Journal of Sensors

Volume 2015, Article ID 915837, 13 pages

http://dx.doi.org/10.1155/2015/915837

## Axis-Exchanged Compensation and Gait Parameters Analysis for High Accuracy Indoor Pedestrian Dead Reckoning

^{1}Key Laboratory of Special Fiber Optics and Optical Access Networks, Ministry of Education, Shanghai University, Shanghai 200072, China^{2}Microelectronic Research and Development Center, Shanghai University, Shanghai 200072, China^{3}Key Laboratory of Advanced Displays and System Application, Ministry of Education, Shanghai University, Shanghai 200072, China

Received 22 September 2014; Revised 12 January 2015; Accepted 27 January 2015

Academic Editor: Zhenhua Zhu

Copyright © 2015 Honghui Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Pedestrian dead reckoning (PDR) is an effective way for navigation coupled with GNSS (Global Navigation Satellite System) or weak GNSS signal environment like indoor scenario. However, indoor location with an accuracy of 1 to 2 meters determined by PDR based on MEMS-IMU is still very challenging. For one thing, heading estimation is an important problem in PDR because of the singularities. For another thing, walking distance estimation is also a critical problem for pedestrian walking with randomness. Based on the above two problems, this paper proposed axis-exchanged compensation and gait parameters analysis algorithm to improve the navigation accuracy. In detail, an axis-exchanged compensation factored quaternion algorithm is put forward first to overcome the singularities in heading estimation without increasing the amount of computation. Besides, real-time heading is updated by R-adaptive Kalman filter. Moreover, gait parameters analysis algorithm can be divided into two steps: cadence detection and step length estimation. Thus, a method of cadence classification and interval symmetry is proposed to detect the cadence accurately. Furthermore, a step length model adjusted by cadence is established for step length estimation. Compared to the traditional PDR navigation, experimental results showed that the error of navigation reduces 32.6%.

#### 1. Introduction

With the increasing popularity of location based service (LBS), as a key factor in LBS, the importance of positioning is widely acknowledged. In practice, outdoor location technology is much more mature than indoor location technology. This imbalance leads to the fact that LBS can hardly be achieved in weak GNSS signal environment such as indoor location. Therefore, numerous scholars and groups are devoted to the research of indoor location, for example, indoor location technologies based on WIFI [1], RFID [2], Bluetooth [3–5], and wireless sensor networks [6]. However, the abovementioned technologies are susceptible to external environment.

Differentiated from other technologies, MEMS-IMU is a technique that applied to positioning with advantages of autonomous measurement. And pedestrian dead reckoning (PDR), one of the most important methods to achieve navigation with MEMS-IMU, was first proposed by Judd and Levi in 1996 [7]. According to the view of Judd and Levi, PDR is simplified by heading detection, filtering, cadence detection, and step length estimation. For convenient analysis, we further simplify four steps to heading detection and walking distance estimation. Cadence and step length are the two gait parameters contained in walking distance estimation.

As for heading estimation, the direction represented by three-parameter method leads to singularities, which have always confused us. To solve this problem, many methods have been put forward. In [8], improved predicted singularity robustness (PSR) is introduced to mitigate the influence of singularities. However, this improvement does not eliminate singularities completely. Thus, according to Lie group, Park and Chung presented the Lie group geometric method which is singularity-free [9]. While the two aforementioned methods focus on avoiding singularities, Yun et al. have chosen to overcome singularities by using “borrow angle” and “return angle” [10]. This method provides a high accuracy overall, but at the cost of an increased calculation workload. Although singularities have been eliminated to a certain extent in the above methods, they are all in static state and are either too deficient or too complex.

As for walking distance estimation, starting with the gait parameters of cadence and step length, [11] calibrates the step length model for each person with two hybridization filters, while it has the inconvenience of offline calibration. To solve this problem, the authors proposed a real-time walking parameters estimation model in [12], where zero-approximation step detection algorithm and walking speed are integrated into the above model to improve the accuracy. Nevertheless, it is a complex calculation process. In application domain, Honeywell first proposed the relationship between cadence and step length in [13], which achieved navigation by accumulating step length obtained from IMU. Most of the step length models are the complex offline training required, and the cadence detection is not sufficiently accurate.

