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A. Ettlinger, H.-B. Neuner, T. Burgess:
"Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors";
Sensors, 414 (2018), 18; 21 pages.

The topic of indoor positioning and indoor navigation by using observations from
smartphone sensors is very challenging as the determined trajectories can be subject to significant
deviations compared to the route travelled in reality. Especially the calculation of the direction
of movement is the critical part of pedestrian positioning approaches such as Pedestrian Dead
Reckoning ("PDR"). Due to distinct systematic effects in filtered trajectories, it can be assumed that
there are systematic deviations present in the observations from smartphone sensors. This article
has two aims: one is to enable the estimation of partial redundancies for each observation as well as
for observation groups. Partial redundancies are a measure for the reliability indicating how well
systematic deviations can be detected in single observations used in PDR. The second aim is to analyze
the behavior of partial redundancy by modifying the stochastic and functional model of the Kalman
filter. The equations relating the observations to the orientation are condition equations, which do
not exhibit the typical structure of the Gauss-Markov model ("GMM"), wherein the observations
are linear and can be formulated as functions of the states. To calculate and analyze the partial
redundancy of the observations from smartphone-sensors used in PDR, the system equation and
the measurement equation of a Kalman filter as well as the redundancy matrix need to be derived
in the Gauss-Helmert model ("GHM"). These derivations are introduced in this article and lead
to a novel Kalman filter structure based on condition equations, enabling reliability assessment of
each observation.

Kalman filter; Gauss-Helmert model; reliability; partial redundancy; orientation determination; indoor navigation

http://dx.doi.org/10.3390/s18020414

https://publik.tuwien.ac.at/files/publik_289707.pdf