Spatially distributed target detection in non-Gaussian clutter

Two detection schemes for the detection of a spatially distributed, Doppler-shifted target in non-Gaussian clutter are developed. The non-Gaussian clutter is modeled as a spherically invariant random vector (SIRV) distribution. For the first detector, called the non-scatterer density dependent generalized likelihood ratio test (NSDD-GLRT), the detector takes the form of a sum of logarithms of identical functions of data from each individual range cell. It is shown under the clutter only hypothesis, that the detection statistic has the chi-square distribution so that the detector threshold is easily calculated for a given probability of false alarm P_F. The detection probability P_D is shown to be only a function of the signal-to-clutter power ratio (S/C)_opt of the matched filter, the number of pulses N, the number of target range resolution cells J, the spikiness of the clutter determined by a parameter of an assumed underlying mixing distribution, and P_F. For representative examples, it is shown that as N, J, or the clutter spikiness increases, detection performance improves. A second detector is developed which incorporates a priori knowledge of the spatial scatterer density. This detector is called the scatterer density dependent GLRT (SDD-GLRT) and is shown for a representative case to improve significantly the detection performance of a sparsely distributed target relative to the performance of the NSDD-GLRT and to be robust for a moderate mismatch of the expected number of scatterers. For both the NSDD-GLRT and SDD-GLRT, the detectors have the constant false-alarm rate (CFAR) property that P_F is independent of the underlying mixing distribution of the clutter, the clutter covariance matrix, and the steering vector of the desired signal     

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     

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.     

Adaptive resolution of mainlobe and sidelobe detections using model order determination

This work presents the development and performance evaluation of a methodology for distinguishing between mainlobe and sidelobe detections that arise in adaptive radar systems operating in adverse environments. Various adaptive detection test statistics such as the adaptive matched filter (AMF), the generalized likelihood ratio test (GLRT), and adaptive coherence estimate (ACE), and combinations of these, have been previously analyzed with respect to their sidelobe rejection capabilities. In contrast to these methods which are based on detecting a single target with known direction and Doppler, the present method uses model order determination techniques applied to the AMF or GLRT data observed over the range of unknown angle and Doppler parameters. The determination of model order, i.e., the number of signals present in the data, is made by using least-squares model fit error residuals and applying the Akaike Information Criterion (AIC). Comprehensive computer simulation results are presented which demonstrate substantial improvement in sidelobe rejection performance and detections of multiple sources compared with previous methods.     

Effects of two-way decorrelation on radar detection inscintillation

A 3 dB gain in average signal-to-noise ratio of a monostatic radar operating in scintillation has recently been established both theoretically and observationally. The statistics of two-way scintillation are derived here for the case where the uplink and downlink both experience Rayleigh fading and where there is arbitrary correlation between the scintillation on the two paths. These statistics are then used to compute radar detection curves. A surprising result is obtained. The probability of detection is only weakly dependent (for P _D in the range 0.1 to 0.9) on the degree of uplink-downlink correlation in the scintillation when the average (nonfading) signal-to-noise ratio is constant and when proper account is taken of the change in mean power between the monostatic and bistatic cases. Much larger differences are seen in the detection curves with scintillation compared with nonfading curves (for P_D equal to 0.7 this scintillation loss is about 7 dB). Thus the difference in detection performance of monostatic and bistatic radars is determined primarily by the difference in the radar cross section (RCS) of the target for the two cases     

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     

Adaptive Radar Detection in Doubly Nonstationary Autoregressive Doppler Spread Clutter

The problem of adaptive radar detection in clutter which is nonstationary both in slow and fast time is addressed. Nonstationarity within a coherent processing interval (CPI) often precludes target detection because of the masking induced by Doppler spreading of the clutter. Across range bins (i.e., fast time), nonstationarity severely limits the amount of training data available to estimate the noise covariance matrix required for adaptive detection. Such difficult clutter conditions are not uncommon in complex multipath propagation conditions where path lengths can change abruptly in dynamic scenarios. To mitigate nonstationary Doppler spread clutter, an approximation to the generalized likelihood ratio test (GLRT) detector is presented wherein the CPI from the hypothesized target range is used for both clutter estimation and target detection. To overcome the lack of training data, a modified time-varying autoregressive (TVAR) model is assumed for the clutter return. In particular, maximum likelihood (ML) estimates of the TVAR parameters, computed from a single snapshot of data, are used in a GLRT for detecting stationary targets in possibly abruptly nonstationary clutter. The GLRT is compared with three alternative methods including a conceptually simpler ad hoc approach based on extrapolation of quasi-stationary data segments. Detection performance is assessed using simulated targets in both synthetically-generated and real radar clutter. Results suggest the proposed GLRT with TVAR clutter modeling can provide between 5–8 dB improvement in signal-to-clutter plus noise ratio (SCNR) when compared with the conventional methods.     

