Gravity-Based Methods for Heading Computation in Pedestrian Dead Reckoning

Abstract

One of the common ways for solving indoor navigation is known as Pedestrian Dead Reckoning (PDR), which employs inertial and magnetic sensors typically embedded in a smartphone carried by a user. Estimation of the pedestrian's heading is a crucial step in PDR algorithms, since it is a dominant factor in the positioning accuracy. In this paper, rather than assuming the device to be fixed in a certain orientation on the pedestrian, we focus on estimating the vertical direction in the sensor frame of an unconstrained smartphone. To that end, we establish a framework for gravity direction estimation and highlight the important role it has for solving the heading in the horizontal plane. Furthermore, we provide detailed derivation of several approaches for calculating the heading angle, based on either the gyroscope or the magnetic sensor, all of which employ the estimated vertical direction. These various methods-both for gravity direction and for heading estimation-are demonstrated, analyzed and compared using data recorded from field experiments with commercial smartphones.

Keywords: gravity direction; heading estimation; indoor navigation; smartphone sensors.

Figure 1

Structure of the filter for gravity direction estimation. Input signals from the accelerometer and gyroscope are $f\left(t\right)$ and $\omega \left(t\right)$, respectively, while the output $\widehat{\gamma }\left(t\right)$ is the estimated gravity unit vector.

Figure 2

Estimated gravity direction along time, comparing the accelerometer-based method with the gyroscope-accelerometer fusion method.

Figure 3

Comparing estimated heading profiles as obtained by the magnetic-based and the three gyroscope-based methods. Upper and lower panes show the results when each of the gravity direction estimation methods is applied.

Figure 4

Comparing turn rate profiles as obtained by three gyroscope-based methods. The gravity direction here is estimated based on the accelerometer only.

Figure 5

Given a general three-component signal, $u\left(t\right)=\left(u_x\left(t\right),u_y\left(t\right),u_z\left(t\right)\right)$, there are two forms of concatenating magnitude calculation and low-pass filtering in the processing implementation.

Figure 6

Magnitude of angular rate vector, comparing two different forms for sequential processing of the gyroscope raw data.