- Open Access
Heading estimation fusing inertial sensors and landmarks for indoor navigation using a smartphone in the pocket
© The Author(s). 2017
- Received: 28 July 2017
- Accepted: 8 September 2017
- Published: 25 September 2017
Principal component analysis (PCA)-based approach for user heading estimation using a smartphone in the pocket suffers from an inaccurate estimation of device attitude, which plays a central role in both obtaining acceleration signals in the horizontal plane and the ultimate global walking direction extraction. To solve this problem, we propose a novel heading estimation approach based on two unscented Kalman filters (UKFs) fusing inertial sensors and landmarks. The first UKF is developed for the recalibration of device attitude estimation. We mathematically derive the measurement equation connecting observed user heading from landmarks with the quaternion vector representing device attitude. To decrease the nonlinearity of the measurement equation and make the filter more robust, we deploy the difference between user heading derived from the landmark and estimation result of PCA-based approach as the observation variable. The second UKF is developed for user heading estimation fusing estimation results of PCA-based approach and observed user headings from landmarks. Besides, we develop a robust landmark identification method by exploiting the acceleration and device pitch patterns, while noisy barometers are no longer required as previous methods. Experiments show that the proposed landmark-aided user heading estimation approach may improve accuracy performance significantly, which is very useful for continuous indoor navigation.
- Indoor navigation
- User heading estimation
- Unscented Kalman filter
- Principal component analysis (PCA)
Indoor positioning techniques have been paid increasing attentions from industry and academia due to the mass market for positioning applications. For outdoor environments, Global Navigation Satellite Systems (GNSSs) may provide reasonable accuracy performance. However, due to signal attenuations, they are always unavailable for indoor environments. Among various indoor positioning approaches [1, 2], pedestrian dead reckoning (PDR) using inertial sensor built-in smartphones is a promising solution, since it is self-contained and requires no extra infrastructures. There are two kinds of PDR, the strapdown approach  and the step-and-heading approach [4, 5]. The accumulated tracking errors of the strapdown approach may grow rapidly, since it involves a double integration of noisy acceleration signals. The strapdown approach is only feasible when continuous corrections are available, such as zero velocity updates for foot-mounted situations.
For unconstrained use of smartphones, such as a device put in the trouser pocket, it is more suitable to deploy the step-and-heading approach . Step-and-heading approach infers the current pedestrian position sequentially by adding relative displacement to the position of previous step. The displacement is determined by estimated step length and user heading. User heading estimation is a central problem and the main error source of the step-and-heading approach. Moreover, user heading estimation may also be used in many other areas [7–9], such as human facing direction estimation in virtual reality and human computer interaction in smart environments. This paper focuses on the user heading estimation using a smartphone put in the pocket, which is one of the most popular device-carrying positions .
Due to the changing device orientations caused by body locomotion, such as leg locomotion, it is inapplicable to compute user heading by the most commonly used device estimation approach , which adds heading offset to device heading. This is because the heading offset between device heading and user heading varies due to the changing device orientations and is difficult to be estimated. For a smartphone put in the pocket, uDirect approach  has been proposed by extracting walking direction in a specific region, where the walking direction dominates the acceleration vector. However, the specific region may be easily corrupted by body locomotion. In contrast, the PCA-based approaches  are more robust, since it exploits all samples in the walking step. Regardless of the changing device orientations, PCA may extract the walking direction along the maximum variations of the acceleration signals in the horizontal plane.
In order to obtain the horizontal accelerations more accurately, our previous work has proposed a PCA-based approach called RMPCA , combining rotation matrix (RM) with principal component analysis (PCA) for user heading estimation. Firstly, we continuously track the device attitude by developing extended Kalman filter (EKF) fusing inertial sensors. Then, we combine related rotation matrix to project the accelerations at local device coordinate system (DCS) into the global coordinate system (GCS). Finally, the global walking direction may be extracted by PCA over horizontal accelerations. Due to gyro and acceleration drifts, the accuracy performance of user heading estimation and positioning may degrade rapidly over a relatively short period.
Exploiting landmarks to aid pedestrian navigation is one of the most promising techniques to guarantee user heading estimation performance and limit accumulated tracking errors. Traditional landmark-based methods mainly rely on a pre-defined database and related infrastructures. For example, the densely deployed ultra-wide bandwidth (UWB)  and radio frequency identification (RFID)  anchors may provide distance information from the landmarks to the pedestrian, through time of arrival (ToA) and received signal strength (RSS) measurements, respectively. Wireless local area network (WLAN) or magnetic fingerprints [17, 18] can also be regarded as landmarks to aid pedestrian navigation. Traditional landmark-based methods may improve positioning accuracy significantly. However, these methods may increase the cost and disrupt self-containedness of the PDR system.
