A selection and estimation test for multiple target detection

The authors apply a selection and estimation procedure for the detection of multiple targets in clutter. The selection and estimation (SE) test performs better than a fixed order statistic (OS) detector. The SE test has some similarity to a variable trimmed mean (VTM) test and has a slight performance advantage. Unlike the VTM, whose performance is evaluated only by simulation studies, the performance of the SE test, for a Rayleigh fluctuating target model, can be evaluated analytically. Further improvement in the performance is possible if a better selection procedure can be found     

High-resolution simulation for rotorcraft aerodynamics in hovering and vertical descending flight using a hybrid method

A high-resolution simulation tool for rotorcraft aerodynamics is developed by coupling CFD with a Vorticity Transport Model (VTM). An Eulerian-based CFD module is used to model the blade near body flowfield, and a Lagrangian-based VTM module is employed for vortex tracking in the far wake. The coupling procedure is implemented by transmitting vortex sources to the VTM module and feeding boundary conditions back to the CFD module. The presented CFD/VTM hybrid solver is firstly validated by hover cases of three different rotor configurations. Simulation results, including the blade surface pressure distribution, rotor downwash, and hover figure of merit, exhibit favorable correlations with available experimental data. Then, a rotor operated in vertical descending flight with a fixed collective pitch is investigated. It is shown that the CFD/VTM coupling method is suitable for rotor wake simulation. Wake instabilities (far wake breakdown in hover and toroidal wake pattern in the vortex ring state) are successfully demonstrated with a moderate computational cost.     

Trimmed Generalized Sign and Modified Median Detectors for Multiple Target Situations

The trimmed generalized sign (TGS) nonparametric detector is introduced. The TGS and the modified median detector (MMD) are considered in situations when more than one target is present. Their performance is obtained through Monte Carlo simulations and compared with that of the generalized sign (GS) detector when detecting nonfluctuating signal in Gaussian noise.     

Optimal CFAR detection in Weibull clutter

Optimal, in the maximum likelihood sense, constant false-alarm rate (CFAR) detection for Weibull clutter statistics, is investigated. The proposed OW (optimal Weibull) estimator is proved to be an asymptotically efficient estimator of the mean power of the Weibull clutter. Theoretical analysis of the OW-CFAR detector is provided, while detection performance analysis is carried out using the Monte Carlo simulation method. The operation of the median and morphological (MEMO)-CFAR detector in Weibull clutter statistics is also explained. It performs almost optimally in uniform clutter and, simultaneously, it is robust in multitarget situations. The performance of the proposed OW-CFAR detector in uniformal Weibull clutter is used as a yardstick in the analysis of the MEMO cell-averager (CA) and ordered statistic (OS) CFAR detectors. Nonfluctuating and fluctuating (Swerling II) targets are considered in detection analysis. The performance of the detectors is also examined at clutter edges     

A mean level adaptive detector using nonconcurrent data

Convergence results for a mean level adaptive detector (MLAD) are presented. The MLAD consists of an adaptive matched filter (for spatially correlated inputs) followed by a mean level detector (MLD). The optimal weights of the adaptive matched filter are estimated from one batch of data and applied to a statistically independent batch of nonconcurrent data. The threshold of the MLD is determined from the resultant data. Thereafter a candidate cell is compared against this threshold. Probabilities of false alarm and detection are derived as a function of the threshold factor, the order of the matched filter, the number of independent samples per channel used to calculate the adaptive matched filter weights, the number of samples used to set the MLD threshold, and the output signal-to-noise power ratio of the optimal matched filter. A number of performance curves are shown and discussed     

Performance of a Mean Level Detector Processing M-Correlated Sweeps

The performance of a mean level detector processing M-correlated consecutive sweeps is derived. Performance when sweeps are independent can be obtained simply as a special case. The background noise is assumed stationary Gaussian and pulses are fluctuating according to the Swerling I model. Results are obtained for both finite and infinite reference noise samples. It is shown that for fixed M the relative improvement over the single hit case increases when the correlation between sweeps decreases and as the probability of false alarm is kept at lower rates.     

A comparison of two adaptive detection schemes

Two schemes for adaptive detection are compared: Kelly's generalized likelihood ratio test (GLRT) and the mean level adaptive detector (MLAD). Detection performance, P_D, is predicted for the two schemes under the assumptions that the input noises are zero-mean complex Gaussian random variables that are temporally independent but spatially correlated; and the amplitude of the desired signal is Rayleigh distributed. P_D is computed as a function of the false alarm probability, the number of input channels, the number of independent samples per channel, and the matched filtered output signal-to-noise (S/N) power ratio. In this analysis the GLRT is shown to have better detection performance than the MLAD. The difference in detection performance increases as one uses fewer input samples. However, the required number of samples necessary to have only a 3 dB detection loss for both detection schemes is approximately the same. This is significant since for the present, the MLAD is considerably less complex to implement than the GLRT     

