Detection of Known Signals in Nonstationary Noise

The basic design of a nonlinear, time-invariant filter is postulated for detecting signal pulses of known shape imbedded in nonstationary noise. The noise is a sample function of a Gaussian random process whose statistics are approximately constant during the length of a signal pulse. The parameters of the filter are optimized to maximize the output signal-to-noise ratio (SNR). The resulting nonlinear filter has the interesting property of approximating the performance of an adaptive filter in that it weights each frequency band of each input pulse by a factor that depends on the instantaneous noise power spectrum present at that time. The SNR at the output of the nonlinear filter is compared to that at the output of a matched filter. The relative performance of the nonlinear system is good when the signal pulses have large time-bandwidth products and the instantaneous noise power spectrum is colored in the signal pass band.     

A Nonadaptive Processing of Radar Pulse Trains for Clutter Rejection

The problem of detecting coherent pulse trains with uniform amplitude in a clutter-plus-noise environment is considered. A radar processor for detecting targets moving radially with respect to the clutter is proposed. The minimum interpulse spacing of the transmitted signal is assumed long enough that returns are not received simultaneously from different ranges within a region of extended clutter, and the central frequency of the clutter power spectrum is postulated to be known. The processor is singled out as the linear filter, orthogonal to the clutter central frequency component, which yields the maximum ratio of peak signal power to average noise power. The filter can be implemented by slightly modifying the structure of the conventional matched filter. The performance of such a filter is compared with that achievable if full a priori knowledge of the input interference were available and with that of the conventional matched filter. This comparison is made on a signal-to-interference power ratio basis after assuming a transmitted signal consisting of equally spaced pulses and an interference characterized by an exponential covariance matrix.     

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.     

Probability Densities and Characteristic Functions for Fluctuating Targets

Probability density functions and characteristic functions for the projected area of a tumbling target object are derived together with the densities and characteristic functions for the corresponding signal-plus-noise voltage output of an infrared sensor. Several cases are considered in which the signal pulse arrival time is either known or unknown, a matched filter or a suboptimum filter is used; the signal pulse shape is either Gaussian or is unspecified; and the target orientation angles are either uniformly or nonuniformly distributed.     

Comments on "Optimum Bandwidth of a Low-Pass Filter for Detection of a Pulse in Nonstationary Noise"

In a recent correspondence1 a calculation of the optimum bandwidth of a low-pass RC filter for the detection of a pulse signal in nonstationary noise was presented. The purpose of this correspondence is: 1) to point out additional references to the work which has been conducted in the stationary noise case, and 2) to present an interesting alternate derivation of the expected output noise power for the nonstationary noise case.     

Signal Resolution via Digital Inverse Filtering

Research in numerous areas is directed toward the resolution of multiple overlapping signals in a noisy environment. These areas include radar, sonar, speech, seismology, and electrophysiology. Sometimes matched filters are used; other times inverse filters are employed. This paper discusses one approach to the analysis of the resolution of inverse filters. Our method is to compromise the trade-off between signal resolution and the output signal-to-noise ratio (SNR). A performance measure for the inverse or deconvolution filter is defined as a quantity proportional to the harmonic mean of the resolution and the SNR. An optimum output pulse duration is obtained using this criterion, where the pulse shape has been previously selected and the input signal waveform is known. In addition, upper and lower bounds for the output pulse duration are presented. Graphs are given which allow the designer to select the optimum inverse filter output pulse duration for a desired signal resolution and an estimated SNR.     

