Hi Sourabh Gothe,

one way could be to use other nonlinear similarity measures like mutual information or rank correlation.

You could also extract some features by looking at the elements in a sliding window (e.g. wavelets) and try to compare these.

But the reason for the invisibility of the correlation could be some kind of time shift in the signals. In this case you could try cross correlation (especially if the time shift is more or less constant over time)  or measures based on dynamic time warping. 

Hope that it will help you.

Regards,

Stephan

You may try some non-parametric similarity criterion. E.g.,

https://en.wikipedia.org/wiki/Simple_matching_coefficient

Flexions toward the extensor of limb occur during walking and the separate individual activity of dorsiflexion. Statistical pattern recognition techniques, as employed for speaker verification, may apply to your problem. I suppose your application involves the use of only a single accelerometer.

Fazel, Amin, and Shantanu Chakrabartty. "An overview of statistical pattern recognition techniques for speaker verification." IEEE Circuits and Systems Magazine 11.2 (2011): 62-81.

Dorsiflexion vs. walking? My best guess is that this will require at least 2 accelerometers as your signal of interest might be some difference between eg. the acceleration of the ankle vs. the acceleration of the forefoot (my guess).

Normalized cross correlation is the standard means to detect similarities on the same scale of time. If the input signals are ok, it gives good and reliable results.

Hello

In order to explore the signal contents I suggest you to use more than  transform

To search any similarities you can explore the spectrum of each signal separately

You can use Fourier Transform, STFT, or RFT transform

I suggest you to explore the Ramanujan Fourier transform RFT

https://www.researchgate.net/publication/200722987_Doppler_spectrum_estimation_by_Ramanujan-Fourier_Transform_RFT

Cordially

Article Doppler spectrum estimation by Ramanujan-Fourier Transform (RFT)

Maybe, volatilty transmission is a solution for this problem.

?

I suppose that You use 6-D accelerometer with gyroscope (such as MPU6050). The 6-D information is too complex for study. So, first of all, You needs to simplify informatin.  Will try to find module of acceleration vector and it's space orientation. Than use amplitude and period analisys.

computing and comparing the RMS error

You said "correlation did not help much". Can you elaborate?

Spearman rank correlation is more robust that Pearson correlation, so you can try that. You can also look at median, IQR etc. if you are interested in a statistical comparison.

If the signal contains the features, you may find them. the correlation of features of the signal is much meaningful.  

I think u may use mutual index for finding out similarity between the signals and also computing MSE  for original and recoverd signal.If it is almost zero the degree of similarity is near to 100%.

Cross-correlation is a reliable technique but only for signals linearly correlated. The coherence spectra can give you also some insights in the frequency domain, again for linearly correlated signals.

The expected relation between the two signals may help to define a deconvolution procedure.

Another vote for mutual information

https://link.springer.com/chapter/10.1007/978-3-662-05605-9_4