Pade approximations for detectability in K-clutter and noise

The Pade approximation (PA) method is used to analyze the detection performance of single and multiple pulse radar systems operating in K-distributed clutter and thermal noise. Simple approximations for false-alarm and detection probabilities are obtained, using lower order moments for the detection decision statistic. Both envelope and squaring detector laws are considered, with noncoherent integration, for independent and correlated K clutter. The target is assumed to be pulse-to-pulse Rayleigh fading. The methods are a substantial application of the PA methods we have previously published     

A real-time statistical polarimetric target model

A statistical approach to modeling and simulation of polarimetric electromagnetic fields backscattered from a reflecting body of a complex shape is described. A statistical scattering matrix is formulated and estimated for Rayleigh and Rician fluctuating (reciprocal and nonreciprocal) targets. The backscattered and received fields are modeled as a stochastic processes for arbitrary combination of transmit and receive polarization. A Monte Carlo simulation of a tank target is performed to verify the assumptions and approximations made and to demonstrate the feasibility of the real-time model. The results presented can be generalized to polarimetric clutter and to decoy modeling and simulation     

Detection Performance of Logarithmic Receivers Employing Video Integrators

The detection performance of logarithmic receivers in Rayleigh and non-Gaussian clutter is investigated. In Rayleigh clutter the performance is determined for steady, Swerling case 1, and Swerling case 2 targets. The detection loss of logarithmic receivers is generally less than the ? log n loss conjectured by Green, but consistent with the 1.08-dB asymptotic loss established by Hansen. The Swerling case 2 loss, important in frequency- agility applications, canbe severe for a small number of integrated pulses and high Pd, and apparently approaches the 1.08-dB asymptotic loss as a lower bound. Graphs of GramCharlier series cumulants are provided to allow determination of logarithmic-receiver performance. Curves are presented to allow the detection performance of logarithmic receivers in log-normal and Weibull clutter to be determineds.     

Adaptive Radar Detection with Asymptotically Regulated False-Alarm Rate

An adaptive detection procedure is described by which the detection threshold is so adjusted as to provide an asymptotic false-alarm probability PFA that is approximately invariant with changes in radar clutter return amplitude probability density functions (pdf's) in a broad class. The class includes Rayleigh, chi, Weibull, and lognormal pdf's. The receiver noise is also taken into account. The clutter-plus-noise pdf is approximated by a truncated generalized Laguerre series, the coefficients of which are estimated from the radar returns using "cell averaging" techniques. This estimation is assumed to be perfect. The results obtained indicate that the "bias" error, defined as the normalized difference between the design PFA and the asymptotic PFA corresponding to the computed threshold, lies within a fraction of an order of magnitude for 10-3?PFA ? 10-6. For PFA ?10-6 the bias error is more than an order of magnitude. These results are for the case when a single independent radar return is processed at a time. The bias error decreases as the number of postdetection integrations of independent returns increases.     

Road-map assisted ground moving target tracking

Tracking ground targets with airborne GMTI (ground moving target indicator) sensor measurements proves to be a challenging task due to high target density, high clutter, and low visibility. The exploitation of nonstandard background information such as road maps and terrain information is therefore highly desirable for the enhancement of track quality and track continuity. The present paper presents a Bayesian approach to incorporate such information consistently. It is particularly suited to deal with winding roads and networks of roads. The target dynamics is modeled in quasi one-dimensional road coordinates and mapped onto ground coordinates using linear road segments taking road map errors into account. The case of several intersecting roads with different characteristics, such as mean curvature, slope, or visibility, is treated within an interacting multiple model (IMM) scheme. Targets can be masked both by the clutter notch of the sensor and by terrain obstacles. Both effects are modeled using a sensor-target state dependent detection probability. The iterative filter equations are formulated within a framework of Gaussian sum approximations on the one hand and a particle filter approach on the other hand. Simulation results for single targets taken from a realistic ground scenario show strongly reduced target location errors compared with the case of neglecting road-map information. By modeling the clutter notch of the GMTI sensor, early detection of stopping targets is demonstrated     

