Signal processing techniques for an accelerometer signal?

Question

I am running some tests where I am recording accelerometer measurements. I am looking to use elements of signal processing on this signal, but I am unsure about where to begin, or what my approach should be.

My ultimate goal is to be able to monitor the acceleration readings in real-time, and then display a notification when the event occurs. As you can see around the 150,000 sample time, an event occurs.

• If I am monitoring this data in real time, what sort of signal processing techniques could be implemented to react to this event?
• Would a Short-Time Fourier Transform (STFT) be an option?

I am monitoring my data in Python, and they have a decent STFT function.

The arguments of this function are as follows:

scipy.signal.stft(x, fs=1.0, window='hann', nperseg=256, noverlap=None, nfft=None, 
detrend=False, return_onesided=True, boundary='zeros', padded=True, axis=-1)

• How do I determine optimal parameters to use to process this signal?

• Are there any other methods that you folks think may help me in identifying when the event occurs in real-time (as opposed to just using the magnitude of the acceleration)?

EDIT 1:

My STFT has been added above.

Answer 1

I'm wondering why the STFT pops out. To me, wouldn't a simple threshold on the signal itself or on its envelope do better / just as well, after removal of the g offset?

Once you decide what "measure" is best to detect your event, you can apply the work of Basseville and Nikiforov, that I answered here.

The classic reference for that problem is Detection of Abrupt Changes - Theory and Application by Basseville and Nikiforov. The whole book is available as a PDF download.

My recommendation is that you read Chapter 2.2 on the CUSUM (cumulative sum) algorithm.

Answer 2

If this graphics represents the most typical application scenario, then I would go for some simple short window variance estimation and perform thresholding afterwards;

$$ \sigma_x^2 = \frac{1}{N} \sum_{n=0}^{N-1} x_{ac}[n]^2$$

Where $x_{ac}[n]$ is the DC removed input signal; i.e., $x_{ac}[n] = x[n] - \bar{x}[n]$ where $\bar{x}[n]$ is the DC (mean) value of the input $x[n]$ which can locally be estimated by $$\bar{x}[n] = \frac{1}{N} \sum_{n=0}^{N-1} x[n]$$ You could also use a DC blocking notch filter to eliminate any DC build up instead of estimating it.

Select a small enough window size $N$ appropriate for your application. You can perform the decision of the event based on a comparison of the standard deviation (square root of this computed variance estimate) to a properly selected threshold.

This will easily be computed in real-time with much less computational burden compared to a frequency domain analysis. Note that in real time application your summation indices should go backwards from the current sample (instead of the above fomulas which use a noncausal summation)

As a second efficient alternative, you could also implement a time domain envelope detection (followed by thresholding) to trigger the event.