GPS Receiver Position Estimation and DOP Analysis Using a New Form of the Observation Matrix Approximations: 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 Taylors 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.

Urban sensing plays a significant role in improving resource management, citizen engagement, environmental monitoring, urban planning, safety and social equality. GPS (Global Positioning System) is a crucial part in urban sensing as it provides accurate location tracking, real-time data collection, location-based services, mobility and transportation solutions, intelligent urban planning, and disaster management. However, there are various challenges associated with accurately estimating positions in urban environments due to various factors such as signal obstruction, urban canyons, multipath interference, noise and signal degradation and differential GPS limitations. In the context of GPS based urban sensing applications; the use of a navigation algorithm plays a critical role in extracting reliable data from corrupt sources, which can significantly impact inference performance for various signal processing applications. However, modeling all error sources that affect data quality can significantly increase system complexity, leading to challenges in terms of hardware and computation. To address this challenge, this paper proposes a novel particle filter-based algorithm, called the Double Resampling-based Least-Squares Particle Filter (DR-LPF), designed specifically for estimating the position of a GPS receiver without the need to model all error sources. By integrating current measurements into the particle before resampling through the least squares method, the DR-LPF allows the double-resampled particles to move towards high likelihood regions, leading to improved estimation accuracy, reduced computation time, and reduced computational load. The application of the proposed DR-LPF algorithm finds wide applications in urban sensing environments where data quality can be affected by multiple error sources. By reducing the computational load and improving estimation accuracy, the proposed DR-LPF algorithm can provide valuable insights into the movement and behavior of individuals and objects within an urban environment, enabling a wide range of smart city applications, such as traffic monitoring, environmental sensing, and crowd management.