Adaptive polarimetric target detection with coherent radar. I.Detection against Gaussian background

The derivation of a completely adaptive polarimetric coherent scheme to detect a radar target against a Gaussian background is presented. A previously proposed Generalized Likelihood Ratio Test (GLRT) polarimetric detector is extended to the case of a general number of channels; this exploits the polarimetric characteristics of the received radar echoes to improve the detection performance. Together with the fully adaptive scheme, a model-based detector is derived that has a lower estimation loss. A complete theoretical expression is derived for the detection performance of both proposed polarimetric detectors. They are shown to have Constant False Alarm Rate (CFAR) when operating against Gaussian clutter, but to be sensitive to deviations from the Gaussian statistic. The application to recorded radar data demonstrates the performance improvement achievable in practice     

Search radar detection and track with the Hough transform. II.detection statistics

For pt.I see ibid., vol.30, no.1, (Jan.1994). This paper describes the calculation of P_F and P_D for the Hough transform technique when the primary threshold crossings are weighted by their power before transforming (i.e., noncoherent integration). After expressions for P_F and P_D are derived, we examine the question of optimal granularity of the Hough accumulator space. We also investigate the relationship between primary and secondary thresholds and its effect on detectability     

A CFAR adaptive matched filter detector

An adaptive algorithm for radar target detection using an antenna array is proposed. The detector is derived in a manner similar to that of the generalized likelihood-ratio test (GLRT) but contains a simplified test statistic that is a limiting case of the GLRT detector. This simplified detector is analyzed for performance to signals on boresight, as well as when the signal direction is misaligned with the look direction     

Reiterative median cascaded canceler for robust adaptive array processing

A new robust adaptive processor based on reiterative application of the median cascaded canceler (MCC) is presented and called the reiterative median cascaded canceler (RMCC). It is shown that the RMCC processor is a robust replacement for the sample matrix inversion (SMI) adaptive processor and for its equivalent implementations. The MCC, though a robust adaptive processor, has a convergence rate that is dependent on the rank of the input interference-plus-noise covariance matrix for a given number of adaptive degrees of freedom (DOF), N. In contrast, the RMCC, using identical training data as the MCC, exhibits the highly desirable combination of: 1) convergence-robustness to outliers/targets in adaptive weight training data, like the MCC, and 2) fast convergence performance that is independent of the input interference-plus-noise covariance matrix, unlike the MCC. For a number of representative examples, the RMCC is shown to converge using ~ 2.8N samples for any interference rank value as compared with ~ 2N samples for the SMI algorithm. However, the SMI algorithm requires considerably more samples to converge in the presence of outliers/targets, whereas the RMCC does not. Both simulated data as well as measured airborne radar data from the multichannel airborne radar measurements (MCARM) space-time adaptive processing (STAP) database are used to illustrate performance improvements over SMI methods.     

Adaptive canceler and pulse compressor interactions

Performance results for the sidelobe level of a compressed pulse that has been preprocessed through an adaptive canceler are obtained. The adaptive canceler is implemented using the sampled matrix inversion algorithm. Because of finite sampling, the quiescent compressed pulse sidelobe levels are degraded due to the preprocessing of the main channel input data stream (the uncompressed pulse) through an adaptive canceler. It is shown that if N is the number of input canceler channels (main and auxiliaries) and K is the number of independent samples per channel, then K/N can be significantly greater than one in order to retain sidelobes that are close to the original quiescent sidelobe level (with no adaptive canceler). Also it is shown that the maximum level of degradation is independent of whether pulse compression occurs before or after the adaptive canceler if the uncompressed pulse is completely contained within the K samples that are used to calculate the canceler weights. This same analysis can be used to predict the canceler noise power level that is induced by having the desired signal present in the canceler weight calculation     

Search radar detection and track with the Hough transform. III.Detection performance with binary integration

For pt.II see ibid., vol. 30, no 1, (Jan. 1994). This paper considers how well a Hough transform detector with binary integration improves the performance of a typical surveillance radar. For Hough transform detection, binary integration offers some advantages over noncoherent integration when multiple targets appear in range-time space or when the detector receives signals with a wide range of power. We derive expressions for P_F and P_D for a Hough transform binary integrator and apply the expressions to a typical surveillance radar. The results show that for the case considered, the binary Hough integrator improves the power budget of the radar by about 3 dB for a nonfluctuating target and 1 dB for a highly fluctuating target     

GLRT Detectors for Aircraft Wake Vortices in Clear Air

 In this article, radar echoes of aircraft wake vortices are modeled as weighted sums of the frequency components of the echoes with a special covariance matrix for the weighted coefficients. With a proposed detection scheme, two generalized likelihood ratio test (GLRT) detectors are derived respectively for aircraft wake vortices with time-varying and time-invariant Doppler spectra. Then the analytical expressions for detection and false alarm probabilities of the detectors are derived and three factors are investigated which mainly influence the detection performance, i.e., the Doppler extension and uncertainty of the aircraft wake vortex, and the number of the detection cells. The results indicate that, the signal-to-noise ratio (SNR) loss induced by Doppler extension is generally several decibels. The SNR loss due to Doppler uncertainty is approximately proportional to the logarithm of the number of spectrum lines in the uncertain Doppler spectrum intervals. For a large number of detection cells, the SNR gain is approximately proportional to the square root of the number of the detection cells.     

