The Pedestrian dead reckoning (PDR) using IMU mounted on trunk (e.g., back or chest), which is called trunk-mounted PDR, based on the inertial navigation system (INS) has better positioning performance due to the use of INS mechanization. However, the positioning error would accumulate rapidly because of the high noise level of low-cost inertial measurement unit (IMU). Existing trunk-mounted PDR are almost based on the assumption that the lateral and vertical velocity are zero, the same with the IMU is affixed to the vehicle, called nonholonomic constraint (NHC). However, the human body is a non-stationary platform with swaying motion observed in pedestrian movement, which does not align with the NHC. In this paper, the pedestrian movement pattern is modeled as an inverted pendulum model (IPM), that one point is the foot on the ground and the other one is the IMU mounted on the trunk, with the length of the pendulum is the distance from the IMU to the ground. At the same time, a trunk-mounted PDR based on IPM is proposed, which contains velocity measurement based on IPM (IPM-V) and distance increasement measurement based on IPM (IPM-D). Based on IPM-V, lateral speed is calculated using angular rate from gyroscope and length of the pendulum without assuming zero value, while lateral and vertical distances remain at zero within a single step cycle depending on IPM-D. Experimental findings demonstrate that the proposed method offers enhanced positioning accuracy and robustness compared to existing trunk-mounted PDR methods, with an 80% improvement in positioning accuracy.
The demands for navigation and positioning have increased rapidly in people’s daily lives[
Current PDR primarily relies on the integration of inertial navigation systems, specifically the
Foot-mounted PDR which utilizes an IMU embedded in shoes. With high frequency of sample,
Footmounted PDR has the ability to provide continuous 3-dimension position in real world space. Indeed,
Proceedings of the Work-in-Progress Papers at the 14th International Conference on Indoor Positioning and Indoor
the errors will accumulate rapidly because of measurement noise when using a built-in Micro-Electro
Mechanical System (MEMS) IMU without any other measurement[
Some researchers have taken attention to the potential of mounting IMU on trunk(e.g., waist,
back, chest) to promote PDR to broader applications. [
This paper introduces a trunk-mounted PDR based on only one IMU, using the inverted pendulum model (IPM) derived from pedestrian movement patterns. This system contains measurement of velocity based on IPM (IPM-V) and measurement of distance increasement based on IPM (IPM-D). Based on IPM-V, lateral speed can be computed by the date from the gyroscope. Based on IPM-D, lateral and vertical distance are zero in one step cycle. The proposed system only relies on an IMU consisted by accelerometers and gyroscopes, without additional devices. The experiment results show the proposed method exhibits superior accuracy and robustness compared to existing methods with nearly 80% improvement.
The rest of the paper is organized as follows. Section 2 introduces the principles of trunk-PDR based on IPM including Extended Kalman Filter (EKF) and the IPM derived from pedestrian moving patterns. In Section 0, experimental analyses are carried out to evaluate the proposed approach against conventional methods, focusing on the positioning accuracy. Section 4 summarizes this paper and looks forward to future research.
There are three primary coordinate systems in this paper: the IMU coordinate system (b), the human coordinate system (h), and the local horizontal coordinate system (n). The b-frame represents the IMU coordinate system, with its origin at the center of the IMU and the x-y-z directions indicating forward-right-down. The h-frame represents the human body coordinate system, sharing the same origin as the b-frame, with x-axis pointing towards the pedestrian's front, y-axis pointing to the right, and z-axis forming a right-handed orthogonal system with x-axis and y-axis. The n-frame represents the local horizontal coordinate system, with x-axis pointing towards virtual north, y-axis towards virtual east, and z-axis pointing downward.
The proposed algorithm workflow is depicted in Figure 1. The IMU provides angular rate and specific force inputs to the INS mechanization module for the computation of the IMU's navigation states, including position, velocity, and attitude (PVA). Concurrently, the IPM module utilizes the gyroscope angular rate with the rotation radius to produce lateral velocity measurements and zero increments in lateral and vertical directions. At the same time, the forward velocity module utilizes specific force data to detect steps and estimate step length. The Extended Kalman Filter (EKF) module then fuses these measurements to improve the system's accuracy and reliability.
