Machine Learning Strategy for Indirect Signal Sensing

Fig. 1: Deep Learning Prediction of an Inaccessible Signal

A widely desired analog physical signal (sound, light, etc.) sensing objective is to transform it into digital data samples with as little noise or artifact as possible. Typically, the emphasis is on sensor and analog-to-digital conversion (ADC) quality – sample rate (f_s), resolution, accuracy, etc. However, often the particular desired signal samples s_o[k] = s_0(t=k/f_s), \; k = 0, 1, 2, \ldots are difficult or costly to access due to extreme heat, safety, etc.

Traditionally, one might try to build a mathematical model to relate s_o[k] to a different signal s_i[k] that he could directly access and sense,

s_o(t) = F(s_i(t), \mathbf{c}, t)

Sometimes this works, but generally only in limited idealized circumstances. Often modeling is a complete practical failure due to system complexity, nonlinearity, time variance, or due to difficulties in solving mathematical “inverse problems”.

Instead, if one could collect a sufficient and diverse enough quantity of synchronized s_i[k] and s_o[k] data samples, he might solve the modeling problem by training a machine learning (ML) algorithm as shown in Fig. 1. In principle a deep learning (DL) approach requires no physical model, but having one may help inspire a particular neural net architecture, and also supports other potential model based learning algorithm options beyond deep learning.

Although machine learning seems able to improve almost any system, most prominent examples require at least gigabytes of data to train neural nets with thousands of parameters running on large, power hungry computers. However, recent examples show that it is challenging, but possible to adapt such methods to the world of small, low-power microcontrollers with kilobytes of memory, relatively weak available computing power, and continuous data flow sometimes situated within feedback loops where long computational delays are often not tolerable.