A mathematical approach to model signal variation in an aquatic robot’s environmental sensor using heavy-tailed distributions

Nain, Anuj; Upadhyay, Govind Murari; Bohra, Navdeep; Soni, Pramod Kumar; Raja, Linesh

doi:10.47974/JIM-2103

Open Access Research Article

A mathematical approach to model signal variation in an aquatic robot’s environmental sensor using heavy-tailed distributions

Anuj Nainanuj.nain.stats@gmail.comDepartment of Statistics Central University of Rajasthan Ajmer, Rajasthan, 305817, IndiaView full profile → , ^*Govind Murari UpadhyayCorresponding authorgovind.upadhyay@jaipur.manipal.eduDepartment of Computer Applications Manipal University Jaipur Department of Computer Applications Manipal University JaipurJaipur, Rajasthan, 303007, IndiaView full profile → , Navdeep Bohranavdeepbohra@msit.inDepartment of Computer Science and Engineering Maharaj Surajmal Institute of TechnologyJanak Puri, Delhi, 110058, IndiaView full profile → , Pramod Kumar Sonipramod.soni@jaipur.manipal.eduDepartment of Computer Applications Manipal University Jaipur Department of Computer Applications Manipal University JaipurJaipur, Rajasthan, 303007, IndiaView full profile → , Linesh Rajalinesh.raja@jaipur.manipal.eduDepartment of Computer Applications Manipal University Jaipur Department of Computer Applications Manipal University Jaipur Jaipur, Rajasthan, 303007, IndiaView full profile →

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pp. 597–606Vol. 28Issue 2March 2025DOI: 10.47974/JIM-2103XML

Received:: 12 Feb 2024
Published Online:: 15 Mar 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2103
Pages:: 597–606

Abstract

In aquatic environments, autonomous robots equipped with environmental sensors play a pivotal role in gathering critical data to monitor and understand complex ecosystems. This research paper explores the modeling of signal variations generated by an aquatic robot submerged in water, considering factors such as temperature, pressure, salt content, and the number of living species in the surroundings. The primary focus is on characterizing and quantifying the random error inherent in the signal, with an emphasis on heavy-tailed probability distributions to account for extreme events and outliers. Various heavy-tailed distributions are examined in the context of their suitability to represent the distribution of errors in the robot’s signal. The research is conducted through extensive simulations enabling controlled experimentation and analysis of signal characteristics. AIC, BIC, K-S test for goodness of fit have been used to identify the best fitting distribution. This interdisciplinary research uses Mathematical Statistics to provide useful insights into the error dynamics of aquatic robots thus helping to improve their quality, consequently proving beneficial for various stakeholders which include, Engineers, Environmentalists, mathematicians, statisticians, and AI developers.

Keywords

Aquatic robots Error dynamics Heavy-tailed distributions Distribution fitting Mathematical statistics Simulation Good health and well-being

Subject Classifications

76B75

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