This paper presents a pedestrian dead-reckoning method that uses seven low-cost wearable sensors distributed on the pelvis, thighs, shanks, and feet. A commercial inertial sensor is also used and mounted on the right foot for the comparison purposes. The proposed method uses the gait kinematics of the lower limbs to compute the positioning solution by estimating the joint angles and step lengths. The positioning solution is compared with Kalman lter based solutions computed from the two types of foot-mounted sensors. Indoor walking experiments with linear and rectangular trajectories are conducted to evaluate the proposed method. The results indicate that the low-cost wearable multisensor system is able to detect the turning motion at corners and provides a 2D position error of less than 1% after walking for 36 m.
Over the past two decades, pedestrian navigation systems have gone into rapid development due to the emergence of micro-electromechanical systems (MEMS). This technology has enabled the miniaturization of many navigation sensors including accelerometers, gyroscopes, magnetometers, and barometers. Most MEMS sensors are as small as integrated circuit chips, lightweight and low-cost and found in consumer devices. These low-cost inertial sensors are available in the market with a price tag of 20 US dollars or less.
The motion of a pedestrian can be estimated using the knowledge of the gait
kinematics of the lower limb segments during walking. Some of the works in
pedestrian navigation can be found in these references [
2.1
There are two advantages in tracking pedestrian motion using foot-mounted
sensors. First, the walking gait can be easily detected using the change of
direction in the gyroscope measurement, especially the sagittal component. Second,
the stance phase during walking introduces a quasi-static period where
pseudomeasurements of zero velocity and zero angular rate can be applied as Kalman
lter updates. The Kalman lter formulation is similar to the implementation
found in the references [
Human walking gait is a cyclic process that alternates between swing and stance
phases. A walking cycle can be de ned as two consecutive gait phases, a pair of
swing and stance in any order. The stance phase is marked by a heel-strike event
and ended by a toe-o event while the swing phase is vice versa. The proposed
method used in this paper requires the information about when the heel-strike
and toe-o events occur. One way is to detect these foot gait events using inertial
sensor mounted on the foot. The detection method for the swing and stance
phases is based on the work reported in [
The human gait kinematic model can be modelled using a skeleton consisting of seven segments connected by joints. These segments are the pelvis, the left and right thighs, the left and right shanks, and the left and right feet. This paper uses a simpli ed skeletal model that replaces the feet with an extended shank from knee to heel, as shown in Fig. 1a, to reduce the complexity. The model has four joints: two hips (HL and HR) and two knees (KL and KR). The hip joints are connected by the pelvis and are allowed to move with three degrees of freedom. Meanwhile, the knees are modelled as single axis revolute joints which can only rotate in the sagittal plane.
The computation of forward kinematics requires one end of the links to be xed while the other end is free to move. This condition ts the cyclic nature of the walking cycle. The computation sets the xed end to be the standing foot while the other end be the swinging foot and alternates between steps. The mechanization of the forward kinematics starts from the xed foot and follows the skeletal linkages until the other foot. Based on the model shown in Fig. 1a, this computation requires all three attitude angles of the pelvis sensor and the pitch angles of the thigh and shank sensors. Assuming the right foot is in stance
HR
KL KR Stance
FL X FR Toe-Of
KL
HL
HR
KR
FR Heel-Strike (a) Human skeletal (b) Step sizes extracted from mechanization model of lower limbs. of forward kinematics of lower limbs. phase and the left foot is in swing phase, the forward kinematics equations can be written as follows where the subscripts are described by Fig. 1a. The position vectors are expressed in the local level frame, denoted by pn, and the symbol Cbn; denotes the direction cosine matrix transforming from body frame to local level frame. This matrix is computed based on the estimated attitude angles. The lengths of body segments are expressed in the body frame and written as `b . For the case where the left foot is in stance phase and the right foot is in swing phase, the forward kinematics equations need to be adjusted by swapping the subscripts L and R. The starting point (pnF R or pnF L) is assumed to be the local origin position in each mechanization.
The attitude estimation algorithm used in this paper is based on the
gradient descent algorithm proposed by Madgwick et al. [
The kinematics of lower limbs can be used to estimate the step length and
its corresponding azimuth at each step. A pedestrian dead-reckoning lter can
then be implemented using these two observations. A simpli ed Kalman lter is
adopted from the reference [
N^ ; E^; ^
k+1 = N^k + s cos ^k; E^k + s sin ^k; ^k where s represents a constant step length estimated assuming the pedestrian moves at 1 m/s. The measurements are the step length and heading estimated by the kinematics of the lower limb segments. (2) (3) 3
Experiments zk = s~k ~k T
In the experiments, one sensor was mounted on each foot, shank, and thigh, and two sensors were mounted on back of the pelvis as shown in Fig. 2a. One of the pelvis sensors is redundant and only one is used in the computation. These wearable sensors were mounted such that the right leg had MPU-9250 modules while the left leg had MPU-6050 modules, while the pelvis had one of each. Both sensor modules are manufactured by TDK Invensense. The sampling rate was set at 50 Hz and two microcontrollers were used to collect the data send to a computer for logging. Additionally an Xsens MTi-G-710 was mounted on the right foot below the low-cost module to use for comparison purposes.
