filter bank. Besides providing a much more constant false-alarm rate than the conventional detector, the Mann-Whitney detector's signal detection performance is found also to be much less sensitive to the form of the noise statistics. In one case, its detection sensitivity is found to be 11 dB better than that of the conventional detector. Even when the noise power density is made moderately nonuniform across the filter bank, the detection performance of the Mann-Whitney detector is found not to be significantly affected.     

On detection using filter banks and higher order statistics

We suggest a method, based on the use of filter bank and higher order statistics (cumulants), for detection of transient signals. The method first uses a bandpass filter bank, which separates the spectrum of the observed signal into narrow frequency bands. Each subfilter of the filter bank is then followed by a cumulant estimator, and thereby suppressing colored noise. By selecting those subfilters that have large output energies, the filter bank can approximate the behavior of a matched filter. Moreover, no a priori information about the waveform of the signal is needed. The performance of the detector is evaluated by using a simulated signal as well as a measured signal. The presented detector is compared with the optimal matched filter detector.     

基于固有模态函数频域熵的目标检测算法

为提高海杂波中慢速目标的检测性能,提出了一种基于固有模态函数(IMF)频域熵的目标检测算法。该算法对原始信号经 EMD分解后得到的固有模态函数采用 Fourier变换,自动地提取其各个分量的频域能量,以此获得 IMF能量分布特点,再运用信息熵的方法构建检验统计量,并将其输入非参量检测器中进行目标检测。研究结果表明,相比于海杂波、海尖峰,慢速目标的能量分布更为分散,熵值更大,对比频域广义符号(GS)检测算法,所提 方法检测性能更优,适用于慢速目标检测。     

PIC检测器解析表达式的偏差修正

由于传统PIC(Parallel Interference Canceller,并行干扰消除)检测器性能分析公式存在偏差,导致与仿真结果有一定的差异,不能准确反映系统性能。在对传统PIC检测器性能表达式和推导过程存在的偏差进行分析的基础上,通过公式推导,得到更为精确的PIC检测器任一级的误码率性能解析表达式。通过数值计算,偏差修正后的解析表达式对误码率估计的准确度比修正前提高了1个数量级,与仿真结果更为接近,并且干扰消除的级数越多效果越好。研究结果表明,修正后的PIC解析表达式是有效的。     

Locally optimal and suboptimal signal detection in transformationnoise

The efficacy of the optimal detector of a known vanishingly small signal in additive nonwhite transformation noise is compared with that of some eleven structurally simpler suboptimal detectors. Simulation is done under various signal choices, marginal densities, and correlation functions. The block g_lo and the block combination g followed by R_v^-1 in the optimal detector structure are found to be important for good performance in constant and oscillating signals, respectively. Two suboptimal detectors with these block structures, D₈ and D₁₀, are found to perform well consistently in all situations considered. A structurally simple suboptimal detector D₂ is found to be good in the cases with less correlated noise     

Decision-Directed Detector for Overlapping PCM/NRZ Signals

A decision-directed (DD) technique for the detection of overlapping PCM/NRZ signals in the presence of white Gaussian noise is investigated. The performance of the DD detector is represented by probability of error PE versus input signal-to-noise ratio (SNR). To examine how much improvement in performance can beachieved with this technique, PE's with and without DD feedback are evaluated in parallel. Further, analytical results are compared with those found by Monte Carlo simulations. The results are shown in good agreement.     

Cascaded detector for multiple high-PRF pulse Doppler radars

A postdetection design methodology for a multiple high-pulse-repetition frequency (PRF) pulse Doppler radar has been developed. The postdetection processor consists of an M out of N detector where range and target ambiguities are resolved, followed by a square-law detector which enhances the minimum signal-to-noise (S/N) power-ratio per pulse burst performance. For given probabilities of false alarm and detection, formulas are derived from which the three thresholds associated with the cascaded detector can be found. Fundamental tradeoffs between the minimum S/N required, number of ghosts, and the number of operations (NOPs) that the cascaded detector must perform are identified. It is shown that the NOPs and the number of ghosts increase and the minimum S/N required decreases as the binary M out of N detector passes more detections to the square-law detector     

