  Sensors measuring real-life physical processes are ubiquitous in today's
interconnected world. These sensors inherently bear noise that often adversely
affects performance and reliability of the systems they support. Classic
filtering-based approaches introduce strong assumptions on the time or
frequency characteristics of sensory measurements, while learning-based
denoising approaches typically rely on using ground truth clean data to train a
denoising model, which is often challenging or prohibitive to obtain for many
real-world applications. We observe that in many scenarios, the relationships
between different sensor measurements (e.g., location and acceleration) are
analytically described by laws of physics (e.g., second-order differential
equation). By incorporating such physics constraints, we can guide the
denoising process to improve even in the absence of ground truth data. In light
of this, we design a physics-informed denoising model that leverages the
inherent algebraic relationships between different measurements governed by the
underlying physics. By obviating the need for ground truth clean data, our
method offers a practical denoising solution for real-world applications. We
conducted experiments in various domains, including inertial navigation, CO2
monitoring, and HVAC control, and achieved state-of-the-art performance
compared with existing denoising methods. Our method can denoise data in real
time (4ms for a sequence of 1s) for low-cost noisy sensors and produces results
that closely align with those from high-precision, high-cost alternatives,
leading to an efficient, cost-effective approach for more accurate sensor-based
systems.
