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.     

406 MHz ELT signal spectra for SARSAT

The signal format and spectral properties of the 406-MHz emergency locator transmitter (ELT) used in the search and rescue satellite aided tracking (SARSAT) system are examined. The ELT improves location estimate accuracies and can relay information about the particular aircraft and its problem, by means of the digitally modulated message fields. It is shown that due to the RF signal frequency characteristics and the Doppler shift, processing must be performed over a frequency band of approximately 25 kHz. Through the use of the fast Fourier transformation (FFT), the frequency spectrum of the ELT is analyzed, taking account of effects due to noise, multiple simultaneously received signals, and Doppler shift. It is demonstrated that the FFT provides an effective means for detecting and recognizing the presence of one or more ELT signals over this 25-kHz frequency band. Some recommendations are made to improve the spectral characteristics and the performance of the ELT     

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.     

Simple Expressions for Determining Radar Detection Thresholds

The threshold value required to obtain a specified false-alarm probability, when postdetection integration follows a square-law or an envelope detector, is frequently needed in theoretical and practical studies of radar signal processor performance. The determination of such threshold values requires a substantial numerical computational effort. In this correspondence, simple expressions are presented with which these thresholds can be determined with excellent accuracy using only a scientific calculator.     

非参量量化秩检测器的性能研究

 许多作者讨论过非参量秩检测器在雷达信号处理中的应用。秩检测器首先把接收波形样本转换为秩。如果检验单元和参考单元的噪声样本独立和分布,则无信号时检验单元的秩具有离散均匀分布,与输入噪声的分布无关。所以秩检测器可能提供分布自由的恒虚警率性能。量化秩检测器（QRD）只对二进量化秩进行积累,所以它实现起来很经济。本文分析QRD的检测性能。证明QRD有一最佳秩量化门限（ORQT）。确定高斯和韦伯噪声中的ORQT。另外,把QRD同高斯噪声中的局部最佳秩检测器和最佳参量检测器进行比较。     

一种低复杂度的极低信噪比高动态信号载波粗捕获算法

 针对传统的时域匹配平均周期图算法计算复杂度高的问题,对极低信噪比高动态信号的载波粗捕获算法进行了研究,提出了一种改进的带有补零的频域移位平均周期图算法。该算法采用多速率频域移位运算简化了多支路多普勒变化率匹配,与原算法相比,其计算复杂度降低倍数为匹配支路数与补零倍数之比,捕获性能几乎不损失。给出了算法中影响捕获性能与计算复杂度的关键参数设计方法。在信噪比(SNR)为－41 dB(载噪比C/N₀=18 dBHz)、载波多普勒频偏为－300～300 kHz、多普勒变化率为－800～800 Hz/s、码速率为20 bps条件下对两种算法进行了仿真,结果表明在基本满足后级载波跟踪需求条件下,即频偏精度均达±12 Hz时,多普勒变化率精度均达±25 Hz/s,捕获概率都在90%以上时,改进算法捕获时间比原算法增加了8%,计算复杂度降低了70%。     

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.     

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.     

Mismatched Filtering of Sonar Signals

A replica correlator (matched filter) is an optimum processor for a receiver employing a pulse of continuous wave (CW) signal in a white Gaussian noise background. In an active sonar, however, when the target of interest has low Doppler shift and is embedded in a high reverberation background, this is not so. High sidelobes of the correlator frequency response pass a significant portion of the signal contained in the mainlobe of the reverberation spectrum. In order to reduce the sidelobes of the correlator output spectrum and at the same time keep the increase in its 3 dB bandwidth to a small amount, we propose lengthening of the replica of the transmitted signal and weighting it by a Kaiser window. It is demonstrated that by extending the weighted replica by 50 percent compared with the transmitted signal, it is possible to reduce the sidelobe levels to at least 40 dB below the mainlobe peak, with the concomitant increase of the 3 dB band-width by less than 5 percent. The degradation in signal-to-noise ratio (SNR) performance for such a ?mismatched? filter receiver with respect to the matched filter is less than 1.5 dB.     

Phase Analysis in Multiple-Sensor Receivers with High Signal-to-Noise Ratio

The ideal phase detector characteristic is analyzed for estimating the phase difference between two stochastic input signals. This can essentially be described as a correlation process formed by multiplying the two input signals and extracting the phase. High signal-to-noise ratio conditions are assumed to linearize the system with respect to the noise. The effects of the nonlinearity on the signal are handled in terms of a series expansion and by using low-pass filtering on the receiver output. The mean square error of the system is calculated for some typical parameters.     

