The GRAIL Project

The GRAIL project is the search for:

General - usable with any radio format
Realtime - results in < 1 second
Adapatable - automatically adapt to changes
Indoor - deal with multipath effects
Localization - generate coordinates for a client

The GRAIL project is part of the PANIC lab and operates under the direction of Dr. Richard Martin. The GRAIL project seeks to not only provide a highly accurate indoor localization system, but also architect the system in such a way as to make it an attractive application, namely by making it highly extensible, easy to set up and operate, and capable of using an extant commodity wireless communication network.

Introduction to Bayesian Localization

Fundamentals of Bayesian Inference:

Bayesian inference is the process of fitting a probability model to a set of data and summarizing the result by a probability distribution on the parameters of the model and on unobserved quantities such as predictions for new observations.

Fundamentals of Bayesian Data Analysis:

Bayesian data analysis is used for making inferences from data using probability models for quantities we observe and for quantities about which we wish to learn. The process of Bayesian data analysis is divided into three steps:

1. Setting up a full probability model: a joint probability distribution for all observable and unobservable quantities in a problem. The model should be consistent with knowledge about the underlying scientific problem and the data collection process.

2. Conditioning on observed data: calculating and interpreting the appropriate posterior distribution which is the conditional probability distribution of the unobserved quantities of ultimate interest, given the observed data.

3. Evaluating the fit of the model and the implications of the resulting posterior distribution: does the model fit the data, are the substantive conclusions reasonable, and how sensitive are the results to the modeling assumptions in step 1?

One can alter and expand the model and repeat the three steps.

Using Bayesian networks in Localization:

The Bayesian network (BN) is a graphical model that encodes dependencies and relationships among a set of random variables. The vertices of the graph correspond to the random variables and the edges represent dependencies. Bayesian inference in conjunction with Bayesian networks offers an efficient and principled approach for avoiding the over-fitting of data.

For localization, we have developed several Bayesian graphical models to encode the relationship between the received signal strength and the location based on signal-to-distance propagation model. The Bayesian networks under study include both non-hierarchical and hierarchical Bayesian graphical models. We first choose the prior distributions for the initial parameters of the model, then use the training data to obtain the posterior distribution of the parameters, and further predict the location of the sensor node. We have proposed the point-based BN as well as the area-based BN for location prediction.

We use the statistical package WinBUGs (www.mrc-bsu.cam.ac.uk/bugs/) for Markov Chain Monte Carlo (MCMC) simulation. In order to reduce the computation cost, we also developed our own statistical sampling tool which is called Fast Solver. The Fast Solver has reduced the computation time significantly when applying Bayesian networks for localization.