Target In Gaussian Noise Research Articles

Robust detection of distributed targets based on Rao test and Wald test

We consider the problem of detecting distributed targets in Gaussian noise with unknown covariance matrix. To make the signal-plus-noise hypothesis more plausible in the mismatched case, we model the received signal under the signal-plus-noise hypothesis as the sum of noise, useful target echoes and fictitious signals. Two adaptive detectors are designed according to the Rao test and Wald test. We prove the proposed Rao test and Wald test exhibit constant false alarm rate properties against the covariance matrix. Numerical examples show that the proposed Rao test has strong robustness against the steering vector mismatches.

Detection Rate Optimization for Swerling Targets in Gaussian Noise

In this paper, we consider a pulse radar and study the tradeoff between integration time and scan rate for diverse target scattering models. At the design stage, we optimize the available degrees of freedom (namely, pulse train length and detection threshold) so as to maximize the detection rate, defined as the average number of detections from the target per unit of time, subject to a constraint on the false alarm rate, which is the average number of false alarms from the monitored area per unit of time. This objective function allows to carefully balance the contrasting needs for a large probability of detection (achievable through a large dwell time) and a short scan time. Closed-form solutions are provided for Swerling's Cases 1 and 3 target fluctuation and for the Marcum nonfluctuating model, while, for the Swerling's Cases 2 and 4, the solution is found with the aid of computer simulation. A thorough performance analysis is given to show the achievable tradeoffs among the principal system parameters under the different target models.

Wideband radar detector based on characteristic parameters of echoes

The statistical characterization of radar range cells with the target signals is much more distinct than that of the range cells with noise-only signals. Hence, the quasi-optimal detection principle based on the characteristic parameters of echo signals is adopted to develop a detector of range-spread targets in Gaussian noise. Firstly, the characteristic parameters of the return signals in the entire range profiles of radar are investigated. Secondly, the clustering analysis of the characteristic parameter matrix is discussed to extract the test statistic of echoes. Finally, the probabilities of detection and false alarm of the proposed detector are provided. Theoretical analysis shows that the proposed detector does not need the prior knowledge about the spatial distribution of the target scattering centers in practical scenarios, and it is simple and robust even in low signal-to-noise ratio (low-SNR) scenarios. Monte Carlo (MC) simulations reveal that the detection performance of the proposed detector outperforms the conventional detectors.

Invariant Adaptive Detection of Range-Spread Targets Under Structured Noise Covariance

The invariance principle is adopted to develop an exhaustive study for adaptive detection of range-spread targets in Gaussian noise sharing a block-diagonal covariance structure. For this problem, the usual generalized likelihood ratio principle is intractable. In this paper, we first determine the largest group of affine transformations that does not alter the decision problem. Then, a maximal invariant identified by this group is derived, which can characterize the totality of the invariant detectors and extends the existing results for the point-target case. A theoretical performance analysis of the maximal invariant is also given. Finally, we propose two classes of invariant detectors, which are distinguished by whether a constant false alarm rate (CFAR) is maintained. Numerical experiments are provided for a comparison of the proposed detectors, where a tradeoff between the CFARness and the improved performance has been observed and studied.

Generalized Likelihood Ratio Test for Detection of Gaussian Rank-One Signals in Gaussian Noise With Unknown Statistics

We consider the classical radar problem of detecting a target in Gaussian noise with unknown covariance matrix. In contrast to the usual assumption of deterministic target amplitudes, we assume here that the latter are drawn from a Gaussian distribution. The generalized likelihood ratio test (GLRT) is derived based on multiple primary data and a set of secondary data containing noise only. The new GLRT is shown to be the product of Kelly's GLRT and a corrective, data dependent term. We also investigate two-step approaches where the GLRT for a known disturbance covariance matrix is first derived. In order to come up with detectors that provide a good tradeoff between detection of matched signals and rejection of mismatched signals, we also investigate the two-step GLRT when a fictitious signal is included in the null hypothesis. The constant false alarm rate properties of the detectors are analyzed. Numerical simulations are presented, which show that for small sample sizes the newly-proposed GLRT can outperform Kelly's GLRT and, in addition, that detectors including a fictitious signal are very powerful, at least for low-to-intermediate clutter to noise ratio values.