Hough transform for long chirp detection

The online detection of a very long and weak chirp signal is studied. The signal has an extremely slowly decreasing frequency, and is corrupted by white Gaussian noise and possibly also by powerful tones. By exploring and comparing candidate methods, it is found that the Hough transform (HT) detector appears to be most suitable given constraints on computational load and detectability. The analytical and the simulational performance of the HT detector are obtained and compared with the analytical performance of the generalized likelihood ratio test (GLRT), which is assumed to be optimal. Applying a suitable threshold for the HT can increase speed dramatically while preserving performance. We have found that both dithering (taking varied frequency shifts for fast Fourier transforms (FFTs)) and increasing the FFT length can reduce the minimum detectable frequency slope with nearly no additional computation     

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.     

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     

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.     

一种提高脉冲雷达多普勒相位精度的方法

针对低信噪比条件下脉冲雷达模糊多普勒相位精度较低,可能导致相位测距时不能正确解相位模糊问题,基于EMD（Empirical Mode Decomposition,经验模式分解）区间阈值去噪方法,提出了一种新的提高多普勒相位精度的方法：利用EMD分解后各层信号的频率特性和能量特性,选取合适的阈值,并对各层信号进行区间阈值化处理,在提高信号信噪比的同时保持了信号的连续性.分别在回波信号噪声为高斯白噪声和AR（2）相关噪声的情况下,以及不同信噪比条件下,对该方法进行验证.仿真结果表明：在低信噪比条件下,当回波信号噪声为白噪声和相关噪声时,EMD区间阈值去噪方法能将回波信号信噪比提高5 dB,去噪性能优于小波阈值去噪方法,其对应多普勒相位精度能提高1倍以上.     

Performance of pulse-pair method of Doppler estimation

Because of its simplicity, the pulse-pair method is usually used in the estimation of Doppler from backscattered acoustic signals. In the literature, various improvements to the basic pulse-pair estimate have been proposed. The statistics of these improved methods have also been derived using simplified assumptions for the signal and noise. By developing a multiplicative noise model for the backscatter signal, in this work, the variance of the Doppler estimate is derived under all signal scenarios. The dependency of the variance on the amplitude correlation length of the data is also discussed. It is demonstrated that the use of parabolic window in the estimate is the proper method of Doppler evaluation under all conditions     

Evaluating the Detectability of Gaussian Stochastic Signals by Steepest Descent Integration

It is shown how to compute the detection probability of certain signals by numerical integration of the Laplace inversion integral involving the characteristic function or the moment-generating function of the detection statistic. The contour of integration is taken as the path of steepest descent of the integrand and is determined numerically as the integration proceeds. The method is applied to calculating the performance of the optimum detector of a Gaussian stochastic signal in white noise when the signals actually present have a different average s.n.r. from that assumed in the design. Results are presented for narrowband signals with Lorentz and rectangular spectral densities. The detectability of the former is shown to be more sensitive than that of the latter to the value of the design s.n.r. The relative disadvantage of the threshold detector, also assessed by this method, is smaller for signals with a rectangular than for those with a Lorentz spectral density.     

基于铱星/INS组合定位技术在船舶中的应用研究

GNSS拒止环境下惯性/GNSS组合导航系统的性能会严重恶化,通过利用并提取机会信号中的有用观测量,可以实现机会信号和惯性系统的联合动态定位。提出了利用铱星/INS组合定位技术实现船舶的动态定位。首先深入研究了铱星的信号体制,建立了利用铱星瞬时多普勒频移进行定位的算法模型;然后,提出了利用基于扩展卡尔曼滤波(EKF)技术的铱星机会信号与INS组合定位算法;最后,通过船舶航行实测数据对所提算法进行了试验验证。结果表明,提出的利用铱星机会信号和INS组合定位方法可以有效改善无GNSS信号条件下的INS定位精度,在GNSS信号拒止环境下解决了船舶定位问题,具有重要的研究意义和实用价值。     

Optimum array detector for a weak signal in unknown noise

We study the design of constant false-alarm rate (CFAR) tests for detecting a rank-one signal in the presence of background Gaussian noise with unknown spatial covariance. We look at invariant tests, i.e., those tests whose performance is independent of the nuisance parameters, like the background noise covariance. Such tests are shown to have the desirable CFAR property. We characterize the class of all such tests by showing that any invariant decision statistic can be written as a function of two basic statistics which are in fact the adaptive matched filter (AMF) statistic and Kelly's generalized likelihood ratio statistic. Further, we establish an optimum test in the limit of low signal-to-noise ratio (SNR), the locally most powerful invariant (LMPI) test. We also derive the bound for the probability of detection of any invariant detector, at a fixed false-alarm rate, and compare the LMPI and the published detectors (Kelly and AMF) to it     

On the Mean Frequency Measurement System Using Correlation Detection

This paper is concerned with the problem of measuring the mean frequency of the power spectrum of a zero-mean, stationary, narrowband Gaussian random signal in the presence of additive Gaussian noise. Signal-to-noise ratios at the output of the mean frequency measurement system using correlation detection are analyzed in terms of input signal-to-noise ratio, input signal and noise bandwidths, and integration time. The results obtained are verified experimentally, and a comparison with a conventional zero-crossing detector is also made.