Comments, with reply, on `Optimal detection and performance ofdistributed sensor systems'

The commenter observes that the general solution proposed in the above paper (see ibid., vol.AES-23, no.1, p.24-30, Jan. 1988) for the global optimization of a distributed sensor detection system with fusion leads to coupled equations whose solution is a formidable computational task. This necessitated several simplifying assumptions that he comments on here. In response, the authors review the extent of the equal local threshold assumption throughout the work and make comments on the numerical performance comparison they gave there     

A Sequential Implementation of Optimal Array Processors

A sequential implementation of the likelihood ratio for doubly composite hypothesis array processing problems is presented in which the likelihood ratio is realized by an appropriate combination ion of single frequency components. The array processos decomposed in such a way that the actual a priori parameter knowledge dge need not be introduced until after a significant portion of the data processing has taken place.     

Optimal Detection and Performance of Distributed Sensor Systems

Global optimization of a distributed sensor detection system withfusion is considered, where the fusion rule and local detectors aresolved to obtain overall optimal performance. This yields coupledequations for the local detectors and the fusion center.The detection performance of the distributed system with fusionis developed. The globally optimal system performance is comparedwith two suboptimal systems. Receiver operating characteristics(ROCs) are computed numerically for the problem of detecting aknown signal embedded in non-Gaussian noise.     

Array Processor Performance Under Directional Uncertainty

Detection performance of four candidate receiver structures for the signal known except for direction (SKED) array problem is investigated. Included are the Bayes optimal detector, two estimate and plug structures, and a fixed estimate structure. Estimators considered are the maximum likelihood (ML) and maximum a posteriori (MAP). Performance degradation from optimal for the estimate and plug structures considered is shown to be significantly more severe the larger the array size.     

Optimal Detection of a Signala with Time-Varying Carrier Phase

The problem considered in this paper is the detection of a signal known except for time-varying carrier phase in white Gaussian noise. The method of attacking this problem is to model the time-varying carrier phase as a Markov process. Fourier transform techniques are then applies to yield a simple time-wise adaptive form for the phasetracking detector. Optimal accounting for the time variations in phase is accomplished via a simple algorithm which serves to update the detector memory. Furthermore, it is shown that this memory updating operation is a discrete linear filter whose impulse response is a simple function of the previous memory state and the Markov transitional statistics on the phase. A priori knowledge regarding the phase is summarized in the initial impulse response of the updating filter.     

On Transient and Periodic Signal Detection in Time-Varying Noise Power

Detectability of periodic and synchronously recurrent transient signals in a noisy environment in which the noise power is time varying is investigated. For at least one noise model, it is shown that the basic nonlinearity of the optimum detector is a limiter. Performance of this optimum detector is compared with analog cross-correlation and clipper cross-correlation (CCC) detectors. It is shown that the CCC performs nearly optimally, especially at low signal-to-noise ratios, and that its performance is significantly better than that of the analog cross correlator.     

Bayesian Detection of Targets of Unknown Location

In this paper the array detection problem for certain deterministic signals in spatially uncorrelated Gaussian noise is formulated in Bayesian terms and the required likelihood ratios and resulting performance characteristics are obtained. Primary emphasis is on detection of targets of unknown spatial location using a likelihood ratio approach, with the target location treated as a random parameter, rather than an estimator-correlator approach. The tradeoff among array parameters and signal parameters is demonstrated. It is shown that the dominant uncertainty affecting detection performance seems to be that of location when compared with uncertainty on energy and/or phase.     

Optimal Array Processor Performance Trade-offs under Directional Uncertainty

Detection performance in terms of the receiver operating characteristic (ROC) curve is obtained for three specific problems involving either signal or noise source location uncertainty. The array processors are optimum in the sense that they form the likelihood ratio of the outputs of the individual array elements. Performance trade-offs due to signal uncertainty, signal and noise source location uncertainty, and array size are presented.     

Design and Performance Comparison of Distributed Detection Networks

Optimization of a distributed detection network using theminimum global cost criterion results in local processors thatindividually form the likelihood ratio when the input observationvectors are statistically independent. In addition, the localthresholds and the network performance can be expressed as afunction of the receiver operating characteristics (ROCs) of the localprocessors. The performance of rive distributed networks arecompared numerically using local ROCs from the conic ROCfamily.