Real-time Calibration Model for Low-cost Sensor in Fine-grained Time series

TL;DR

This work tackles real-time calibration of low-cost sensors under hardware constraints by introducing TESLA, a Transformer-based model that uses logarithmic-binned attention, multi-view embeddings, and feature-wise aggregation. TESLA achieves high calibration accuracy while maintaining efficiency comparable to linear models, with an attention complexity of $O( ext{log}^2 N)$ due to binning. Experiments on the SensEURCity dataset show TESLA outperforms both linear and Transformer baselines in RMSE/MAE and hardware metrics, including deployment feasibility on microcontrollers. The study demonstrates TESLA’s potential to improve data quality in IoT sensing and highlights design tradeoffs between accuracy, speed, and energy use for practical sensor calibration. The findings push forward real-time, resource-conscious calibration methods for fine-grained time series in edge devices.

Abstract

Precise measurements from sensors are crucial, but data is usually collected from low-cost, low-tech systems, which are often inaccurate. Thus, they require further calibrations. To that end, we first identify three requirements for effective calibration under practical low-tech sensor conditions. Based on the requirements, we develop a model called TESLA, Transformer for effective sensor calibration utilizing logarithmic-binned attention. TESLA uses a high-performance deep learning model, Transformers, to calibrate and capture non-linear components. At its core, it employs logarithmic binning to minimize attention complexity. TESLA achieves consistent real-time calibration, even with longer sequences and finer-grained time series in hardware-constrained systems. Experiments show that TESLA outperforms existing novel deep learning and newly crafted linear models in accuracy, calibration speed, and energy efficiency.

Figures (5)

• Figure 1: Overview of Tesla, which consists of (a) multi-view embedding, (b) logarithmic binned attention, and (c) feature-wise aggregation in data process order.
• Figure 2: Illustrative example of logarithmic binning in case $N=12$. Then we have $z=\left\lceil{\log_2 12}\right\rceil = 4$ with reverted indices $(\alpha_0, \alpha_1, \alpha_2, \alpha_3, \alpha_4)=(1, 6, 10, 12, 13)$. $l_1, \cdots, l_4$ are mapping functions that satisfy Equation \ref{['eq:lb']}.
• Figure 3: Comparison of model efficiency for average $\textbf{PM}_\textbf{10}$ performance across three regions in case $N=360$. (a) Comparison of RMSE and memory footprint across models. (b) Scatter map of FLOPS, RMSE, and parameters (diameter of the circles).
• Figure 5: Case study of actual $\textbf{PM}_\textbf{10}$ calibration results with different calibration models for sensor 'Oslo_643217', comparing results across three windows with different distributions (low-, mid-, and high-distribution). Gain represents the average increase in performance in terms of RMSE and MAE compared to iTransformer.
• Figure 6: Evaluation of the Arduino Nano 33 BLE Sense microcontroller. The scatter map illustrates RMSE, inference time, and Flatbuffer size (diameter of the circles) with varying windows (15, 60, 360, 720, 1440) for average $\textbf{PM}_\textbf{10}$ performance across three regions. Missing window sizes indicate non-applicability. The dotted line represents the trend.

Theorems & Definitions (2)

• Definition 1: Fine-grained time series
• Definition 2: Sensor calibration model