PVA velocity in the n-frame at the k-th epoch; Cbn,k donates the direction matrix from the b-frame to the n-frame at the k-th epoch. vkb fkb ba,k dt and kb kb bg,k dt donate velocity increasement and angle increasement in the b-frame, respectively. fkb is the specific force. kb is the angular rate. ba ,k and bg,k are the bias of the acceleration and the gyroscope, respectively. g n is the location gravity vector in the n-frame, and is the cross-product form of the vector.
In this article, the 15-dimensional error state based EKF is chosen to integrate the IMU information and virtual measurement.
X r n vn ba bg
T (2)
Where r n is the position error in the n-frame; vn is the velocity error in the n-frame; is the attitude error; ba and bg are errors of bias of the accelerometer and the gyroscope, respectively, which are modeled as a first-order Markov process.
In this paper, the IMU is mounted on the back as an example to analyze the data from the IMU and model the movement when a pedestrian moving. Existing trunk-mounted PDR methods almost depend on the assumption that the lateral velocity is zero. However, as shown in Figure 2, the output of the accelerometer on the y-axis in the h-frame cannot be disregarded because of its notable strength and repetitive characteristics. ) s / m ( n o it a r e l e c c
A
Hence, as shown in Figure 3, a pedestrian's gait involves a rhythmic alternation of the left and right feet swinging and resting while moving. To maintain balance, the pedestrian's center of gravity shifts to the right when the left foot swings forward and the right foot is planted on the ground. This process is mirrored when the right foot swings forward and the left foot is grounded. As a result, the IPM is proposed to describe the pattern of an individual’s movement. The trajectory of the IMU mounted on the trunk follows a curve, represented by a red point in Figure 3.
IMU
When the IMU is firmly affixed to the trunk, it will exhibit lateral movement in accordance with the body's motion. The dynamics of the IMU can be modeled as an inverted pendulum. The foot, in contact with the ground, serves as the pivot point, and the IMU traces a curved path. Consequently, the tiny displacement of the curve can be articulated as follows, as illustrated in Figure 4, when viewed from the xh direction of Figure 3:
Where d s is the tiny displacement of the IMU; d is the tiny angle through which the lever rotates; l is the arm of the inverted pendulum, which is nearly the height from IMU to the ground. By deducing the above equation and projecting the vector to the h-frame, the lateral velocity obtained from the IPM can be expressed as:
ds d l vyh Cbhnbb,xl (3) (4)
Where vyh is the velocity of y-axis in the h-frame; Cbh is the translation matrix form the b-frame to the h-frame, which is confirmed by the mounting angle. nbb,x is the angular rate from the b frame to the n frame. Considering that the MEMS IMU cannot measure the earth rotation for its high noise level, hence, nbb ibb .
The forward velocity is calculated by step-model, which includes detecting steps and estimating
step length[
Where vh means the measurement of velocity in the h-frame; vh is the truth of velocity vector. SL is the step length and dt is the time of step interval at n-th step. SL divided by dt is the forward velocity. v is the noise of measurement of velocity. Given that the velocity update occurs within the h-frame, it is necessary to convert the velocity of the state from the n-frame to the h-frame. Therefore, the velocity from the INS mechanization in the n-frame from can be expressed as: vh [
SL dt
Cbhibb,xl 0] vh v vˆh CbhCˆ bvˆn
n CbhCnb (I )(vn vn ) vh CbhCnb vn CbhCnb (vn)
Where I is the Identity matrix; is the attitude error; is the Skew-symmetric matrix of the vector. Therefore, the measurement of error states can be written as: zv vˆh vh vh CbhCnb vn CbhCnb (vn ) (vh ev ) CbhCnb vn CbhCnb (vn ) v Hence, the measurement transition matrix is:
Hk 013
Cbh，,kCn,k b Cbh，,kCnb,k vkn 013
013 IMU l (5) (7) (8) (9)
Simultaneously, the movement of the IMU and feet is depicted in Figure 5 (seeing Figure 3 from the zh direction). The illustration shows that when both feet are in contact with the ground, the IMU is positioned centrally between the feet. Consequently, during a single step cycle, the lateral and vertical distances of the IMU are zero, based on the IPM. As Figure 5 shows, the right foot moves forward from k-1 to k, and in this step, the lateral distance of the IMU is zero. This establishes a motion constraint where there is no change in the y-axis and z-axis coordinates in the h-frame.
