Research Article GPS Receiver Position Estimation and DOP Analysis Using a New Form of the Observation Matrix Approximations Ashok Kumar N , 1 P. Sirish Kumar , 2 Md. Khaja Mohiddin , 3 Mulugeta Tegegn Gemeda , 4 and Anup Mishra 5 1 Department of Electronics and Communication Engineering, Anil Neerukonda Institute of Technology and Sciences (A), Visakhapatnam, India 2 Department of Electronics and Communication Engineering, Aditya Institute of Technology and Management (A), Tekkali, India 3 Department of Electronics and Telecommunication Engineering, Bhilai Institute of Technology, Raipur, Chhattisgarh, India 4 Faculty of Electrical and Computer Engineering, Jimma University, Jimma Institute of Technology, Jimma, Ethiopia 5 Department of Electrical and Electronics Engineering, Bhilai Institute of Technology, Durg, Chhattisgarh, India Correspondence should be addressed to Ashok Kumar N; ashok0709@gmail.com, P. Sirish Kumar; sirishdg@gmail.com, and Mulugeta Tegegn Gemeda; mulugeta.geneda@ju.edu.et Received 29 July 2022; Accepted 22 August 2022; Published 19 September 2022 Academic Editor: Sweta Bhattacharya Copyright © 2022 Ashok Kumar N et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A location sensor is a feature that communicates with a Global Positioning System (GPS) receiver to learn about the status of the current location. This work presents the GPS receiver position estimation and Dilution of Precision (DOP) analysis using a new approximate form of observation matrix which can be used in place of the classic observation matrix that was derived from the Taylor’s series. It has been realized that, the approximate observation matrix is numerically stable and provides greater precision in calculating DOP values and estimating the position of a GPS receiver. The experimental results show that the proposed observation matrix provides better precision in DOP analysis and GPS receiver position estimation with a fast convergence rate and improved algorithm stability. Therefore, it can be concluded that the proposed new observation matrix plays a significant role to estimate accurately the location of the GPS receiver position and to enhance all parameters of the DOP. 1. Introduction The GPS sensors estimation process mathematically depends on the observation matrix which is formed by using the pseudo-range equations at a particular epoch. The observa- tion matrix in use was derived from the first order Taylor’s series. Thus, the classical observation matrix has a constant (unity) as the fourth parameter which affects the iteration pro- cess of position estimation and DOP computation in terms of precision. Therefore, a direct difference method is used in this paper to improve the order of the observation matrix. A direct difference method was used to the Extended Kalman Filter (EKF) to modify its gain [1, 2]. Thus, EKF was modified and the developed new method was named as modified gain EKF (MGEKF). This method was used to obtain an approximate gain matrix “g” to replace the measurement matrix (hðXÞ) in the EKF covariance during the measurement update stage. The only distinction between EKF [3] and MGEKF is the covariance matrix in the measurement update stage. The new gain matrix “g” has proved to be effective in SONAR tracking applications [4, 5]. In this article, an attempt is made to obtain an approximate form of observation matrix ( ~ H) for GPS applications by using the direct difference method. Although classical observation matrix (H) is the standard Hindawi Journal of Sensors Volume 2022, Article ID 6772077, 12 pages https://doi.org/10.1155/2022/6772077