Kalman Filtering Applied to Low-Cost Navigation Systems: A Preliminary Approach Jos´ e Vieira Duque 1 , Victor Pl´ acido da Concei¸ c˜ao 1 , and M. Filomena Teodoro 1,2(B ) 1 CINAV, Portuguese Naval Academy, Portuguese Navy, Base Naval de Lisboa, Alfeite, 2810-001 Almada, Portugal {vieira.duque,placido.conceicao,maria.alves.teodoro}@marinha.pt 2 CEMAT - Center for Computational and Stochastic Mathematics, Instituto Superior T´ ecnico, Lisbon University, Avenida Rovisco Pais, n. 1, 1048-001 Lisboa, Portugal Abstract. The development of the technology in the last decades, and in particular of the navigation and positioning systems, with the appear- ance of the Micro-Electro-Mechanical Systems (MEMS) allowed solu- tions of positioning and navigation low-cost. The objective of this work is the construction of a low-cost positioning solution for small sailboats. Kalman filtering is used to process data from an MEMS inertial sensor and a GPS receiver on small sailing vessels. The validation of the work is done by comparing the results obtained by the low-cost system with those obtained by higher precision systems. Keywords: Systems of navigation and positioning · Kalman filters Low-cost · Small vessels 1 Introduction The development of technology has been a constant in modern times. Navigation and positioning systems were no exception to the rule. With the emergence of Micro-Electro-Mechanical Systems (MEMS) it has become possible to reduce the size and cost of these systems [1–3]. The integration of MEMS and Global Positioning Sytem (GPS) (INS/GPS) inertial systems has allowed the creation of low-cost navigation and positioning solutions. This technology has become so accessible that, if a few years ago, they were only part of leading edge systems, nowadays they are present in almost all existing smartphones. Due to its dimensions and costs, it is difficult to install conventional naviga- tion systems in small boats, this work intends to give an answer to this problem using a technique widely used as a tool of excellence in signal processing, the Kalman filters (KF), see, for example [4, 5]. In some cases, Kalman et al. [6] have described the Kalman filtering, where signal processing is based on stochastic c  Springer International Publishing AG, part of Springer Nature 2018 O. Gervasi et al. (Eds.): ICCSA 2018, LNCS 10961, pp. 509–524, 2018. https://doi.org/10.1007/978-3-319-95165-2_36