Indoor Ultra-Wide Band Network Adjustment using Maximum Likelihood Estimation

This study is the part of our ongoing research on using ultra-wide band (UWB) technology for navigation at the Ohio State University. Our tests have indicated that the UWB two-way time-of-flight ranges under indoor circumstances follow a Gaussian mixture distribution that may be caused by the incompleteness of the functional model. In this case, to adjust the UWB network from the observed ranges, the maximum likelihood estimation (MLE) may provide a better solution for the node coordinates than the widely-used least squares approach. The prerequisite of the maximum likelihood method is to know the probability density functions. The 30 Hz sampling rate of the UWB sensors enables to estimate these functions between each node from the samples in static positioning mode. In order to prove the MLE hypothesis, an UWB network has been established in a multi-path density environment for test data acquisition. The least squares and maximum likelihood coordinate solutions are determined and compared, and the results indicate that better accuracy can be achieved with maximum likelihood estimation.