Analysis of CA-CFAR processors for linear-law detection

A method for evaluating the performance of cell-averaging constant false alarm rate (CA-CFAR) processors which use the amplitude of echo signals rather than their squared amplitude is presented. Results for the case of Rayleigh clutter/noise statistics are given. Detection probabilities are evaluated for the case of a Rayleigh fluctuating target embedded in Rayleigh clutter/noise for linear-law CA-CFAR processors. These results are observed to be practically identical to those of square-law CA-CFAR processors for which analytical expressions are readily available. These observations are verified using Monte Carlo simulations. The same conclusion is reached in the case of a nonfluctuating target embedded in Rayleigh clutter/noise for which only simulation results are presented     

A new distributed constant false alarm rate detector

A new constant false alarm rate (CFAR) test termed signal-plus-order statistic CFAR (S+OS) using distributed sensors is developed. The sensor modeling assumes that the returns of the test cells of different sensors are all independent and identically distributed In the S+OS scheme, each sensor transmits its test sample and a designated order statistic of its surrounding observations to the fusion center. At the fusion center, the sum of the samples of the test cells is compared with a constant multiplied by a function of the order statistics. For a two-sensor network, the functions considered are the minimum of the order statistics (mOS) and the maximum of the order statistics (MOS). For detecting a Rayleigh fluctuating target in Gaussian noise, closed-form expressions for the false alarm and detection probabilities are obtained. The numerical results indicate that the performance of the MOS detector is very close to that of a centralized OS-CFAR and it performs considerably better than the OS-CFAR detector with the AND or the OR fusion rule. Extension to an N-sensor network is also considered, and general equations for the false alarm probabilities under homogeneous and nonhomogeneous background noise are presented.     

Pade approximations to matched filter amplitude probabilityfunctions

Performance analysis of echolocation systems requires the probability density function (pdf) or survival function of a matched filter output. A method is presented to derive approximations to these functions using a Pade approximation to their associated characteristic function (CF). The method is based on the Hankel transform. It allows computation of detection probabilities when the matched filter responses to clutter and a target are separately known. Several numerical examples are presented     

Coherent detection of radar targets in a non-gaussian background

The problem of detecting radar targets against a background of coherent, correlated, non-Gaussian clutter is studied with a two-step procedure. In the first step, the structure of the amplitude and the multivariate probability density functions (pdfs) describing the statistical properties of the clutter is derived. The starting point for this derivation is the basic scattering problem, and the statistics are obtained from an extension of the central limit theorem (CLT). This extension leads to modeling the clutter amplitude statistics by a mixture of Rayleigh distributions. The end product of the first step is a multidimensional pdf in the form of a Gaussian mixture, which is then used in step 2. The aim of step 2 is to derive both the optimal and a suboptimal detection structure for detecting radar targets in this type of clutter. Some performance results for the new detection processor are also given     

Performances of order statistics CFAR

A previous analysis of order-statistics constant-false-alarm-rate (OS-CFAR) radar receiving a single pulse from a Rayleigh fluctuating target in a Rayleigh background is extended to a Rayleigh-plus-dominant target. The analysis includes effects of a multitarget environment. A detailed comparison of OS-CFAR, cell-averaging (CA) CFAR, and censored CA-CFAR is provided for a Rayleigh target in the presence of strongly interfering targets. The false-alarm analysis of OS-CFAR is extended to the more general case of a Weibull background. The deterioration of the CFAR property of OS as the shape factor, C, of a Weibull probability density function changes from Rayleigh (C=2) to a longer-tailed one (C<2) is evaluated. The analytic comparison between CA-CFAR and OS-CFAR is extended to an integration of pulses reflected from a Swerling II target. The OS-CFAR performance (with and without interfering targets) yields an integral equation that is solved numerically     

