## 3 A Prototype System for Pedestrian Positioning
### Electronic Module
#### 3.1.1 6 DOF Sensor  
The 6 DOF sensor, ADIS16355 from Analog Devices, comprises a 3-axial accelerometer and 3-axial gyro. The data from the sensor is read out through a digital interface, SPI. The samples are of 14-bit resolution whereby practically the three least significant bits are random. The ADIS16355 has been superseded by much less noisy ADIS16375. The static parameters of the former were investigated by the Allan variance [30]. **Gyroscope. ** The gyroscope is used to estimate the pedestrian orientation. Angular velocity \(\omega(t)\), returned by the gyroscope, is corrupted mainly by white and flicker noise. The relative direction change \(\Delta\phi\) is calculated by integrating the angular velocity according to Equation (1). \[\Delta\phi(t) =\int\limits_{0}^{t}\omega(T)dT=\int\limits_{0}^{t}(\hat{\omega}(T)+ \omega_{w}(T)+\omega_{f}(T))dT \tag{1}\] \[\Delta\phi(t) =\Delta\hat{\phi}(t)+\phi_{\mathrm{ARW}}(t)+\phi_{F}(t)\] (2) \[\phi_{\mathrm{ARW}}(t) =\int\limits_{0}^{t}\omega_{w}(T)dT\] (3) \[\phi_{F}(t) =\int\limits_{0}^{t}\omega_{f}(T))dT \tag{4}\]  
where \(\hat{\omega}(t)\) denotes the true angular velocity, \(\omega_{w}(t)\) white noise and \(\omega_{f}(t)\) flicker noise in angular velocity readouts. \(\Delta\hat{\phi}(t)\) is the true change in the heading direction. Integrated white noise \(\omega_{w}(t)\) results in a first-order random walk, called in this case angular random walk (ARW), and is denoted by \(\phi_{\mathrm{ARW}}(t)\) in Equations (2) and (3). Angular random walk \(\phi_{\mathrm{ARW}}(t)\) is described by the Gaussian distribution but it is not a stationary process as its standard deviation is growing with the square root of the integration time [31]. For the sensor used in the project the standard deviation of \(\phi_{\mathrm{ARW}}\) grows at a rate of \(2.77^{\circ}/\sqrt{\mathrm{h}}\). Figure 1: The block diagram of the system. The electronic module is a dedicated electronic circuit comprised of a 6 DOF sensor, GPS receiver and microcontroller. The module is connected with the PC via USB interface. The stereovision block represents a stereo camera. Similarly, integrated flicker noise \(\omega_{f}(t)\) causes an angular error \(\Delta\phi_{F}(t)\), according to Equation (4). The values of \(\Delta\phi_{F}\) are described by the Gaussian distribution whose standard deviation grows proportionally with the time and therefore it is a non-stationary process. In case of the gyroscope used in the project, the standard deviation of \(\Delta\phi_{F}\) grows at a rate of \(48^{\circ}/\mathrm{h}\). Therefore, confidence intervals for estimating \(\Delta\phi(t)\) widens with the time \(t\). After an hour, a motionless gyro can drift by \(\pm 144^{\circ}\) for \(\pm 3\sigma\) confidence interval. Hence, dead reckoning is justified for short periods only, e.g., during GPS outages. Inertial sensors also suffer from other errors like non-linearity or temperature random bias. The former error is \(\pm\)0.3\({}^{\circ}/\mathrm{s}\). The experienced random bias due to temperature was much higher than the manufacturer claimed and it reads 0.5\({}^{\circ}/\mathrm{s}\) for \(\pm\)3\(\sigma\) confidence interval. This is, however, easy to compensate by leaving the sensor motionless and measuring the constant offset to be later subtracted from the readouts. **Accelerometer. ** The accelerometer is used in the project to estimate the user's steps and their lengths. This method is more precise than integrating twice the acceleration readouts to obtain the displacement. The accelerations readouts are also used to estimate the gravity direction which is necessary for correct calculation of the orientation change. By analogy, velocity random walk is a product of integration of white noise in acceleration. On average, the velocity random walk was 0.5 \(\mathrm{m}/\mathrm{s}/\sqrt{\mathrm{h}}\). Flicker noise introduces an error of 9.3 \(\mathrm{m}/\mathrm{s}/\mathrm{h}\). The displacement errors are much larger since they are products of integrating velocity errors.