GLRT subspace detection for range and Doppler distributed targets

A generalized likelihood ratio test (GLRT) is derived for adaptive detection of range and Doppler-distributed targets. The clutter is modeled as a spherically invariant random process (SIRP) and its texture component is range dependent (heterogeneous clutter). We suppose here that the speckle component covariance matrix is known or estimated thanks to a secondary data set. Thus, unknown parameters to be estimated are local texture values, the complex amplitudes and Doppler frequencies of all scattering centers. To do so, we use superresolution methods. The proposed detector assumes a priori knowledge on the spatial distribution of the target and has the precious property of having a constant false alarm rate (CFAR) with the assumption of a known speckle covariance matrix or by the use of frequency agility.     

Convergence bounds of an SMI/Gram-Schmidt canceler in colored noise

The performance of the sampled matrix inversion (SMI) adaptive algorithm in colored noise is investigated using the Gram-Schmidt (GS) canceler as an analysis tool. Lower and upper bounds of average convergence are derived, indicating that average convergence slows as the input time samples become correlated. When the input samples are uncorrelated, the fastest SMI algorithm convergence occurs. When the input samples are correlated then the convergence bounds depend on the number of channels N, the number of samples per channels K , and the eigenvalues associated with K×K correlation matrix of the samples in a given channel. This matrix is assumed identical for all channels     

Difference beam aided target detection in monopulse radar

The classical detection step in a monopulse radar system is based on the sum beam only,the performance of which is not optimal when target is not at the beam center. Target detection aided by the difference beam can improve the performance at this case. However, the existing difference beam aided target detectors have the problem of performance deterioration at the beam center, which has limited their application in real systems. To solve this problem, two detectors are proposed in this paper. Assuming the monopulse ratio is known, a generalized likelihood ratio test(GLRT) detector is derived, which can be used when targeting information on target direction is available. A practical dual-stage detector is proposed for the case that the monopulse ratio is unknown. Simulation results show that performances of the proposed detectors are superior to that of the classical detector.     

非高斯杂波背景中距离扩展目标的盲积累检测器

在采用球不变随机向量(SIRV)建模的非高斯杂波背景下,研究了导向矢量失配或未知时距离扩展目标的检测问题。先假设导向矢量已知,采用广义似然比检验(GLRT)得到每个距离单元的归一化匹配滤波器(NMF)统计量,再将多个距离单元的统计量进行非相干积累得到扩展目标的NMF积累检测器(NMFI),然后通过最大化检测统计量的方法,结合特征值分解技术,对导向矢量进行估计,提出了距离扩展目标的盲NMFI(B-NMFI)。仿真分析表明:当导向矢量失配时,NMFI的检测性能优于GLRT;当导向矢量未知时,B-NMFI能有效地检测目标,并且对不同方位的目标具有很好的鲁棒性。     

Error Performance of M-ary DPPM Communication System

Error performance in optical communication, where the information is transmitted by means of the differential pulse-position modulated optical carrier, is discussed. Additive independent background radiation and thermal noise are taken into account. Both threshold type and maximum value type of decision schemes are also considered. The effects of several parameters, such as the number of time slots, the duty ratio, the extinction ratio, the count dimension, the signal-to-background radiation power ratio, and the signal-to-thermal noise power ratio are discussed in detail. The detection characteristic of this system are made clear by comparison with a pulse-position modulation system.     

On joint track initiation and parameter estimation under measurement origin uncertainty

The problem of joint detection and estimation for track initiation under measurement origin uncertainty is studied. The two well-known approaches, namely the maximum likelihood estimator with probabilistic data association (ML-PDA) and the multiple hypotheses tracking (MHT) via multiframe assignment, are characterized as special cases of the generalized likelihood ratio test (GLRT) and their performance limits indicated. A new detection scheme based on the optimal gating is proposed and the associated parameter estimation scheme modified within the ML-PDA framework. A simplified example shows the effectiveness of the new algorithm in detection performance under heavy clutter. Extension of the results to state estimation with measurement origin uncertainty is also discussed with emphasis on joint detection and recursive state estimation.