Positioning and Navigation in Complex Environments by Kegen Yu

Author:Kegen Yu
Language: eng
Format: epub
Publisher: IGI Global

Algorithm 2. OMP based Multi-TOA estimator

Input: Measurements at the -th anchor, Dictionary, Number of searched paths

Output: after K iterations

1: Initialization

2: while do

3:       {finding the column in dictionary A with maximum correlation with residual.}

4:

5:      .

6:      i=i+1

7: end while

8:

In line 5, denotes the matrix composed by the columns defined in the set. The term represents the pseudo inverse of. Finally, λ denotes the time resolution of the dictionary, i.e. the ability to resolve paths, and is related to the sampling period. The number of columns of the dictionary is related to the time resolution in the following manner:. By a simple examination of Algorithm 2, it can be seen that the number of identified paths by the CS procedure corresponds to the number of iterations K as well.

Numerical Results

Next, we present some numerical experiments to evaluate the performance of the proposed method and its comparison to a non-CS benchmark TOA algorithm. We focus on the IEEE 802.15.4a UWB channel models, a standard developed with actual real measurements as described in (Molisch et al. 2004). In particular, we focus in the CM3 LOS Office model which is an indoor office environment characterized to exhibit dense multipath. The simulation setup is configured as follows: A single target is randomly allocated in a room with four beacons placed at the corners and is continuously transmitting. The transmitted pulse is a baseband Gaussian monocycle of duration. The received signal is low pass filtered to avoid aliasing and then sampled at 2 GHz at each beacon. This set-up is performed using a total of 500 distinct realizations of the IEEE 802.15.4a CM3 channel model and with different target’s positions.

The time of frame denotes the time between consecutive pulses. The total observation window or integration time at the receiver is determined by the coherence time of the fading channel and it limits the number of frames that can be used for averaging. Finally, the time resolution of the dictionary is set to be multiple of the sampling period, defined as. Therefore by decreasing the resolution, the estimator accuracy can be improved at the expense of a gain in coherence of the dictionary, which can reduce the performance of the CS algorithm.

To strictly focus on the performance behavior due to compression and remove the effect of insufficient data records, the size of the compressed observations was forced to be the same for any compression rate. Thus, for a high compression rate, the estimator took samples for a larger period of time. In Table 1, this effect is illustrated:

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