# Use of Wearable Sensor Technology in Gait, Balance, and Range of Motion Analysis
## 5 A Taxonomy for Gait, Balance, RoM Analysis
### Gait Analysis
#### 5.1.2 Gait Analysis: Pace  
The parameters that represents pace include _step length_, _stride length_, and _walking speed_ (or gait velocity). Step length is the distance between one foot's heel-strike to the opposite foot's heel strike when walking. Stride length is the distance travelled by a person when they perform a stride; i.e., the distance from one foot's heel-strike to the next heel-strike of the same foot. Step and stride length can be calculated once the steps are detected. Knowing the step and stride lengths helps to determine how symmetric the subject is walking. Researchers have discovered that step length is affected linearly by walking frequency and acceleration variance [109]. Walking frequency (WF) can be calculated using Equation (2), where \(WF_{k}\) is the walking frequency for step \(k\) and \(t_{k}-t_{k-1}\) is the step time for step \(k\). Acceleration variance (AV) can be calculated using Equation (3), where \(AV_{k}\) is the acceleration variance for step \(k\), \(n_{k}\) is the number of samples during the sequence of step \(k\), \(a_{k,i}\) is the acceleration at time i-th on step \(k\), and \(a_{k}\) is the acceleration mean during the same sequence of step \(k\). \[WF_{k}=\frac{1}{t_{k}-t_{k-1}} \tag{2}\]  
\[AV_{k}=\frac{1}{n_{k}-1}\sum_{i=1}^{n_{k}}(a_{k,i}-\bar{a}_{k})^{2} \tag{3}\]  
After walking frequency and acceleration variance are calculated, then step length (SL) can be determined using a linear approximation (Equation (4)), where \(\alpha\), \(\beta\) and \(\gamma\) are the step length estimation constant parameters for the linear equation [109]. \[SL_{k}=\alpha*WF_{k}+\beta*AV_{k}+\gamma \tag{4}\]  
Other researchers have calculated step length using the change of height of the center of mass \(h\) (vertical position) and the length of a pendulum \(l\) (sensor height from the ground), as shown in Equation (5) [48; 110]. Once step lengths are calculated, stride length can be determined by adding the left step length to the right step length. \[SL=2*\sqrt{2 lh-h^{2}} \tag{5}\]  
Step length and stride length has been used in the literature to compare the variability pre- and post-training as well as the variability between healthy subjects and subjects with a particular neurological disorder [25; 35; 36; 37; 34; 38; 39; 43; 50; 60; 62; 65; 70]. Gait velocity, also known as walking speed, is the distance travelled in a given period of time and is thought to be indicative of a person's functional capacity [111; 112]. Gait speed represents the overall performance of the walking pattern. According to [PERSON], it can be calculated using Equation (6), where gait velocity (GV) is expressed in meters per second, cadence is in steps per minute, and stride length (SL) is in meters [80]. Researchers have found that while cadence increases linearly, step length increases logarithmically, and it tends to stabilize at high speeds but changes at low speeds [104]. Gait velocity is correlated with functional ability and balance confidence and can be used to determine outcomes such as functional status, discharge location, and the need of rehabilitation [111]. \[GV=\frac{Cadence\times SL}{120} \tag{6}\]  
Gait velocity estimation algorithms can be divided into three categories: abstraction model, human gait model, and direct integration [113]. Abstraction model takes advantage of machine learning techniques to approximate the speed and decide to ignore the details of the human gait biomechanics; human gait models estimate the gait velocity by using the stride length of the subject; and lastly, direct integration method is when the acceleration of the sensor is integrated in the global coordinate system from the starting point to obtain instantaneous sensor velocity and the associated stride length. Direct integration is the most common approach used in gait and balance studies [113]. Direct integration seems like a straight-forward approach, but the accuracy of the integration can be inaccurate since the gravitational force is difficult to separate from the inertial force.