Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors

Abstract

Abstract: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.

Grid-Based Bayesian Filtering Methods for Pedestrian Dead Reckoning Indoor Positioning Using Smartphones

“…Moreover, they integrated a model to limit outliers in the measurement data and to resist negative effects of state model disturbances. Ettlinger et al [ 40 ] observed systematic deviations present in the data obtained from sensors. Their research is focused on an analysis of a measure for the reliability (so-called partial redundancies), i.e., how well systematic deviations can be detected in single observations, and the behavior of partial redundancy by modifying the stochastic and functional model of the Kalman filter.…”

Georeferencing of an Unmanned Aerial System by Means of an Iterated Extended Kalman Filter Using a 3D City Model

“…Indirect 4 georeferencing comprises methods where the pose of the MSS is determined by measurements towards known targets. These targets may be flat markers with a specific pattern (Abmayr et al 2008) or simple 3D geometries, such as cylinders or spheres (Elkhrachy and Niemeier 2006). The position of the targets within the superordinate coordinate system is determined using an external sensor, for example, a total station.…”

Heading Estimation for Pedestrian Dead Reckoning Based on Robust Adaptive Kalman Filtering

“…Regarding the steady holding modes, the device attitude heading should be estimated first by fusing the aforementioned sensor data. The fusion is always by means of complementary filters (CFs) [ 10 , 11 , 12 ] and Kalman filters (KFs) [ 13 , 14 , 15 , 16 , 17 ].…”

“…The system was fixed on waist of pedestrian and the quadrotor unmanned aerial vehicle (UAV) to test the heading estimation accuracy, and the results show that the mean heading estimation errors are less than 10° and 5° respectively. Ettlinger et al [ 17 ] found that the systematic deviations in the observed data caused significant divergence between the estimated and the reference trajectory, and thus proposed a Gauss-Helmert model-based Kalman filter for reliability analysis in orientation determination with smartphone sensors. Deng et al [ 4 ] proposed a quaternion-based EKF for heading estimation using smartphone-embedded sensors.…”