Table 1 Gait parameters collected by the smart phone app in this study

Step frequency (Hz)

The step frequency is calculated by fast Fourier transform. The original vertical acceleration is low-pass filtered, and the frequency corresponding to the peak of the power spectrum is the step frequency [28]. Step frequency is found to be sensitive to age, according to [10]

RMS Acceleration (m/s²)

RMS acceleration represents an index of the average amplitude of acceleration in a walking test. It is calculated as

RMS = \(\sqrt{\frac{{\int }_{{t}_{1}}^{{t}_{n}}{a\left(t\right)}^{2}dt}{{t}_{n}-{t}_{1}}}\)

a(t) represents the acceleration data at time t, \({t}_{1}\) and \({t}_{n}\) represent the start time and end time of data collection, respectively. The RMS acceleration is a proxy of the gait speed [11, 29]

Step time variability

Step time variability = [\(\frac{{t}_{SD}}{{t}_{MEAN}}\)]\(\times 100{\%}\)  

\({t}_{SD}\) represents the standard deviation of each time step in a walking test and \({t}_{MEAN}\) represents the average time per step. Step time variability is associated with frailty [30], fatigue [31, 32] and falls [33]

Step regularity

Step regularity \({D}_{1}\) is calculated as the autocorrelation coefficient peak near one step. The autocorrelation coefficient peak near one stride (two steps) is recorded as the stride regularity \({D}_{2}\). A higher value of step regularity indicates a greater degree of balance [28]. Step regularity is sensitive to frailty [11] and discriminates between stroke patients and healthy participants [12]

Step symmetry

The symmetry is calculated as the ratio of \({D}_{1}\) to \({D}_{2}\). If \({D}_{2}\)> \({D}_{1}\), it is calculated as \({D}_{1}\)/\({D}_{2}\); if \({D}_{1}\)> \({D}_{2}\), it is calculated as \({D}_{2}\)/\({D}_{1}\). If the symmetry value is closer to 1, it is more symmetrical [34]. Step symmetry is useful to discriminate between stroke patients and healthy participants [12]