Matched-Filter Response to a Linear FM Signal Transmitted Through a Phased Array

The response of a linear phased array with a matched filter connected at its output is investigated when a linear FM signal is incident on the array at an arbitrary angle. The filter is assumed to be matched to the linear FM signal. The dispersion produced by the array results in a mismatch at the receiver which depends on the scan angle and on the type of feed system used with the array. The distortion of the compressed pulse is studied for the series end-fed arrays, the series     

Multistatic adaptive pulse compression

A new technique denoted as multistatic adaptive pulse compression (MAPC) is introduced which exploits recent work on adaptive pulse compression (APC) in order to jointly separate and pulse compress the concurrently received return signals from K proximate multistatic radars operating (i.e., transmitting) within the same spectrum. For the return signal from a single pulse of a monostatic radar, APC estimates the particular receive filter for a given range cell in a Bayesian sense reiteratively by employing the matched filter estimates of the surrounding range cell values as a priori knowledge in order to place temporal (i.e., range) nulls at the relative ranges occupied by large targets and thereby suppress range sidelobes to the level of the noise. The MAPC approach generalizes the APC concept by jointly estimating the particular receive filter for each range cell associated with each of several concurrently-received radar return signals occupying the same spectrum. As such, MAPC is found to enable shared-spectrum multistatic operation and is shown to yield substantial performance improvement in the presence of multiple spectrum-sharing radars as compared with both standard matched filters and standard least-squares mismatched filters     

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.     

Energy Detection of a Random Process in Colored Gaussian Noise

A likelihood receiver for a Gaussian random signal process in colored Gaussian noise is realized with a quadratic form of a finite-duration sample of the input process. Such a receiver may be called a "filtered energy detector." The output statistic is compared with a threshold and if the threshold is exceeded, a signal is said to be present. False alarm and detection probabilities may be estimated if tabulated distributions can be fitted to the actual distributions of the test statistic which are unknown. Gamma distributions were fitted to the conditional probability densities of the output statistic by equating means and variances, formulas for which are derived assuming a large observation interval. A numerical example is given for the case in which the noise and signal processes have spectral densities of the same shape or are flat. The optimum filter turns out to be a band-limited noise whitener. The factors governing false alarm and detection probabilities are the filter bandwidth, the sample duration, and the signal level compared to the noise. Two sets of receiver operating characteristic curves are presented to complete the example.     

Adaptive pulse compression via MMSE estimation

Radar pulse compression involves the extraction of an estimate of the range profile illuminated by a radar in the presence of noise. A problem inherent to pulse compression is the masking of small targets by large nearby targets due to the range sidelobes that result from standard matched filtering. This paper presents a new approach based upon a minimum mean-square error (MMSE) formulation in which the pulse compression filter for each individual range cell is adaptively estimated from the received signal in order to mitigate the masking interference resulting from matched filtering in the vicinity of large targets. The proposed method is compared with the standard matched filter and least-squares (LS) estimation and is shown to be superior over a variety of stressing scenarios.     

Optimum Constrained Image Restoration Filters

An optimum image restoration filter is described which minimizes the radius of gyration of the corrected or composite system point-spread function subject to constraints on the radius of gyration of the restoration fitter point-spread function, the total noise power in the restored image, and the shape of the composite system frequency spectrum. The filter function is obtained as the solution to a set of simultaneous differential equations subject to nonlinear integral constraints. Except for an assumption regarding the general shape of noise spectral density, the filter design is data independent. By constraining the radius of gyration of the restoration filter point-spread function, truncation errors resulting from edge effects are controlled. An iterative technique is introduced which virtually eliminates the sidelobes of the composite system point-spread function. The resulting suboptimal restoration filter effectively suppresses undesirable secondary oscillations which may otherwise appear in the composite system point-spread function and introduce "ghosts" in the restored data. A detailed study of the restoration filter performance as a function of its parameter variations is described and a number of examples are provided to demonstrate the fundamental properties of the restoration filter.     

扰动基座下惯组信号消噪方法对比研究

针对捷联惯导系统在扰动基座下对准时,惯组信号中存在干扰角运动和线运动的特点,进行了车载扰动基座初始对准试验,对试验数据进行频谱分析,得到车载扰动基座环境的频域特性。根据分析结果,设计并实现了FIR数字滤波器滤波和小波滤波对惯组信号的消噪,频谱分析和惯性系粗对准的结果显示,这两种方法都能有效地消除惯组信号中的噪声。数据分析显示,小波滤波的效果要优于FIR数字滤波器滤波的效果。     

