Time delay estimation in dense multipath with matched subspace filters

Efficient multipath time delay estimation is of great importance for positioning with Ultra-Wide-Band signals in indoor environments. In dense multipath environments a simple assumption is to model the multipath terms as attenuated and delayed copies of a known waveform. A more realistic model is however the scenario where the pulse shape is different for every multipath term due to scattering effects and the directionality of the antennas. For the purposes of positioning we face three problems. Signal detection, time delay estimation of the strongest path, and leading edge detection. Leading edge detection is necessary since the strongest path may not be the first. We apply Maximum Likelihood Estimation and Generalized Likelihood Ratio Tests to these problems. In the case of a known pulse shape this leads to the well known matched filter. In the case of unknown pulse shape we show that the matched subspace filter is the optimal solution. Another significant property of the matched subspace filter is that it does not require Nyquist rate sampling. Beyond these advantages, the matched subspace filter is not computationally demanding. Finally we discuss various leading edge detection methoods like generalized likelihood rule (GLR) and energy detectors.