Bayesian Multi-sensor Navigation Incorporating Pseudo-ranges and Multipath Model

Abstract

The accuracy provided by a Global Navigation Satellite System (GNSS) is sufficient for many outdoor applications, but it strongly suffers in indoor and urban canyon environments from multipath and signal blockage. In consequence, the quality of location based services is often poor indoors. One of the successful approaches to tackle this problem is to combine GNSS position outputs with other sensors in order to increase the accuracy, availability and integrity of GNSS positioning. Examples of such sensors are inertial sensors, compasses, mobile phone networks (TOA, AOA and Cell ID), WLAN and RFIDs. Maps and floor-plans can provide additional information that improves navigation. In this paper a Sequential Bayesian Estimator that performs enhanced fusion of heterogeneous sensors and pedestrian mobility models will be presented. Additionally, the performance of an implementation of this estimator will be evaluated. In order to utilize GPS in indoor and urban canyons, where often less than 4 satellites are visible it is advantageous to use individual pseudoranges in the fusion process, instead of the receiver´s estimated position. To facilitate this, the following steps are carried out: - Raw pseudo-ranges and other satellite parameters are extracted from the receiver. - Standard ionospheric, tropospheric, satellite and user clock error models are implemented. - Correction models for the remaining (un-modeled) errors are built. Namely fast and slow errors. - Spatial and temporal correlation multipath error model is additionally implemented. Sequential Bayesian positioning estimators are used widely to combine such sensors due to their ability to include the dynamics of the pedestrian " movement models" and additionally, propagate the estimates using probabilistic representations. With such probabilistic representations different sensors can be represented with their appropriate accuracy. This representation is the basis for optimally combining measurements of heterogeneous sensors. Several other sensors are included in the framework. In this paper, various combinations of foot mounted inertial sensors, compass, altimeter, floor-plans with GNSS and the resulting accuracy are investigated quantitatively. Mobility models: The prediction stage of sequential Bayesian positioning estimators depends entirely on the movement model to determine the probability density function of the pedestrian´s location and motion at each time step. A movement model that accurately represents the pedestrian´s motion ensures that measurement data used for positioning is consistent with how a pedestrian might move. The three-dimensional pedestrian movement model presented in [1] is used. Its incorporation of the knowledge of maps and floor-plans is one of the advantages of this model. Fusion algorithm: The proposed sensor fusion scheme is based on a cascaded estimation architecture. At a lower level an extended Kalman filter is used for the foot mounted inertial sensor to estimate the step-wise change of position and direction of one or optionally both feet respectively. These estimates are combined in turn as measurements in an upper Rao-Blackwellised particle filter with the measurements of the other sensors. The two levels are needed since the inertial sensor provides output in much higher data rate than the other sensors. A Rao-Blackwellised particle filter is used in order to reduce the complexity resulting from the increase of the number of states when working on the pseudo-range level. Examples of these states are fast errors, slow errors and multipath errors for each visible satellite. This is in addition to user clock, user position, speed, altitude and direction. Performance Analysis: Quantitative and qualitative analysis of the performance of the framework was carried out. Several ground truth were carefully measured to the centimeter accuracy indoor and outdoor in our office environment. Several indoor/outdoor walks were done were the error between the estimated position and the ground truth points were calculated when passing by each of them. Some results of the estimation error during these walks will be shown.