Recently, user motion states , including walking stairs and taking elevators and escalators, have been considered as indoor landmarks to aid indoor positioning. These landmarks  require neither extra infrastructures nor complex pre-defined database. Previous works [21, 22] have proposed these landmarks for both location estimation and direct user heading estimation recalibration. Significant user heading and positioning accuracy improvement has been reported. However, a re-estimation of the quaternion vectors describing device attitude is neglected. The accurate estimation of the quaternion vector is critical for ultimate user heading estimation, since it may directly affect the acceleration signal extraction in the horizontal plane and the ultimate global walking direction extraction by PCA. Besides, the previous device attitude estimation method fusing inertial sensors and magnetometers relies on EKF , which cannot adapt the nonlinearity of the measurement equation well.
In this paper, we propose a novel landmark-aided heading estimation approach based on two unscented Kalman filters (UKFs) and a recalibration of device attitude estimation. The main novelty is to fuse landmark information for device attitude recalibrations by constructing an explicit measurement equation in an UKF. The measurement equation relating landmarks with the quaternion vector describing device attitude is mathematically derived upon the principle of PCA-based approach. In order to reduce the nonlinearity of the measurement equation, we deploy the difference between user heading derived from the landmark and estimation result of RMPCA as the observation variable. For ultimate user heading estimation, we develop the second UKF fusing landmarks and estimation results of an improved RMPCA. The improved RMPCA may reduce the nonlinearity of the state equation of the second UKF, by extracting walking direction at a reference coordinate system. Besides, we develop a more robust user motion recognition method for landmark identification. Instead of requiring noisy barometers for vertical displacement detection as previous methods , we just deploy inertial sensors based on the acceleration and device pitch patterns.
We propose a novel heading estimation approach fusing inertial sensors and landmarks based on two developed UKFs and a recalibration of the device attitude estimation.
We derive measurement equation of the first UKF mathematically upon the principle of the PCA-based approach. To decrease the nonlinearity of the measurement equation and make the filter more robust, the heading estimation difference is deployed as the observation variable.
We develop the second UKF fusing landmarks and estimation results of an improved RMPCA, which may reduce the nonlinearity of the state equation of the second UKF.
We develop a robust landmark-identification method without requiring barometers, by only exploiting the inertial sensors and magnetometers.
The rest of the paper is organized as follows: Section 2 gives an overview of the proposed heading estimation approach. Section 3 presents the user motion recognition method for landmark identification. Section 4 describes the first UKF-based device attitude estimation module. Section 5 presents ultimate user heading estimation based on the second UKF. Section 6 provides experimental evaluations of the proposed approach. Finally, conclusions are presented in Section 7.
The landmark identification module deploys a decision tree-based approach to recognize the motion states, including normal walking, standing, walking stairs, taking elevators, and taking escalators. Among these motion states, walking stairs, taking elevators, and taking escalators can be considered as landmarks to aid user heading estimation.
The device attitude estimation module deploys the first UKF to continuously estimate device attitude. The state model of the first UKF involves quaternion-based time evolution equation, while the measurement model involves measurement update from magnetic field values, accelerations under quasi-static situations, and identified landmarks. An explicit measurement equation relating the quaternion vector and user heading is mathematically derived upon the principle of PCA-based user heading estimation approach.
In order to describe the user heading estimation module, we define three coordinate systems, including global coordinate system (GCS), device coordinate system (DCS), and reference coordinate system (RCS). GCS consists of three axes X G, Y G, and Z G, which point east, north, and the opposite direction of the gravity vector. We collect all raw inertial signals including acceleration and angular velocity samples at DCS. DCS consists of three axes X D, Y D, and Z D. The two axes X D and Y D point rightward and forward, respectively, which are parallel with the phone screen. The axis Z D is the cross product of axes X D and Y D. To reduce nonlinearity of the measurement equation in the first UKF and state equation in the second UKF, we define RCS by rotating GCS UHRMPCA radians around Z G counterclockwise, which also includes three related axes X R, Y R, and Z R. The angle UHRMPCA is user heading initially estimated by RMPCA approach for each walking step. It should be noted that DCS and RCS may change with the body locomotion, while GCS is a fixed coordinate system.
User heading is defined as the angle that rotates from positive direction of the Y G axis to the walking directions at GCS counterclockwise. The user heading estimation module deploys the second UKF to fuse identified landmarks with an improved RMPCA. For the improved RMPCA, rotation matrix obtained from the first UKF-based attitude estimation model is firstly used to project the accelerations at DCS into GCS. For each walking step, the accelerations at GCS are then projected into the related RCS. Finally, accelerations in the horizontal plane at RCS are obtained, and the global walking direction is extracted by PCA at RCS. The walking direction is extracted at RCS to reduce nonlinearity of the state equation.