In a single step cycle, assuming that the velocity is linear over a short period, the distance of
measurement and the INS mechanization can be expressed as [
1
xk N k1/k N xk (13)
Where, k /kN is the state transition matrix from tk N to tk , and N is the sample times in a single step cycle. Finally, in a single step cycle, the measurement transition matrix is:
1 k 1
H s 2 Hk N k1/kN dt ik N 1 Hik1/idt 2 H k dt (14)
Figure 6 illustrates the positional relationship of the sensors worn by the tester, including the back
and heel. The experimental area comprises the standard office indoor environment and the outdoor
environment. The MTw IMU device from Xsens is used to collect data with 100Hz and its
specification is shown in Table 1. Five methods are used to handle the data form the IMU. They are:
1)IPM-V: This method uses the IPM-V to constrain the accumulated error from INS mechanization;
2)IPM-D: This method uses the IPM-D to constrain the accumulated error from INS
mechanization;
3)IPM-VD: This method uses the IPM-V and IPM-D both;
4)NHC-PDR: This method is state-of-the-art with the assumption that lateral velocity is zero all
the time[
5)Foot-PDR: This method uses the IMU mounted on the foot with basic zero-velocity update (ZUPT) and zero-integrated heading rate (ZIHR), without additional observation such as environment information.
The step detection and step length estimation methods in IPM-V, IPM-D, IPM-VD and NHC-PDR are the same. FOOT-PDR uses the data from IMU mounted on the foot; IPM-V, IPM-D, IPM-VD and NHC-PDR use the data from the IMU mounted on the back. Since FOOT-PDR is relative positioning methods, use the angle between the tenth step and reference line to correct the test trajectory. This procedure enables the conformity of the trajectory of the five methods.
Table 1 The specification of the MTw IMU
Sensor Types Accelerometer Gyroscope Range (of scales) ±160m/s2 ±1200deg/s Linearity 0.2% 0.1% Stability - 20deg/hour
Noise 0.003m/s2/Hz1/2 0.05deg/s/Hz1/2
The indoor trajectory is 54.4 m in length with two 90-degree turns. This test contains 10 tests for each method. The end position error for each method, along with its average and variance, is presented in Table 2 and Figure 7 to assess the accuracy of the position estimation in meters. In Table 2, the best and second-best results among the five methods in each trial are highlighted in red and blue, respectively. According to Table 2, IPM-VD and IPM-V achieve the best and second-best results, outperforming NHC-PDR and FOOT-PDR.
20 15 10 /ym 5 0 -5 -10
GroundTruth IPM-V IPM-D IPM-VD NHC-PDR Foot-PDR ) m ( r o r r E 0 5 10 15 30 35 40
45 20
25 x/m (a) (b) closing error/m positioning error of the second 3.711 7.456 2.540 11.2639 19.1625 turning/m
This paper presents trunk-mounted PDR based on IPM to use only an IMU to fulfill pedestrian positioning. The proposed method constraints the accumulated errors in the INS mechanization with IPM derived from pedestrian movement patterns， which matches the real observations with the lateral velocity caused by tiny slosh and the lateral and vertical distance are zero in one step cycle in h-frame, which called IPM-V and IPM-D. The results of the experiments suggest that the proposed methods demonstrate superior position accuracy compared to current methods, showing an approximate 80% improvement in positioning accuracy in the outdoor test. Trunk-PDR based on IPM provides a simple way to install and has huge potential to promote to smartphone-based pedestrian navigation when the smartphone is put in a jacket pocket. In the future, Trunk-INS is expected to integrate with additional techniques employed in foot-INS systems to enhance positional accuracy.