With the problems of deficiency and complexity in heading estimation, offline training, and inaccuracy in walking distance, to deal with the above problems, this paper proposed axis-exchanged compensation and gait parameters analysis algorithm of PDR to achieve a relatively high accuracy indoor navigation by MEMS-IMU. At the beginning, heading singularities are fixed by axis-exchanged compensation factored quaternion algorithm in static state. Then we updated the quaternion by R-adaptive Kalman filter to obtain a real-time heading. Subsequently, walking distance, especially cadence and step length, is estimated according to the characteristic of walking pedestrian. To address cadence, method of cadence classification and interval symmetry is applied to detection; meanwhile, a step length model adjusted by cadence is built to estimate the step length. In addition, since the step length of pedestrian is influenced by walking speed, cadence, individual differences, and other reasons, we customized the step length model for every pedestrian to improve the accuracy of indoor PDR navigation. As the above algorithms and methods are applied to PDR navigation, experiments showed that the navigation error reduces 32.6% by axis-exchanged compensation and gait parameters analysis algorithm.

The rest of this paper is organized as follows. Section 2 describes the heading estimation with axis-exchanged compensation factored quaternion algorithm. To achieve real-time heading output, R-adaptive Kalman filter is proposed as well. Section 3 proposes the estimation method of walking distance in cadence by classification and interval symmetry and in step length by model which is adjusted by cadence. Then, Section 4 describes the entire PDR when it applies axis-exchanged compensation and gait parameters analysis algorithm, while experiments and performance are listed in Section 5. Finally Section 6 concludes this paper.

#### 2. Heading Estimation

Heading direction is an important factor for PDR navigation. In order to obtain the direction, factored quaternion algorithm is used with the advantage of only one-step calculation. However, this method inevitably brings in singularities at some situation because it derived from 3D orientation Euler angles. To eliminate the singularities, axis-exchanged compensation algorithm is applied to factored quaternion without increasing the amount of computation. While the above algorithm is based on static state, for obtaining a real-time heading direction, Kalman filter is used to update the direction. In addition, R-adaptive mechanism is proposed to improve the Kalman estimation accuracy.

##### 2.1. Axis-Exchanged Compensation and Factored Quaternion

###### 2.1.1. Factored Quaternion Algorithm

To describe the factored quaternion algorithm and orientation, we first introduce two coordinate systems including body coordinate and North-East-Down coordinate. The body coordinate represents the orientation of MEMS-IMU, and North-East-Down (NED) coordinate represents the orientation of earth. Initially, body coordinate coincides with the NED coordinate, and body coordinate rotates the yaw angle (heading direction) degree around -axis. Then, it rotates pitch angle degree around -axis as well. Subsequently, the coordinate rotates roll angle degree around -axis. In this way, the above three Euler angles can represent any orientation. Moreover, we applied factored quaternion algorithm to Euler angles and computed quaternions along with Euler angles, respectively. And finally three direction quaternions are fused to one unit quaternion.

*(1) Quaternion of Pitch and Roll*. Due to the rotation independence of horizontal plane and vertical plane, for convenience, pitch and roll are calculated in advance.

The quaternions are derived in [10] and quaternion of pitch iswhere

Here, when ; conversely, when .

Similarly, quaternion of roll is given bywhere

Here, and are the acceleration of -axis and -axis, respectively.

*(2) Quaternion of Yaw.* For obtaining yaw , the magnetic flux density is assumed as and then converted to horizontal plane. The transformation formula is

In order to further simplify the problem, the declination exists in magnetic north and due north is ignored, and the geomagnetic field north is represented by symbol . At this point, relationship between magnetic flux density and geomagnetic field intensity in horizontal plane can be described as follows:

Calculating the normalized magnetic flux densities and in horizontal plane, the sine and cosine value for yaw are

Finally quaternion of yaw can be represented as

*(3) Quaternion Data Fusion*. To improve the accuracy, formulas (1), (3), and (8) are fused together as a unit quaternion , which can be expressed as

The flow of fusion is illustrated in Figure 1.