Measurement and modeling in sensor networks

In this project we are constructing a least-squares model based on measured data. What is provided are noisy data from one or more sensors. Also is known that an unknown model is generated by set of functions that come from a known family of functions. However it is unknown ahead of time what subset of functions and parameters generated the data. The task is to estimate this model using as few measurements as possible. The method of least-squares provides a model with small total error. This model is optimal in the least-squares sense but the variance of the model is not guaranteed and can be large in certain subdomain. With large data samples consistency theorems guarantee convergence to the true model, but small data samples can result in a catastrophic fit, so additional measurements are required. The purpose of these measurements is to decrease model variance. We propose a minimization procedure that tests new measurement points and selects an optimal point.