增减材复合制造内部缺陷的涡流检测

涡流检测（ECT）技术具有非接触、无需耦合剂、检测灵敏等特点，适用于加工环境较为特殊的增减材复合制造（ASHM）中。本文建立了无缺陷半无限大试样内部涡流分布的解析模型，开展了预制人工缺陷的钛合金增材试样检测实验，研究了ECT深度与激励频率、提离量之间的关系。理论分析与实验结果均表明，内部缺陷较深时，低激励频率条件下缺陷产生的电抗增量信号较大，不同提离量下的电抗增量信号相差不大，因此检测位置较深的内部缺陷时可采用较低的激励频率并适当提高提离量。在本文实验条件下，ECT最佳激励频率为90 kHz；提离量增加到0.97 mm时，有效检测深度略有减小。这一结论可为ECT技术与ASHM的集成提供理论依据。     

Carrier loop architectures for tracking weak GPS signals

The performance of various carrier recovery loop architectures (phase lock loop (PLL), Doppler-aided PLL, frequency lock loop (FLL), and Doppler-aided FLL) in tracking weak GPS signals are analyzed and experimentally validated. The effects of phase or frequency detector design, oscillator quality, coherent averaging time, and external Doppler aiding information on delaying loss of lock are quantified. It is shown that for PLLs the metric of total phase jitter is a reliable metric for assessing low C/N performance of the tracking loop provided the loop bandwidth is not too small (~> 5 Hz). For loop bandwidths that are not too small, total phase jitter accurately predicts carrier-to-noise ratio (C/N) at which loss of lock occurs. This predicted C/N is very close to the C/N predicted by bit error rate (BER). However, unlike BER, total phase jitter can be computed in real-time and an estimator for it is developed and experimentally validated. Total phase jitter is not a replacement for BER, since at low bandwidths it is less accurate than BER in that the receiver loses lock at a higher C/N than predicted by the estimator. Similarly, for FLLs operating at small loop bandwidths, it is found that normalized total frequency jitter is not a reliable metric for assessing loss of lock in weak signal or low C/N conditions. At small loop bandwidths, while total frequency jitter may indicate that a loop is still tracking, the Doppler estimates provided by the FLL will be biased.     

新型Σ-Δ多通道动态测试分析系统研究与实现

 动态测试与分析系统需要动态范围（DRN）大、信噪比（SNR）高,传统方法实现复杂且成本高。本文分析了Σ-Δ调制的动态特性,提出基于Σ-Δ ADC(模-数转换器)ADS1271,Σ-Δ DAC（数-模转换器）AIC23及浮点数字信号处理器（DSP）芯片TMS320C6713的新型高精度动态测试与分析系统,实现了多通道实时动态测试与分析,系统具有24位采集精度,8通道可级联基本模块,实时频率细化FFT（Zoom-FFT）、功率谱密度（PSD）等分析功能, 正弦、瞬态扫频、随机和冲击响应谱等信号源功能以及高速USB2.0数据传输功能。系统用于振动、冲击、噪声工程等测试与分析系统,可取代国外最新产品。     

Small Signal Compensation of Magnetic Fields Resulting from Aircraft Maneuvers

Tolles and Lawson identified three permanent, five induced, and eight eddy-current fields as sources of magnetic interference associated with airframe maneuvers. Small signal approximations are used here to separate the eddy-current terms and thus decouple the sixteen equations into two sets of eight equations. It was found that a singularity exists in the small signal equations for the permanent and induced terms. This causes an ambiguity amoung three of the coefficients which can be resolved mathematically by resorting to large maneuvers. Flight test data exhibit a large amount of magnetic hysteresis and the magnetic anomality detector (MAD) equipped aircraft will not remain compensated from one flight to the next. This complicates the problem of resolving the dip angle ambiguity. Furthermore, significant differences exist in the compensation terms as determined from manual pilot maneuvers and the terms when the maneuvers are performed by the automatic pilot. This has been attributed to differences in altitude stability and the frequency content of the maneuvers. It was found that both optimal frequency filtering and altitude compensation can be used to improve the figure of merit (FOM) resulting from pilot maneuvers.     

An Optimum Phase Reference Detector for Fully Modulated Phase-Shift Keyed Signals

Many modern telemetry systems which use phase-shift keying (PSK) have receivers which derive a coherent reference from the fully modulated PSK signal itself and thus conserve the energy which otherwise would be allocated to a discrete reference signal. In this paper, an optimum receiver structure for estimating a phase reference from the PSK signal itself is derived and its realization discussed. It is shown that at low signal-to-noise ratios, the optimum detector can be realized with a Costas loop. Since a Costas loop and squaring loop exhibit identical performance, it follows that either of these simple devices gives optimum performance for low-input signal-to-noise ratios.     

