On the Effect of Correlated Measurements on the Performance of Distributed Estimation

We address the distributed estimation of an unknown scalar parameter in Wireless Sensor Networks (WSNs). Sensor nodes transmit their noisy observations over multiple access channel to a Fusion Center (FC) that reconstructs the source parameter. The received signal is corrupted by noise and channel fading, so that the FC objective is to minimize the Mean-Square Error (MSE) of the estimate. In this paper, we assume sensor node observations to be correlated with the source signal and correlated with each other as well. The correlation coefficient between two observations is exponentially decaying with the distance separation. The effect of the distance-based correlation on the estimation quality is demonstrated and compared with the case of unity correlated observations. Moreover, a closed-form expression for the outage probability is derived and its dependency on the correlation coefficients is investigated. Numerical simulations are provided to verify our analytic results.Comment: 5 page

Optimization of Automatic Target Recognition with a Reject Option Using Fusion and Correlated Sensor Data

This dissertation examines the optimization of automatic target recognition (ATR) systems when a rejection option is included. First, a comprehensive review of the literature inclusive of ATR assessment, fusion, correlated sensor data, and classifier rejection is presented. An optimization framework for the fusion of multiple sensors is then developed. This framework identifies preferred fusion rules and sensors along with rejection and receiver operating characteristic (ROC) curve thresholds without the use of explicit misclassification costs as required by a Bayes\u27 loss function. This optimization framework is the first to integrate both vertical warfighter output label analysis and horizontal engineering confusion matrix analysis. In addition, optimization is performed for the true positive rate, which incorporates the time required by classification systems. The mathematical programming framework is used to assess different fusion methods and to characterize correlation effects both within and across sensors. A synthetic classifier fusion-testing environment is developed by controlling the correlation levels of generated multivariate Gaussian data. This synthetic environment is used to demonstrate the utility of the optimization framework and to assess the performance of fusion algorithms as correlation varies. The mathematical programming framework is then applied to collected radar data. This radar fusion experiment optimizes Boolean and neural network fusion rules across four levels of sensor correlation. Comparisons are presented for the maximum true positive rate and the percentage of feasible thresholds to assess system robustness. Empirical evidence suggests ATR performance may improve by reducing the correlation within and across polarimetric radar sensors. Sensitivity analysis shows ATR performance is affected by the number of forced looks, prior probabilities, the maximum allowable rejection level, and the acceptable error rates

Decentralized Detection With Correlated Gaussian Observations: Parallel And Tandem Networks With Two Sensors

Signal detection in cognitive radio involves the determination of presence or absence of a primary user signal so that the secondary user may opportunistically gain access when the spectrum is unoccupied. In decentralized sensing scheme, two or more secondary users sense the spectrum, process individual observation and then pass the quantized data to a fusion center where a decision with regard to which hypothesis being true, that is, a signal being present or absent, is made. In the second part of the thesis, we study Bayes error performance of two-sensor tandem network designed to detect the presence or absence of deterministic signals in correlated Gaussian noise. Hence, the correlation coefficient remains identical under both hypotheses. Specifically, we address the question of which sensor ought to serve as the fusion center for optimal detection performance. In the process of this query, we draw some inference parallel to the “Good, Bad and Ugly’’ signal regions formulated originally for the two-sensor one-bit-per-sensor parallel fusion network by Willet,et.al. In the tandem “Good” region, numerical results conclusively show that the strategy of placing better sensor, i.e the sensor with higher signal to noise ratio, serving as the fusion center is preferred for better detection performance. In the first part of thesis, we study the error performance in a parallel network consisting of two sensors. In the parallel configuration, each sensor quantizes it\u27s own observation into a single-bit and transmits them to the fusion center. At the fusion center, the performance of AND and OR rules are examined by assuming the observations at the two sensors are jointly Gaussian, with specific means, variances and correlation coefficient, under hypothesis H1, whereas the observations under H0 are still Gaussian with specific means and variances but are statistically independent. The optimum quantizers at each sensor are found by minimizing the probability of error at the fusion center. We use a genetic algorithm (GA) to find a sub-optimal solution. It was observed that, when prior probabilities of hypotheses are equal, AND performs at least as well as OR

Accurate Cooperative Sensor Fusion by Parameterized Covariance Generation for Sensing and Localization Pipelines in CAVs

A major challenge in cooperative sensing is to weight the measurements taken from the various sources to get an accurate result. Ideally, the weights should be inversely proportional to the error in the sensing information. However, previous cooperative sensor fusion approaches for autonomous vehicles use a fixed error model, in which the covariance of a sensor and its recognizer pipeline is just the mean of the measured covariance for all sensing scenarios. The approach proposed in this paper estimates error using key predictor terms that have high correlation with sensing and localization accuracy for accurate covariance estimation of each sensor observation. We adopt a tiered fusion model consisting of local and global sensor fusion steps. At the local fusion level, we add in a covariance generation stage using the error model for each sensor and the measured distance to generate the expected covariance matrix for each observation. At the global sensor fusion stage we add an additional stage to generate the localization covariance matrix from the key predictor term velocity and combines that with the covariance generated from the local fusion for accurate cooperative sensing. To showcase our method, we built a set of 1/10 scale model autonomous vehicles with scale accurate sensing capabilities and classified the error characteristics against a motion capture system. Results show an average and max improvement in RMSE when detecting vehicle positions of 1.42x and 1.78x respectively in a four-vehicle cooperative fusion scenario when using our error model versus a typical fixed error model