OR Fusion Research Articles

The Dependence of Fusion Gain on Signal-Amplitude Distributions and Position Errors

This paper considers statistical detection theory for a system of two geographically distributed sensors. The performance of the two main fusion rules (OR and AND) is evaluated in the absence and presence of position errors in the observations, by means of receiver operating characteristics (ROC) curves. The analysis is restricted to three distributions that are representative of a Rician: Rayleigh, one-dominant-plus-Rayleigh (1D+R), and nonfluctuating signal amplitude. Rice's distribution is considered to be relevant for sonar and radar applications. In the absence of position errors, the performance is derived theoretically. It is shown that the best fusion rule depends on the assumed signal amplitude distribution and on the signal-to-noise ratio (SNR). Under operational conditions, position inaccuracies of the multiple observations are of main importance, raising association problems. In this case, the ROC curves are evaluated by means of simulations. It is found that position errors degrade detection performance by 3-6 dB if the AND fusion is used, whereas OR fusion is hardly affected.

Distributed CFAR target detection

We present a review of different distributed constant false alarm rate target detection techniques. We argue that for optimum results involving multiple targets and clutter of variable characteristics, the proper choice is an architecture involving decentralizing processing at multiple sensor sites. A new radar target detection example shows that a simple Boolean OR fusion rule can provide robust and competitive performance when compared to more complex fusion rules.

Performance of distributed CFAR test under various clutter amplitudes

We evaluate the performances of several distributed constant false-alarm rate (CFAR) tests operating in different background clutter conditions. The analysis considers the detection of Rayleigh target in various clutters with the possibility of differing clutter power levels in the test cells of distributed radars. Numerical results studied for a two-radar system show how the false-alarm rate of the maximum order statistic (MOS) test changes with differences in the clutter power levels of the test cells. The analysis for the detection of Rayleigh target in Rayleigh clutter indicates that, with the power levels of differing test cells, the OR fusion rule can be quite competitive with the new normalized test statistic (NTS). However, for the detection of Rayleigh target in Weibull or K-distributed clutter, the results show that NTS outperforms both the OR and the AND rules under the condition of large signal-to-clutter power ratio and moderate shape parameter values.

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.

OS-CFAR thresholding in decentralized radar systems

In a decentralized detection scheme, several sensors perform a binary (hard) decision and send the resulting data to a fusion center for the final decision. If each local decision has a constant false alarm rate (CFAR), the final decision is ensured to be CFAR. We consider the case that each local decision is a threshold decision, and the threshold is proportional, through a suitable multiplier, to a linear combination of order statistics (OS) from a reference set (a generalization of the concept of OS thresholding). We address the following problem: given the fusion rule and the relevant system parameters, select each threshold multiplier and the coefficients of each linear combination so as to maximize the overall probability of detection for constrained probability of false alarm. By a Lagrangian maximization approach, we obtain a general solution to this problem and closed-form solutions for the AND and OR fusion logics. A performance assessment is carried on, showing a global superiority of the OR fusion rule in terms of detection probability (for operating conditions matching the design assumptions) and of robustness (when these do not match). We also investigate the effect of the hard quantization performed at the local sensors, by comparing the said performance to those achievable by the same fusion rule in the limiting case of no quantization.

Threshold optimization for distributed order-statistic CFAR signal detection

Distributed signal detection schemes have received significant attention recently, but usually under the assumption of stationary observations which are independent from sensor to sensor. Here, order statistics based constant false alarm rate (OS-CFAR) detection techniques are applied to a distributed detection system with nonstationary observations where the signal observations are assumed to be dependent from sensor to sensor. Cases are considered where weak narrowband random signals are observed in additive Gaussian noise-plus-clutter of unknown power. Necessary conditions are given which specify the best sensor thresholds for some n-sensor cases. The best schemes using nonrandomized fusion rules are found for some specific two-sensor cases. The best schemes map use either AND or OR fusion rules depending on the specific false alarm probability and the number of reference observations used in the OS-CFAR scheme. Distributed OS-CFAR and cell-averaging CFAR (CA-CFAR) schemes are compared in terms of their capability to maintain false alarm probability in nonhomogeneous backgrounds. At least for the specific cases we have studied, there are OS-CFAR schemes which generally outperform the CA-CFAR schemes in this regard.

Distributed cell-averaging CFAR detection in dependent sensors

Constant false alarm rate detection is considered in a decentralized, two-sensor context. Cases with observations which are dependent from sensor to sensor are investigated, for which results have been lacking. The in-phase and quadrature components of the received narrowband observation at each sensor consist of a common weak random signal in additive Gaussian combined clutter and noise. The sensors use cell-averaging CFAR tests to each generate binary decisions which are sent to a fusion center. Optimal sensor thresholds are found and the performance of the best schemes using AND and OR fusion rules are compared. The ability of these schemes to maintain constant false alarm probability in the presence of clutter edges is also studied.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>