Waveform Design for Multistatic Radar Detection

We derive the optimal Neyman-Pearson (NP) detector and its performance, and then present a methodology for the design of the transmit signal for a multistatic radar receiver. The detector assumes a Swerling I extended target model as well as signal-dependent noise, i.e., clutter. It is shown that the NP detection performance does not immediately lead to an obvious signal design criterion so that as an alternative, a divergence criterion is proposed for signal design. A simple method for maximizing the divergence, termed the maximum marginal allocation algorithm, is presented and is guaranteed to find the global maximum. The overall approach is a generalization of previous work that determined the optimal detector and transmit signal for a monostatic radar.     

Modified Savage and Modified Rank Squared Nonparametric Detectors

A modified form of the basic Savage statistic is considered and the performance of a modified Savage (MS) nonparametric detector using this modified statistic is derived. Also, a detector using a modified rank squared statistic (MRS) is introduced. The asymptotic relative efficiency (ARE) of the detectors is determined for chisquare, Rician, and log-normal signal fluctuations when the background noise is assumed Gaussian. The ARE performance of the generalized sign (GS) and Mann-Whitney (MW) detectors is also determined for these families of fluctuations. The ARE performance of the various detectors is then compared, and the results of a computer simulation are presented in which, for a finite number of samples, the performance of the modified detectors is compared with the performance of the GS and MW detectors. It is shown that when using a large number of reference noise samples, the ARE of the GS and MW detectors, the MRS and RS detectors, and the MS and Savage detectors are 0.75, 0.868, and 1, respectively. It is also shown that when using a finite number of reference noise samples the MS and MRS detectors can give a superior performance to that obtained with the MW detector, and that this is particularly true in the cases in which the degree of signal fluctuation is high.     

Spatial Correlation of Reverberation Noise in Active Sonar

A linear array of hydrophones is considered for detecting a signal echo from a stationary target in the presence of reverberation. The structure of the optimum (likelihood ratio) detector is compared with that of a beamformer-matched filter detector. The conditions causing an increase in the spatial noise correlation between two hydrophones are the conditions under which the optimum spatial detector performs significantly better than the beamforming detector. A study of the space-time correlation function of reverberation shows that 1) a decrease in scatterer angular spread (or a narrowing of the receiver directivity pattern) tends to increase the spatial correlation, 2) if the scatterer Doppler spread is much less than the signal carrier frequency and if the angular spread is uniform, it is still possible to get a high correlation if the intersensor distance is much smaller than the carrier wavelength. These conditions indicate situations where optimum techniques may be worthwhile.     

Weak Signal Detection in Non-Gaussian Noise of Unknown Level

An adaptive threshold detector to test for the presence of a weak signal in additive non-Gaussian noise of unknown level is discussed. The detector consists of a locally optimum detector, a noise level estimator, and a decision device. The detection threshold is made adaptive according to the information provided by the noise level estimator in order to keep a fixed false-alarm probability. Asymptotic performance characteristics are obtained indicating relationships among the basic system parameters such as the reference noise sample size and the underlying noise statistics. It is shown that, as the reference noise sample size is made sufficiently large, the adaptive threshold detector attains the performance of a corresponding locally optimum detector for detecting the weak signal were the noise level known.     

Nonparametric Radar Extraction Using a Generalized Sign Test

A nonparametric procedure used in a constant false alarm rate (CFAR) radar extractor for detecting targets in a background of noise with unknown statistical properties is described. The detector is based on a generalization of the well-known two-sample sign test and thus requires a set of reference noise observations in addition to the set of observations being tested for signal presence. The detection performance against Gaussian noise is determined for a finite number of observations and asymptotically, for both nonfluctuating and pulse-to-pulse Rayleigh fluctuating target statistics. It is noted that the performance loss, as compared to the optimum parametric detector, depends critically on the number of reference noise observations available when the number of hits per target is not large. In the same case a much larger loss is also found for a pulse-to-pulse fluctuating target even though the asymptotic loss is the same as for a nonfluctuating target. A comparison is finally made with a detector based on the Mann-Whitney test, which usually is considered to be one of the better nonparametric procedures for the two-sample case.     

Frequency domain approach to guidance system design

The frequency domain approach to guidance system design is presented. The model of the guidance control system reflects the most important characteristics of the flight control system that combines airframe and autopilot dynamics (damping, natural frequency, time constant, and airframe zero frequency). The analytical expressions for frequency response and related expressions for missile system performance are given. The analytical results obtained can be utilized for missile system design.