**4. Integration of PDR with inertial positioning**

Precise tracking of people, especially of first responders, in a harsh environment, remains an open research area. For a practical person tracking system, the measuring device of the system should be portable or wearable for the person being tracked. Inertial positioning can be applied in people tracking theoretically. However, the integral drift of accelerometers and gyroscopes, as well as the tilt errors of gyroscopes, make the inertial positioning not practical. As a result, as mentioned earlier, the characteristic of the movement of the person should be incorporated to improve positioning accuracy. If pedestrian dead reckoning (PDR) is integrated with IPS, the performance will be significantly improved, as shown is Fig. 3.

### **4.1 Pedestrian dead reckoning**

PDR is the application of dead reckoning in pedestrian tracking. Due to the difficulty in measuring the speed of a walking person directly, PDR estimate a pedestrian's present position based on estimated step length and heading from the last known position. Using probability models, Mezentsev et al (2005) confirm that the main source of errors in a PDR system is related to the estimation of the step length and the heading. Different random noise models can be applied to heading estimation and step length estimation (Mezentsev et al, 2005). Suppose the modeled mean step length *s* is a constant, and the *i*th length error *ωi* is normally distributed with a standard deviation σ, then the true *i*th step length satisfy *si*=*s*+*ωi*. Assuming the step errors are uncorrelated during a walk, the distance error variance after *N* steps is

The Application of Magnetic Sensors in Self-Contained Local Positioning 75

T1 T2 T3 T4 T5 T6

Swing Phase Swing Phase

ΔT Stance Phase

T1 T2 T3 T4 T5 T6

Time

In order to detect stance phase we can use sensor data, including all three components of angular velocity, acceleration, and even magnetic field, provided by a typical inertial/magnetic sensor module. Because the y-axis angular rate is the most significant indicator of stride events, Huang et al (2010) use the y-axis angular rate to detect the stance

Theoretically, the velocity in the l-frame is zero in the stance phase. In practice, zero-velocity updates (ZUPT) are performed when the acceleration and rate gyro measurements drop below empirically determined thresholds for a certain period of time. The main purpose of these updates is to mitigate both movement measured in the stance phase of a gait and increasing integral drifts. ZUPT is used by Stiring and Fyfy (2005), Mezentsev and Lachapelle (2005). Stirling and Fyfy stopped integrating and reset the velocity before each swing phase. The positioning accuracy of their system is of 10 to 20 percent of distance

In order to obtain a higher tracking accuracy, Huang et al (2010) further use additional methods to remove integral drifts. Some methods should be applied in the swing phase of

Huang et al (2010) update orientation using magnetic field signals from magnetic sensors,

In order to determine the orientation of the sensor module for rotation representation and transformation between the l-frame and the b-frame, the Euler angles must be determined. In the swing phases, the Euler angles are calculated through integration of the angular velocity over time assuming that the original orientation of the sensor module is known. However, the original orientation is usually unknown in reality. In addition, the gyroscope signal summed during integration is perturbed by gyroscope bias. Thus the accuracy of the

**4.3 Zero-Velocity update and swing phase integral error reduction** 

**4.4 Orientation update using magnetic sensors** 

Fig. 4. Stance phase in a stride

phases instead.

Ground Speed

traveled.

each stride.

i.e., magnetometers.

Fig. 3. Performance of positioning with IPS and PDR integrated

$$\left(\sigma\_{s}^{2}\right) = \operatorname{Var}\left(\sum\_{k=1}^{n} \alpha\_{k}\right) = \sum\_{k=1}^{n} \operatorname{E}(\alpha\_{k}^{2}) = \operatorname{N}\sigma^{2}\tag{9}$$

Hence, the error variation equals the product of the step count and the variation of the driving noise. Accordingly, the position error maximizes when the pedestrian walk continuously along a straight line with a constant step length error. Therefore, if not assisted by other methods, PDR is not able to provide precise positioning. For further improvement of accuracy, the kinetics of human walk is investigated.

### **4.2 Human gait and phase detection**

According to Rose and Gamble (1994), the human motion during a walk is cyclical and repeatable. Such a basic pattern is significantly constant among individuals. The gait cycle during human walk comprises two phases: a stance phase and a swing phase. In the stance phase, a foot keeps in touch with the ground from the time when the heel strikes the ground to the time when the toes leave the ground. The swing phase starts when the foot is taken away and carried forward. When the foot touches the ground again, the swing phase ends and the next stance phase starts. Each gait cycle is completed and restart in such a way. The other foot performs the same process, but lags 180° behind. Fig. 4 shows how the stance phase is started and ended. For a certain point at the front part of sole, its ground speed is almost zero from *T*3 to *T*5 (the period Δ*T*). If this time periodΔ*T* can be dependably detected every stride, referential data may be acquired and used to reset computations and get rid of accumulating errors, the critical problem in pedestrian tracking.

Huang et al (2010) advocate the integration of inertial navigation and pedestrian dead reckoning. With the stance phase detected, the velocity and angles can be updated in the stance phase and swing phase respectively. Thus both the integral drift of velocity and positions, as well as the tilt error caused by integral errors of rotated angles, can be greatly reduced. The positioning performance of the integration is illustrated in Fig. 3. The details of these updates are explained in the sub-sections that follows.

Fig. 4. Stance phase in a stride

2 2 2 1 1

Hence, the error variation equals the product of the step count and the variation of the driving noise. Accordingly, the position error maximizes when the pedestrian walk continuously along a straight line with a constant step length error. Therefore, if not assisted by other methods, PDR is not able to provide precise positioning. For further improvement

According to Rose and Gamble (1994), the human motion during a walk is cyclical and repeatable. Such a basic pattern is significantly constant among individuals. The gait cycle during human walk comprises two phases: a stance phase and a swing phase. In the stance phase, a foot keeps in touch with the ground from the time when the heel strikes the ground to the time when the toes leave the ground. The swing phase starts when the foot is taken away and carried forward. When the foot touches the ground again, the swing phase ends and the next stance phase starts. Each gait cycle is completed and restart in such a way. The other foot performs the same process, but lags 180° behind. Fig. 4 shows how the stance phase is started and ended. For a certain point at the front part of sole, its ground speed is almost zero from *T*3 to *T*5 (the period Δ*T*). If this time periodΔ*T* can be dependably detected every stride, referential data may be acquired and used to reset computations and

Huang et al (2010) advocate the integration of inertial navigation and pedestrian dead reckoning. With the stance phase detected, the velocity and angles can be updated in the stance phase and swing phase respectively. Thus both the integral drift of velocity and positions, as well as the tilt error caused by integral errors of rotated angles, can be greatly reduced. The positioning performance of the integration is illustrated in Fig. 3. The details of

get rid of accumulating errors, the critical problem in pedestrian tracking.

these updates are explained in the sub-sections that follows.

*n n s kk k k*

 

( )

(9)

 *E N*

Fig. 3. Performance of positioning with IPS and PDR integrated

*Var*

of accuracy, the kinetics of human walk is investigated.

**4.2 Human gait and phase detection** 

In order to detect stance phase we can use sensor data, including all three components of angular velocity, acceleration, and even magnetic field, provided by a typical inertial/magnetic sensor module. Because the y-axis angular rate is the most significant indicator of stride events, Huang et al (2010) use the y-axis angular rate to detect the stance phases instead.