基于先验门限优化准则的探测阈值自适应选择

针对 2维测量和 4 -sigma确认门 ,把先验检测门限优化准则和修正 Riccati方程的解析近似表示相结合 ,得到了在瑞利起伏环境下使跟踪性能优化的信号探测阈值解析表示式 ,从而使在线求解自适应信号探测阈值能比较容易地实现。通过研究和仿真发现 :在滤波稳定阶段 ,本文给出的自适应信号检测门限方法的跟踪性能优于固定虚警率方法的跟踪性能 ;基于先验检测门限优化准则实现检测 -跟踪的联合优化要求信噪比要大于一定的门限 ,在瑞利起伏环境下 ,对 2维测量和 4 -sigma确认门 ,该门限为 1 .57     

High resolution radar clutter statistics

The generalized compound probability density function (GC-pdf) is presented for modeling high resolution radar clutter. In particular, the model is used to describe deviation of the speckle component from the Rayleigh to Weibull or other pdfs with longer tails. The GC-pdf is formed using the generalized gamma (GΓ) pdf to describe both the speckle and the modulation component of the radar clutter. The proposed model is analyzed and thermal noise is incorporated into it. The validation of the GC-pdf with real data is carried out employing the statistical moments as well as goodness-of-fit tests. A large variety of experimental data is used for this purpose. The GC-pdf outperforms the K-pdf in modeling high resolution radar clutter and reveals its structural characteristics     

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     

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     

Pade approximations of probability density functions

The analysis of radar detection systems often requires extensive knowledge of the special functions of applied mathematics, and their computation. Yet, the moments of the detection random variable are often easily obtained. We demonstrate here how to employ a limited number of exactly specified moments to approximate the probability density and distribution functions of various random variables. The approach is to use the technique of Pade approximations (PA) which creates a pole-zero model of the moment generating function (mgf). This mgf is inverted using residues to obtain the densities     

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     

Basic belief assignment approximations using degree of non-redundancy for focal element

Dempster-Shafer evidence theory, also called the theory of belief function, is widely used for uncertainty modeling and reasoning. However, when the size and number of focal elements are large, the evidence combination will bring a high computational complexity. To address this issue, various methods have been proposed including the implementation of more efficient combination rules and the simplifications or approximations of Basic Belief Assignments (BBAs). In this paper, a novel principle for approximating a BBA into a simpler one is proposed, which is based on the degree of non-redundancy for focal elements. More non-redundant focal elements are kept in the approximation while more redundant focal elements in the original BBA are removed first. Three types of degree of non-redundancy are defined based on three different definitions of focal element distance, respectively. Two different implementations of this principle for BBA approximations are proposed including a batch and an iterative type. Examples, experiments, comparisons and related analyses are provided to validate proposed approximation approaches.     

The intersection of a Loxodrome with a great circle

The intersections of a loxodrome (rhumb line) and a great circle are of interest for some navigational problems, but a closed-form solution cannot be formulated. An algorithm is given for computing approximations to any desired degree of accuracy using Newton's method. By using the equatorial angle φ as an independent variable all solutions can be found rapidly using the modest computational capabilities of a personal computer     

Asymptotic distribution of the conditional signal-to-noise ratio in an eigenanalysis-based adaptive array

The statistical characterization of the conditioned signal-to-noise ratio (SNR) of the sample matrix inversion (SMI) method has been known for some time. An eigenanalysis-based detection method, referred to as the eigencanceler, has been shown to be a useful alternative to SMI, when the interference has low rank. In this work, the density function of the conditioned SNR is developed for the eigencanceler. The development is based on the asymptotic expansion of the distribution of the principal components of the covariance matrix. It is shown that, unlike the SMI method, the eigencanceler yields a conditional SNR distribution that is dependent on the covariance matrix, It is further shown that simpler, covariance matrix-independent approximations can be found for the large interference-to-noise case. The new distribution is shown to be in good agreement with the numerical data obtained from simulations.     

Recursive Methods for Computing Detection Probabilities

Recursive methods are drived for computing detection probabilities for general fluctuating targets in Gaussian noise. For the generalized chi-square family of fluctuating targets, very simple and convenient recursive algrithms result. The methods are also extended to cell-averaging CFAR. Although the detection probability is expressed iw: terms of an infinite series, a convenient expression is derived for the resulting error when the series is truncated. Cell-averaging CFAR results are computed for nonfluctuating, Swering case I, and Swerling case II fluctuating targets.