The experiments were conducted in an empty o ce room with approximate dimensions of 6:5 11 m. There were 44 reference points marked on the ground with one 1 m spacing. The room layout and walking paths are shown in Fig. 2b. Two walking scenarios were conducted: straight line walk and rectangular loop. In the straight line walk, the test subject walk with approximately equal step lengths of 75 cm while the rectangular walk consisted of approximately 75 steps in total. In addition to the low cost and commercial inertial sensors, the test subject was also video recorded in order to compare the estimated leg segment angles with those obtained from the wearable multi-sensor system. 4 4.1
Orientations of Lower Limb Segments (a) Pose estimation using OpenPose library. ]10 g e 0 d [ l lo-10 R -2016 17 18 19 20 21 22 23 24 25 26 ]g10 ed 0 [ h tc-10 i P -2016 17 18 19 20 21 22 23 24 25 26 ]10 g e 0 d [ aw-10 Y -2016 17 18 19 20 Tim2e1 [s] 22 23 24 25 26 (b) Attitude angles of pelvis. ]40 g ed20 [ h itc 0 P t fLe-20 -40 17 ]g40 [ed20 ch itP 0 t h ig-20 R -40 17
OMpaedngPwoicske AHRS OMpaedngPwoicske AHRS ]50 g [e d h itc 0 P ft e L -50 ]50 g [ceh d itP 0 it h g R -50 18 19 20 21 22 23 24 17 18 19 20 21 22 23 24 18 19
To check the validity of the estimated pitch angles from thighs and shanks, a
publicly released computer vision library (OpenPose [
gyroscope and magnetometer errors. The pitch angles estimated by OpenPose and sensor fusion algorithm are plotted in Fig. 3c and Fig. 3d. These two results have a good agreement between the two estimated pitch angles. The OpenPose results have larger variation on the thigh segment and smaller variation on the shank due to the fact that the 2D projected area of the thigh is both larger and less rectangular than the shank. There are some outliers due to the failure of the classi cation algorithm in di erentiating between the left and the right limbs (shown by the rst foot step in Fig. 3a). 4.2
The equations of the forward kinematics require two inputs, the segment attitude angles and the segment lengths. The attitude angles are estimated using the gradient descent algorithm. The segment lengths can be obtained by measuring the limb segments directly.
MPU-9250 EKF-ZUPT
ZUPT 3 2 1 0 ]-1 [m-2 h tr-3 o N -4 -5 -6 -7 -8
The results of mechanizing the forward kinematics are plotted in Fig. 4a as position trajectories of the lower limb joints and heels. Based on the position of the right foot, the nal position solution has drifted 0.42 m to the left and 0.56 m downward. The total forward travelled distance error is 0.08 m over 4.5 m. The vertical error is due to the e ect of ignoring the foot segments in the forward kinematics model. During walking, the foot segment rotates the heel upward after each heel-strike. Treating this foot rotation as quasi-static motion causes the position solution to drift on the vertical axis. The other components of the position errors are caused by the accumulation of the errors of the attitude angles. 4.3
For comparison, the typical foot-mounted EKF algorithm is implemented an applied both the MPU-9250 and Xsens MTi-G-710 data. The lter is tuned such that an optimal solution can be obtained by selecting the values of the process noise matrix and measurement covariance. For both sensors, the process noise models of the attitude and the velocity are modelled as random walks driven by the noises in the gyroscope and accelerometer. The augmented bias states are simply modelled as random constants.
The results shown in Fig. 4a indicate that there are signi cant di erences in the position solutions computed with the EKF-based algorithm (Section 2.1). The zero measurement updates cannot correct the error drift on the lowcost MPU-9250 sensor that is signi cantly larger than the accumulated error on the Xsens. The purple line (INS-ZUPT) represents the foot position solution computed by mechanizing the inertial equations with zero velocity pseudomeasurement. This computation strategy is better for the low-cost inertial sensors than applying the EKF framework.
The Fig. 4a also indicates that the kinematics of the lower limbs can be used to improve the positioning solution of the low-cost sensors. The angular rates and accelerations estimated from the inertial sensors can accumulate huge errors when going through multiple time integrals to get the position estimates. By using the kinematics of lower limbs, there is only one time integral function used in order to estimate the attitude angles from the angular rate measurements. 4.4
The motion data collected during a rectangular walk are processed using di erent algorithms described in Section 2. The size of the rectangular path is about 4 m 5 m. The test subject starts and ends the walking experiment at the same location. The EKF lters of the two foot-mounted sensors are tuned with the same values with the straight line walk.
The performance comparison is tabulated in Table 1. The result computed by mechanizing the inertial equation with ZUPT (INS-ZUPT) has a smaller error, but the foot-mounted sensor is not able to estimate the heading accurately. The PDR results do not represent the best possible PDR solution due to the simplicity of the lter architecture. This simple lter was implemented to demonstrate that the step length and heading estimated by the equations of the forward kinematics can be used as the inputs to the navigation lter. The kinematics of lower limb can detect the turns at the corners despite using such a simple attitude estimator. The heading is mainly estimated from using using the pelvis mounted sensor. The error of the forward kinematics is small. Thus, this computation strategy is able to estimate the step lengths.
This paper proposes a method to use step lengths and orientation angles as the inputs to the pedestrian dead-reckoning lter. These gait parameters are estimated using the gait kinematics of the lower limbs. The kinematics of lower limbs are able to detect turns and provide positioning error of < 1% of total travelled distance while using low cost inertial sensors. The results of this paper cannot assess the complete performance of a PDR system due to the small testing area. Future work will include larger experiment area and vertical displacement.