Distributed Estimation of Ambient Temperature with Missing Data

Abstract

Air quality and weather monitoring over large geographical areas is typically performed using expensive equipment, which limits spatial resolution and coverage. Wireless sensor networks (WSN) technology enables the large-scale deployment of affordable sensing nodes. However, such networks operate under challenging conditions, including noisy measurements, missing data, faulty sensor readings, and the absence of reliable noise statistics. These factors significantly degrade the performance of conventional distributed estimators that rely on accurate stochastic models. Because low-cost sensors are typically not very reliable and inherently noisy, distributed estimators exploit spatial redundancy to mitigate individual sensor imperfections. In this work, we develop a distributed unbiased finite impulse response (UFIR) filtering framework to conduct robust ambient temperature estimation in WSNs under realistic data-quality constraints. The proposed method combines local UFIR estimation, which does not require prior knowledge of noise statistics, with a consensus-based information fusion mechanism that enables cooperative estimation across the network. This structure enhances robustness against missing measurements and allows the evaluation of performance in the presence of faulty sensor readings and the absence of reliable knowledge about noise statistics while preserving distributed operation. The solution is validated using real environmental measurements containing missing data, together with an analysis of the influence of network connectivity on estimation performance. Results demonstrate that the proposed estimator achieves accurate and stable temperature estimation across the network even under significant data degradation, confirming its suitability for real-world WSN monitoring applications.

Received: 3 December 2025 | Revised: 10 March 2026 | Accepted: 1 April 2026

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

The data that support the findings of this study are openly available from Guillermo Barrenetxea. (2019). Sensorscope Data [Data set]. Zenodo. https://doi.org/10.5281/zenodo.2654726 [29]

Author Contribution Statement

Miguel A. Vazquez-Olguin: Conceptualization, Software, Formal analysis, Writing – original draft. Oscar G. Ibarra-Manzano: Methodology, Validation, Investigation. Yuriy S. Shmaliy: Conceptualization, Methodology, Formal analysis, Supervision, Project administration.