# A Review of Wireless Positioning Techniques and Technologies: From Smart Sensors to 6G
## 2 Localization Techniques
### Tracking Techniques
#### 2.5.1 Dead Reckoning (DR)  
The DR tracking algorithm estimates the change from the last known position. The receiving node's current position is estimated based on the previous determined positions, orientation, and speed. The initial position, orientation, and velocity must be known a priori. For instance, the pedestrian dead reckoning (PDR) is used for approximating a pedestrian's relative position against a defined location and can be classified as the strapdown inertial navigation system (INS) or the Step and heading system (SHS), shown in Figures 10 and 11, respectively.  
Figure 10: Strapdown Inertial Navigation System (INS), reproduced with permission from Correa, _A Review of Pedestrian Indoor Positioning Systems for Mass Market Applications_, published by MDPI, 2017.  
Both INS and SHS estimate the pedestrian's position and orientation by using the accelerator's and gyroscope's measurements, as well as the user's step length and heading [8; 17]. Analytically, the INS utilizes the gyroscope and stride through the double integration of the combination of the accelerometer and gyroscope data. The rotation transformation is then used for transforming the non-inertial reference frame (the one attached to the sensor) to the inertial reference frame. The obtained result is integrated twice for obtaining the position estimation. The integration operand commonly results in acceleration errors, which can be eliminated by subtracting the gravitational field \(g\) before the integration, as follows:  
\[v(t)=v(0)+\int_{0}^{t}(a(t)-g)dt. \tag{22}\]  
On the other hand, the SHS detects the pedestrian's steps by using the acceleration measurements. The body movements cause acceleration signal rises, called peaks, followed by a signal fall. For determining the number of peaks, numerous threshold-based methods can be used. The steps counting, together with the compass or gyroscope measurements, are used for estimating the pedestrian's heading and position by using the following equations [8]:  
\[m_{x}(k)=m_{x}(k-1)+l_{step}(k)\cos(\theta(k)) \tag{23}\]  
\[m_{y}(k)=m_{y}(k-1)+l_{step}(k)\cos(\theta(k)), \tag{24}\]  
where \(m_{x}\) and \(m_{y}\) are the \(x\) and \(y\) components of the position, respectively, \(k\) is the time index, \(l_{step}\) the step length, and \(\theta\) is the heading.  
Similar to INS, the SHS heading is estimated by using the integration of the gyroscope signal, which causes accuracy limitations, due to the gyroscope errors [64]. Therefore, the final position can drift, so an alternative solution is the utilization of the magnetometer measurements, at the expense of degraded accuracy, due to the spanning over a long period of time and bias from the external ferromagnetic interference. The optimum solution may be the fusion of different sensor measurements, i.e., the gyroscope and magnetometer, the accelerometer and gyroscope, or the accelerometer and magnetometer. In [64], the combination of the accelerometer, gyroscope, and magnetometer measurements is effectively used for reducing the accumulated errors. Moreover, in [17], the deployment of body-mounted sensors demonstrated a better performance, in terms of both step detection and orientation.