In the first level, we firstly distinguish the elevator from the other motion states by exploiting the unique acceleration pattern of an elevator . For the whole period of taking an elevator, the process includes standing still to wait for the elevator, entering the elevator, standing inside, and finally walking out of it. When standing inside the elevator for a short duration, a pair of positive/negative impulses of accelerations along the gravity direction occur, due to the related hyper-gravity/hypo-gravity effects. Between two impulses, there is a stationary duration, depending on the number of floors the elevator passes. In order to accurately capture the user heading information, when users enter or walk out of an elevator, we deploy the magnitude change of the magnetic field, since the total magnitude notably decreases or increases, respectively.
In the second level, we distinguish taking escalators/standing from walking stairs/walking by exploiting their acceleration variances. The acceleration variances of walking stairs/walking motion states are notably bigger than those of taking escalators/standing, since the former states involve the higher locomotion intensity. Furthermore, in the third level, we distinguish taking escalators from standing by exploiting the variances of the magnetic field values. The magnetic field values of taking escalators change rapidly due to the changed locations of moving escalators, while those of standing remain unchanged.
According to the observations, we may compute the average opening angle, the maximum and minimum leg pitch values for normal walking and walking upstairs/downstairs during offline phase. The related angle values can be seen as the pitch value pattern. During online phase, the pattern-matching process comparing the related angles as seen in (2) and (3) may be carried to distinguish between normal walking and walking upstairs/downstairs.
Confusion matrix for landmark identification
We deploy quaternion vector as the state vector of UKF to describe the time evolution of device attitude. Firstly, we give the state and measurement models of UKF. Then, we derive the measurement equation relating quaternion vector with user heading mathematically upon the PCA-based approach. Finally, we describe unscented transformation and UKF equations.
4.1 Unscented Kalman filter design
4.2 Derivation of measurement equation relating quaternion vector with user heading
Usually, the absolute difference between user heading derived from a landmark and from RMPCA approach may be restricted into a small value, such as less than π/8. As a result, the arc tangent function in Eq. (25) may be approximated by a low-order polynomial function. If the absolute difference exceeds 45°, though the probability is rather low, we will not exploit the landmark to recalibrate the device attitude estimation module.
4.3 UKF equations for device attitude estimation
The state equation of the quaternion vector is linear, while the measurement equation is nonlinear. Therefore, we only need to deploy UT on the measurement equation.
For different landmarks, the uncertainties of the derived user heading are different. User heading of taking an escalator or entering an elevator has a smaller variance than that of walking upstairs/downstairs. We set the measurement noise of each landmark at the target environment during the offline phase. Firstly, we define an interval covering all possible user headings of a specific landmark. Secondly, for simplicity, the measurement noise is assumed to follow Gaussian distribution. We choose a three-sigma interval, where the probability of the user heading values lying in can reach up as high as 98.89%. Thirdly, the center value of the defined interval is set as the observed user heading of the landmark, and the standard deviation is set to one sigma. The parameter settings may vary with different types of the landmarks and realistic environments.
6.1 Experimental setup
6.2 Performance analysis
The proposed landmark-aided approach improves the heading estimation accuracy from two aspects. First, the improved RMPCA approach is developed for user heading estimation without landmarks. The improved RMPCA deploys UKF for quaternion-based device attitude estimation, which may better adapt the nonlinearity of the related measurement equation than previous RMPCA approach using EKF. This aspect can also be verified by the heading estimation result comparisons between the improved RMPCA and RMPCA approaches. Second, we not only deploy landmarks for direct user heading recalibrations, but also for device attitude estimation recalibrations, which may render more accurate extraction of the horizontal accelerations. This is also the reason why the proposed landmark-aided approach performs better than that of landmark-aided improved RMPCA without device attitude recalibration.
In this paper, we propose two UKF-based user heading estimation approach by fusing inertial sensors and landmarks. The second UKF fusing landmarks and estimation results of an improved RMPCA is developed for direct user heading estimation, while the first UKF is developed for device attitude estimation. The proposed approach not only exploits landmarks for direct user heading estimation recalibration, but also for device attitude recalibration, which is important for accurate walking direction extraction. Compared with previous RMPCA approach, instead of using EKF, the improved RMPCA using the first UKF may better adapt nonlinearity of measurement equation. Besides, we develop a robust user motion recognition method for landmark identification, without requiring noisy barometers. Experimental results show that the proposed landmark-aided approach may obtain significant user heading estimation accuracy improvement. Compared with previous landmark-aided RMPCA approach, the proposed approach may reduce the mean absolute heading estimation error by 23.0% (2.05°).
In our future works, more kinds of landmarks such as passing doors and corners will be used to aid user heading estimation and indoor navigation. Besides, more complicated and a large-scale indoor environment including more landmarks will be tested.
This research is supported by National Natural Science Foundation of China (Granted No. 61671168, 61301132, 61601221, and 61301131), and the Fundamental Research Funds for the Central Universities No. 3132017129.
ZD proposed the original idea and wrote this paper; WS and ZQ gave some valuable suggestions and improved the paper; ZN and XL supervised and revised the paper. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
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