Statistical Characterisation of the Indoor Pseudorange Error using Low Cost Receivers

Kurzfassung

The Global Positioning System (GPS) has made outdoor localizsation broadly available and is commonly employed for automotive navigation by a very large number of users. Low cost devices available on the mass market are currently able to track satellite signals down to a signal power of -159dBm. With these high sensitivity devices, receiving (i.e. acquiring) GNSS signals indoor becomes possible. However, the building material used and the kind of construction greatly influences the signal propagation. For instance, European houses are more affected by attenuation as they are now mostly built of concrete compared to many American houses which are often built of wood and brick work. Typical wave propagation mechanism into most European buildings is through windows as ordinary glass is attenuates electromagnetic waves less compared to thick concrete walls. Bearing this in mind, diffraction at window frames, as well as outdoor and indoor reflections play an important role in indoor GNSS positioning through the effects on the propagation channel. In this contribution we will report on characterizations of both the temporal and spatial correlations of the errors that are caused by multipath propagation and diffraction/refraction. Since a room and its major fixtures such as furniture and windows, as well as the surrounding building(s), are largely static, a temporal correlation of pseudorange errors measured at a fixed point introduced by the propagation channel is to be expected (note that the satellite´ s motion is too slow to cause sudden channel changes due to changes in the incoming wave angles). A certain spatial correlation is also to be expected as echo contributions will often cover an area of several meters or more in receiver position change. For the case of a moving subject, such as a pedestrian, both temporal and spatial correlations will play a role while the person moves through the building. In order to investigate this we performed measurements using low cost receivers with commercial Sirf III chipset to characterize pseudorange errors in indoor environment. Our main motivation is indoor pedestrian navigation using low cost sensors available in the mass market. Of particular interest is the fact that pedestrians walk slowly and errors in the pseudorange estimates cannot be considered as independent in time and spatial dimension. For the measurements performed we simultaneously used five receivers placed with a certain separation in order to measure spatial correlation of the pseudorange error. Measurements took place at several positions located in a large entrance hall of a three-story building. At each measurement point the separation was varied from 20cm to 5m. As ionospheric and tropospheric errors were corrected using an outside receiver placed on the roof of a nearby building, the error sequences are mostly the result ofwave propagation effects as well as thermal noise. The latter, of course, will be essentially uncorrelated over time and space. In the paper we will present the pseudorange error correlation in time and space as well as other statistical characterisations such as the error probability distribution. We belief that these results are of special interest for designing optimal position estimators such as sequential Bayesian estimators, since any colored error processes need to be included in the dynamic system model to achieve optimal performance. In this sense the results are interesting for data fusion in order to combine GNSS sensors with other sources of information like Inertial-Navigation sensors, mobile radio positioning, or map matching techniques.