A noncoherent adaptive detection technique

An adaptive detection technique suitable for both stationary and nonstationary noise environments based upon a generalized likelihood ratio test (GLRT) formulation is presented. The detector, which is statistically equivalent to a special form of the Wilks's lambda test, noncoherently combines the information contained in a pulse train of arbitrary length for decision-making purposes. The probability density function of the test under the noise only hypothesis is shown to be central χ². Under the signal plus noise hypothesis, an exact statistical characterization of the test cannot be obtained, and, therefore, a Chernoff bound is derived. Results in terms of the probability of detection versus signal-to-noise ratio (SNR) obtained from Monte Carlo simulation, the Chernoff bound, and the optimal matched filter case are examined. The performance of the noncoherent detector is shown to be a function of the covariance matrix estimate and the number of data samples     

自适应的光纤布拉格光栅图像寻峰算法

根据实际光谱特征, 提出了自适应的光纤布拉格光栅图像寻峰算法。针对 不同环境物理场及噪声分布下的光栅谱型,该算法能自动检测光谱的带宽和信噪比,自 适应地调整算法的高斯模板带宽大小,提高谱型匹配及滤波效果,从而提高寻峰精度。 将该算法与高斯拟合法、质心法进行对比,分析了其在不同噪声大小及非均匀温度场分 布下光纤布拉格光栅反射光谱的寻峰精度。理论仿真及实际寻峰结果表明,该寻峰算法 具有较强的抗噪能力及谱型适应性,较质心法、高斯拟合法具有显著优势。     

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.     

Spectral Moment Estimates from Correlated Pulse Pairs

Estimates statistics of the first two power spectrum moments from the pulse pair covariance are analyzed. The input signal is assumed to be colored Gaussian and the noise, white Gaussian. Perturbation formulas for the standard deviation of both mean frequency and spectrum width are applied to a Gaussian shaped power spectrum, and so is a perturbation formula for the bias in the width estimate. Mean frequency estimation from interlaced pulse pairs is presented. Throughout this study, estimators from independent, spaced, and contiguous pulse pairs are compared to provide a continuum of statistics from equispaced tightly correlated to statistically independent pulse pairs.     

Signal-to-Noise Ratio Calculations in Pulse and Pulse Doppler Radars

In low pulse-repetition frequency (PRF) pulse radars, signal-to-noise ratio (SNR) is usually calculated on a per pulse basis and this value is then multiplied by the number of pulses integrated to obtain the SNR for a given duration of target illumination. In high PRF pulse Doppler radars, SNR is usually calculated by using the centerline power of the transmitted signal spectrum as the target return power because the centerline is kept in the receiver and returns of the PRF lines are notched out [1]. We show here that both methods of SNR calculations are entirely equivalent for matched transmit-receive radar systems.     

灵巧噪声干扰本质含义探讨

文章对灵巧噪声干扰概念的表述提出了质疑,在多项质疑中选取了SLB技术进行简要分析,并指出,SLC等抗干扰技术的作用与是否实施灵巧噪声干扰没有直接关系。进一步,基于匹配滤波器理论对灵工j噪声干扰的本质含义进行了分析,指出：灵巧噪声干扰的本质含义是使干扰由多个分量组成,并且使干扰中的每一个分量的频谱都与雷达发射信号的频谱相...     

Operational modal parameter identification with colored noise excitation

Operational Modal Analysis (OMA) refers to the modal analysis of a structure in its operating state. The advantage of OMA is that only the output vibration signal of a system is used in the analysis process. Classic OMA is based on the white noise excitation assumption and many identification methods have been developed in both time domain and frequency domain. But in reality, many environmental excitations are not compliance with the white noise assumption. In this paper, a method of half power bandwidth analysis is applied to power spectrum analysis to deal with the colored noise and trapezoidal spectral excitation. The modal frequencies and modal damping ratios are derived and the error caused by trapezoidal spectral and colored noise excitation are analyzed. It is proved that the OMA algorithm based on the white noise assumption can be extended to the colored noise environments under certain conditions. Finally, a simulation example with a cantilever beam and a vibration test with four kinds of colored noise and trapezoidal spectrum base excitation are carried out and the results support the proposed method.