**4.4.1 Definition of dynamic stability**

Subject's walking is one kind of periodic movements and the same events will happen during different walking cycles, so the similarity of the data between adjacent cycles to assess subject's walking stability.

This paper used dynamic time warping (DTW) to calculate this similarity, which is a method for flexible pattern-matching scheme. It translates, compress and expands a pair of patterns so similar features within the two patterns are matched (Li, 2003). Fig. 28 and Equation (14) show details.

$$D(\mathbf{S}\_i) = \frac{\sum\_{j=1}^{n-1} DTW(\theta\_j, \theta\_{j+1})}{n-1} (n > 1) \tag{14}$$

where *D* is the number of walking cycles, *D(Si)* is the average of similarity at feature *Si*.

(b) Compare between two adjacent cycles

Fig. 28. Similarity between two adjacent cycles by DTW

#### **4.4.2 Extracting of dynamic stability features**

According to FL model, it's easy to get corresponding position, velocity and acceleration motion data of 19 points. Therefore, 19×3=57 features are extracted to describe human dynamic stability.