Sonar Array Detection of Gaussian Signals in Gaussian Noise of Unknown Power

A statistical test is postulated for detecting, with an M-element hydrophone array, a Gaussian signal in spatially independent Gaussian noise of unknown power. The test is an extension of the uniformly-most-powerful (UMP) unbiased test for a two-element array. The output signal-to-noise ratio of the test is calculated and, for a large number of independent space-time samples, is shown to be no better than a mean-level detector (MLD). Receiver operating characteristic curves (ROC) for the MLD are computed and compared to the ROC curves for the optimum (Bayes) parametric detector. The input signal-to-noise power ratios required to provide a detection probability of 0.5 differ by less than 0.2 dB for a fifty-element array with wide variation in false-alarm probability and time-bandwidth product. This result suggests that both the extended bivariate UMP unbiased test and the MLD perform close to the unknown UMP unbiased test for independence of a multivariate Gaussian distribution.     

Importance sampling for characterizing STAP detectors

This paper describes the development of adaptive importance sampling (IS) techniques for estimating false alarm probabilities of detectors that use space-time adaptive processing (STAP) algorithms. Fast simulation using IS methods has been notably successful in the study of conventional constant false alarm rate (CFAR) radar detectors, and in several other applications. The principal objectives here are to examine the viability of using these methods for STAP detectors, develop them into powerful analysis and design algorithms and, in the long term, use them for synthesizing novel detection structures. The adaptive matched filter (AMF) detector has been analyzed successfully using fast simulation. Of two biasing methods considered, one is implemented and shown to yield good results. The important problem of detector threshold determination is also addressed, with matching outcome. As an illustration of the power of these methods, two variants of the square-law AMF detector that are thought to be robust under heterogeneous clutter conditions have also been successfully investigated. These are the envelope-law and geometric-mean STAP detectors. Their CFAR property is established and performance evaluated. It turns out the variants have detection performances better than those of the AMF detector for training data contaminated by interferers. In summary, the work reported here paves the way for development of advanced estimation techniques that can facilitate design of powerful and robust detection algorithms     

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.     

New SAR Processor Based on Matched Subspace Detectors

This paper deals with a new synthetic aperture radar (SAR) Processor based on a subspace detector designed for man-made target (MMT) detection. As MMTs are more accurately decribed by a set of canonical elements than with isotropic points, we develop a new algorithm which aims at using new models, instead of the isotropic point model commonly used in SAR processors. A subspace detector matched to canonical elements is included in the SAR processing. The implementation and the optimization of subspace detector SAR (SDSAR) algorithm is described. Simple examples of MMT detection in simulations and real data with a target hidden in a forest show the power of our approach. The SDSAR algorithm is shown to be the first robust and tractable algorithm relying on realistic scattering assumptions about the target.     

Parametric Rao Test for Multichannel Adaptive Signal Detection

The parametric Rao test for a multichannel adaptive signal detection problem is derived by modeling the disturbance signal as a multichannel autoregressive (AR) process. Interestingly, the parametric Rao test takes a form identical to that of the recently introduced parametric adaptive matched filter (PAMF) detector for space-time adaptive processing (STAP) in airborne surveillance radar systems and other similar applications. The equivalence offers new insights into the performance and implementation of the PAMF detector. Specifically, the Rao/PAMF detector is asymptotically (for large samples) a parametric generalized likelihood ratio test (GLRT), due to an asymptotic equivalence between the Rao test and the GLRT. The asymptotic distribution of the Rao test statistic is obtained in closed form, which follows an exponential distribution under the null hypothesis H ₀ and, respectively, a noncentral Chi-squared distribution with two degrees of freedom under the alternative hypothesis H ₁. The noncentrality parameter of the noncentral Chi-squared distribution is determined by the output signal-to-interference-plus-noise ratio (SINR) of a temporal whitening filter. Since the asymptotic distribution under H ₀ is independent of the unknown parameters, the Rao/PAMF asymptotically achieves constant false alarm rate (CFAR). Numerical results show that these results are accurate in predicting the performance of the parametric Rao/PAMF detector even with moderate data support.     

Logarithmic Detection with Postdetection Filtering

An analysis is presented of the performance of a logarithmic detector or followed by a low-pass filter, under the assumption of a large ratio of IF bandwidth to postdetection bandwidth. This allows for the probability of detection and similar quantities to be computed in a straightforward manner. The mean and variance of the filter output are found by first deriving the autocorrelation function of the logarithmic detector output and then obtaining the power spectral ral density. A useful engineering approximation is made for the variance which is valid for all signal-to-noise ratios.     

The Nonparametric Detection of Signals Embedded in Log-Normal Noise

The nonparametric detection of signals embedded in log-normal noise is discussed. The generalized sign (GS), Mann-Whitney (MW), modified Savage (MS), and modified rank squared (MRS) non-parametic detectors are considered and are compared with the mean and trimmed mean (TM) detectors when envelope detection is used. The detection of both nonfluctuating and Rayleigh fluctuating signals is considered.     

