Multi Stage based Time Series Analysis of User Activity on Touch Sensitive Surfaces in Highly Noise Susceptible Environments

This article proposes a multistage framework for time series analysis of user activity on touch sensitive surfaces in noisy environments. Here multiple methods are put together in multi stage framework; including moving average, moving median, linear regression, kernel density estimation, partial differential equations and Kalman filter. The proposed three stage filter consisting of partial differential equation based denoising, Kalman filter and moving average method provides ~25% better noise reduction than other methods according to Mean Squared Error (MSE) criterion in highly noise susceptible environments. Apart from synthetic data, we also obtained real world data like hand writing, finger/stylus drags etc. on touch screens in the presence of high noise such as unauthorized charger noise or display noise and validated our algorithms. Furthermore, the proposed algorithm performs qualitatively better than the existing solutions for touch panels of the high end hand held devices available in the consumer electronics market qualitatively.

💡 Research Summary

The paper addresses the problem of accurately interpreting user interactions on touch‑sensitive surfaces when the raw sensor data are heavily corrupted by environmental noise such as electromagnetic interference from unauthorized chargers, power‑line fluctuations, or display‑induced jitter. Existing solutions typically rely on a single denoising technique—low‑pass filtering, moving‑average smoothing, Kalman filtering, or machine‑learning‑based correction—and therefore struggle to cope with noise that is both non‑stationary and multi‑modal. To overcome these limitations, the authors propose a three‑stage processing pipeline that combines complementary mathematical tools: a partial‑differential‑equation (PDE) based diffusion filter, a linear‑Gaussian Kalman filter, and a simple moving‑average (MA) smoother.

Stage 1 – PDE Diffusion Denoising
The first stage treats the noisy touch trajectory as a scalar field defined over a two‑dimensional domain (time × spatial coordinate). By discretizing the heat equation (∂u/∂t = α∇²u) and applying an explicit finite‑difference scheme, high‑frequency components are diffused away while preserving the overall shape of the trajectory. The diffusion coefficient α and the time step Δt are chosen to satisfy the Courant‑Friedrichs‑Lewy (CFL) stability condition, ensuring that the filter does not oversmooth sharp gestures such as quick taps or sudden direction changes.

Stage 2 – Kalman Filtering
After the PDE stage, residual low‑frequency drift and model‑based errors remain. The authors model the touch state as a vector x =