Rank-Order Adaptive CFAR: Performance Bounds and Efficient Implementation

The uniformly most powerful (UMP) rank-order analog to the cell-averaging constant false alarm rate (CA-CFAR) detector is developed for both the single and multi-scan case. The detector is capable of false alarm control in arbitrary noise while achieving maximum detection probability for the case of a Swerling II target in Gaussian noise. Relationships with earlier tests are discussed. A divide-and-conquer method is developed that allows for rapid implementation of a large class of two-sample rank tests.

Adaptive detection for distributed targets in Gaussian noise with Rao and Wald tests

The problem of adaptively detecting a range distributed target or targets in Gaussian interference is considered in this paper. It is assumed that a set of secondary data is available. Firstly, we derive the adaptive Rao and Wald tests with one-step detection algorithm, and find that both of them are of the same asymptotic performance as the GLRT one. Secondly, the Rao and Wald tests are derived by resorting to the two-step design strategy. To our surprise, our derivations show that all the Rao, Wald and GLR tests in the two-step design strategy are equivalent. Thirdly, the property assessments are presented. It is shown that these new detectors guarantee CFAR property with respect to the Gaussian noise. Finally, simulation results show that these results are accurate.

Polarimetric adaptive detection of range-distributed targets

We address the problem of polarimetric adaptive detection of range-spread targets in Gaussian noise with unknown covariance matrix. At the design stage, we model the target echo from each polarimetric channel as a deterministic signal known up to a scaling factor (possibly varying from cell to cell), which accounts for the polarimetric scattering properties of the target. We first show the failure of the generalized likelihood ratio test (GLRT) procedure to deal with this kind of problem, and thus, we propose a fully adaptive detector based on the method of sieves. We also derive the analytical expression for the probability of false alarm and show that the newly introduced receiver can be made bounded constant false alarm rate (CFAR). Finally, we present simulation results highlighting the performance gain that can be achieved by resorting to polarization diversity in conjunction with high resolution.

Three types of distributed CFAR detection based on local test statistic

Three types of distributed constant false-alarm rate (CFAR) detection based on local test statistic (LTS) are developed under the condition that all the samples in different sensors are independent and identically distributed (IID). They are called R (ratio), S (substract) and P (plus) types. For a two-sensor network and local order statistics CFAR (OS-CFAR) algorithm, we derive their closed-form expressions for false alarm and detection probabilities of detecting a Swerling II target in Gaussian noise. The numerical results show that /spl rho/, the ratio between the noise power levels in two local sensors, has very strong effects on the performances of the S and P type schemes and the centralized detection. They can't hold to be CFAR when there isn't the precise prior knowledge of /spl rho/. Compared with the centralized detection, the distributed detection scheme is more robust for the effect of /spl rho/. Fortunately, the R type scheme is not affected by the /spl rho/ at all. It implies that the local CFAR processing can immunize the distributed detection against the /spl rho/.

Distributed CFAR detector based on local test statistic

Distributed CFAR detector based on unquantized local test statistic (LTS) is considered. LTSs are provided by local processors (LP) and transmitted to the fusion center (FC) where they are fused to generate global decision. Two types of schemes called S and P types are proposed. For local OS-CFAR processing, three schemes are analyzed, i.e. OS-S-CA, MOS and mOS. Samples in different sensors are assumed to be independent and identically distributed. For a two-sensor network, some explicit expressions for probabilities of false alarm and detection of a Swerling II target in Gaussian noise are derived. With the consideration of both detection performance and the amount of data transmitted between LP and FC, OS-S-CA is the best, and the MOS little inferior.

On distributed signal detection with multiple local free parameters

In this work, we propose an efficient approach to the optimization of distributed multiradar systems with parallel topology, employing decision fusion from local detectors with discrete and continuous free design parameters. This approach, termed hierarchical optimization approach, can be applied to a variety of optimization criteria including the Neyman-Pearson (NP) and the locally optimum detection (LOD) criteria. It avoids the exhaustive search for the optimal discrete parameters and greatly reduces the computational load required for global system optimization. The effectiveness of the proposed approach is demonstrated by means of a numerical example, where ordered statistic (OS) constant false-alarm rate (CFAR) decentralized radar detection of Swerling I targets in Gaussian noise is considered.

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.

Equivalence of the Likelihood Ratio Processor, the Maximum Signal-to-Noise Ratio Filter, and the Wiener Filter

It is shown that for the problem of detecting a nonfluctuating target in Gaussian noise, three common optimality criteria lead to identical multichannel filter designs.

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.