Ordered Statistic CFAR Processing for Two-Parameter Distributions with Variable Skewness

Rohling has developed a constant false alarm rate (CFAR) technique based on ordered statistics of the reference cells. An extension of his technique is presented that maintains a CFAR for two-parameter distributions, with both mean power and skewness variable. The new method is therefore more robust, but has higher CFAR loss than the single-parameter technique.     

Detection of stochastic signals in the frequency domain

The optimum detector for a random signal, the estimator-correlator, is difficult to implement. If the power spectral density (PSD) of a continuous time signal is known, a locally optimum detector is available. It maximizes the deflection ratio (DR), a measure of the detector output signal-to-noise ratio (SNR). A discrete version of this detector is developed here, called the discrete-MDRD, which takes a weighted sum of the spectral components of the signal data as the detection statistic. Its derivation is applicable to nonwhite noise samples as well. A comparison of this new detector against three other common types, through their DR values and simulation results, reveals that the discrete-MDRD is near optimal at low SNRs. When the PSD of a signal is not known, a common test statistic is the peak of the PSD of the data. To reduce spectral variations, the PSD estimator first divides the data sequence into several segments and then forms the averaged PSD estimate. The segment length affects the DR values; the length that maximizes the DR is approximately the reciprocal of the signal bandwidth. Thus for unknown signal PSD, a detector that approaches the maximum DR is realizable from just the knowledge of the signal bandwidth, which is normally available. Examples and simulation results are provided to illustrate the properties and performance of the new detector     

Analysis of some modified ordered statistic CFAR: OSGO and OSSOCFAR

It is necessary for automatic detection radars to be adaptive to variations in background clutter in order to maintain a constant false alarm rate (CFAR). A CFAR based on an ordered statistic technique (OS CFAR) has some advantages over the cell-averaging technique (CA CFAR), especially in clutter edges or multiple target environments; unfortunately the large processing time required by this technique limits its use. The authors present two new OS CFARs that require only ahlf the processing time. One is an ordered statistic greatest of CFAR (OSGO), while the other is an ordered statistic smallest of CFAR (OSSO). The OSGO CFAR has the advantages of the OS CFAR with only a negligible increment to the CFAR loss     

Structures for radar detection in compound Gaussian clutter

The problem of coherent radar target detection in a background of non-Gaussian clutter modeled by a compound Gaussian distribution is studied here. We show how the likelihood ratio may be recast into an estimator-correlator form that shows that an essential feature of the optimal detector is to compute an optimum estimate of the reciprocal of the unknown random local power level. We then proceed to show that the optimal detector may be recast into yet another form, namely a matched filter compared with a data-dependent threshold. With these reformulations of the optimal detector, the problem of obtaining suboptimal detectors may be systematically studied by either approximating the likelihood ratio directly, utilizing a suboptimal estimate in the estimator-correlator structure or utilizing a suboptimal function to model the data-dependent threshold in the matched filter interpretation. Each of these approaches is studied to obtain suboptimal detectors. The results indicate that for processing small numbers of pulses, a suboptimal detector that utilizes information about the nature of the non-Gaussian clutter can be implemented to obtain quasi-optimal performance. As the number of pulses to be processed increases, a suboptimal detector that does not require information about the specific nature of the non-Gaussian clutter may be implemented to obtain quasi-optimal performance     

M-correlated sweeps performance analysis of mean-level CFARprocessors in multiple target environments

This paper is devoted to the detection performance evaluation of the mean-level (ML) constant false-alarm rate (CFAR) detectors processing M-correlated sweeps in the presence of interfering targets. The consecutive pulses are assumed to be fluctuating according to the Swerling I model. Exact expressions are derived for the detection probability of the conventional mean-level detector (MLD) and its modified versions under Rayleigh fluctuating target model. Performance for independent sweeps can be easily obtained by setting the sweep-to-sweep correlation coefficient equal to zero. Results are obtained for both homogeneous and nonhomogeneous background environments. It is shown that for fixed M, the relative improvement over the single sweep case increases as the correlation between sweeps decreases. For the same parameter values, the minimum MLD has the best performance in the presence of extraneous target returns among the reference noise samples     

Detection of random signals via spectrum matching

Using a priori knowledge of the signal power spectral density (PSD), a spectrum matching approach which effectively utilizes the available signal spectral shape is developed for random signal detection. Two spectrum matching detector (SMD) structures, which are implemented by correlogram and periodogram, respectively, are examined. Theoretical calculation of their false alarm rates is derived and confirmed by simulations. It is also demonstrated that the proposed detectors outperform the standard periodogram, Bartlett method, and energy detector under constant false alarm rate (CFAR) condition for two different random signals.