An Advanced Unscented Kalman Filter and Fuzzy-Based Approach for GPS Position Estimation Real-Time Applications

Introduction

GPS is a satellite-based navigational system or Global Positioning System delivers navigation, aligning, timing, and other services. Computation of GPS receiver is computed by taking the distance between a satellite and its receiver and the orbit's distance (Julier et al., 1995). Worldwide, people use GPS to determine the position of their devices. The system provides a three-dimensional image of the device's position as shown in Figure 1. The applications include positioning of GPS receiver in the applications of defense and civilian corresponding to the senior citizens tracking location, online transportation tracking status, school kids besides in dissimilar applications under surveying process and so forth

Figure 1.

3D Position of a GPS receiver using 4 satellites

There are two main methods for estimating GPS orbit: the geometric method and the dynamic method. The geometric method is usually used for estimating the observed orbit, while the dynamic method is for integrating orbit and obtaining the necessary parameters (Julier & Uhlmann, 1996). The dynamic method is commonly used for estimating orbit. This method is proposed to be compared with the non-linear estimation algorithms that include extended kalman filter (EKF), sigma point or unscented kalman filter (UKF) explained in (Julier & Uhlmann, 1997).

EKF is a recursive filter algorithm that is commonly used for estimating parameter values in nonlinear systems shown in fig 1 It is mainly used for estimating the nonlinear motion system and its related systems. The linearized second order EKF algorithm is prone to filter initial stage precision because of its interceptive error, which can lead to filter divergence and instability. It is also shown that the linearized second order EKF algorithm is not able to adapt to the motion equation with too many items (Gordon & Pitt, 1998). UKF is like EKF in that it uses the covariance matrix and predicted mean value for the random variable probability distribution over serval strategies. It also eliminates the need to linearize the measurement and motion equation. The most used technique for orbit estimation in the application of numerical technique to calculate the ephemeris and the state transition matrix. This method is very efficient if the orbit is not too long as GPS real-time PPP (Kumar et al., 2018). In this technology orbital path errors are eliminated through EKF and 2^nd order Tylor expressions. The following process is a fusion mechanism which can improves the application accuracy.

An Inertial Navigational System (INS) is a self-contained system that uses inertial sensors to determine a vehicle's attitude, velocity, and location. The GPS is a global tracking mechanism but INS is inertial navigation model which is limited in operation. As a result, its navigation error develops exponentially over time because of inertial sensors' drift. The GPS, on the other hand, is able to accurately track a vehicle's speed and location over a lengthy period of time. Because of this, GPS has a limited ability to provide real-time navigation information because it relies on the external environment and satellite availability. Because of their complementing properties, the combination of INS and GPS provides an optimistic approach for improving navigation accuracy by taking full use of the specific benefits of each system.