3.2.2. Signal Processing Methods

Signal processing techniques were also exploited to detect walking and to count steps, generally in a transformed domain, by methods such as fast Fourier transform (FFT), short time Fourier transform (STFT) and discrete/continuous wavelet transform (DWT/CWT). Matching methods, such as auto-correlation, cross-correlation, template matching, dynamic time warping (DTW), etc., were also used.

The Pan-Tompkins method (PTM) [27] uses a series of a filter, integration and derivative module to extract step events. STFT [28,50,51] exploits the energy ratio of different frequency bands to perform walk detection, and the period information is used to perform step counting. DWT/CWT [50,52] decompose the original signal into multiple resolutions of the frequency and time domain, which could discriminate walking activity by comparing the ratio between different wavelet coefficients.

Autocorrelation, cross-correlation, template matching and DTW all exploit the similarity between a predefined typical signal of a step cycle and the test sensor data to count steps. The autocorrelation method [53] thresholds the coefficients to detect walk activity and count steps by using the repetitiveness walk activity. Cross-correlation and template matching [27,54] threshold the high positive correlation coefficients to count steps. Ying et al. [27] extracted the first step cycle as the template and computed the normalized cross-correlation to count steps. Although these methods are accurate, the predefined typical template is different in various contexts and hard to find. Similarly, the DTW [55] method measures the similarity between a predefined typical template and the test sensor data, which is time-invariant and robust at various speeds.
