Comparison of various interpolation techniques to infer localization of audio files using ENF signals

Abstract [pdf]

Electrical Network Frequency (ENF) is a frequency of the electrical power signal of the power grid that plays a key role in the level of security. There is a difference in the values on the supply and demand on power usage. Due to its distinctive value, the ENF data hold great importance in the field of security. Examining the ENF signal makes it possible to trace the location where the ENF signal was generated. By making the most use of certain interpolation techniques, we can estimate the ENF value of a specific location and evaluate the estimated performance. Interpolating the ENF signals on the target location can increase the accuracy of the estimate for the unacquainted ENF signals. In this paper, we interpolated the ENF values of the power grid of the United States by using three different methods: IDW, Ordinary Kriging, and Universal Kriging. Then we evaluated the RMSE calculated by varying the hyper-parameters and models of interpolation methods. As a result, it was found that applying the Ordinary Kriging in the Western grid had the lowest RMSE. For the Eastern power grid, it was the IDW with λ = −1 which showed the lowest RMSE. We concluded that each power grid had different characteristics. Therefore different interpolation techniques should be applied to each case for precise approximation.

Overall process

First, we gathered audio files and their location information from online multimedia services and extracted ENF signals. The location dependency idea was then used to interpolate the ENF value of the uncharted area through the adjacent ENF values.

Collected audio data

Among the collected audio data, only some of them contain ENF signals.

Collected audios

ENF-containing audios

Location Dependence of ENF signals

At the intra-grid level, most existing works have assumed that ENF signals across different locations in an interconnected power grid are the same at a given time. However, minor variations are likely to be present in the frequency fluctuations at different locations. This can be attributed to local changes in the load and the finite propagation speed of the effects that such load changes would have on other parts of the grid.

As a result, ENF signals have greater similarity for locations close to one another that those further apart. We drew inspirations from this fact Interpolating uncharted ENF values to build an ENF map!

(a) Estimated ENF using nearby ENF values

(b) Estimated ENF using distant ENF values

Comparison of various interpolation techniques

With the inspiration of the location dependence of ENF, we used three discrete interpolation techniques to create an ENF map by estimating uncharted ENF signals.

Inverse Distance Weighted (IDW) Ordinary Kriging Universal Kriging