Methodology4.1 Iterative Least Squares for GPS Navigation This chapter describes an experiment on using iterative least squares (ILS) with the application of the GPS navigation base on the software of Matlab programming. The pseudo-orange and satellite position of a GPS receiver at a fixed position for a period of 812 seconds is given. Below is a brief illustration of the principles of GPS. For further information see the previous chapter. The Global Positioning System (GPS) is a satellite navigation system that provides the user with adequate access to positioning information. The most commonly used approaches for GPS positioning are the Iterative Least Square (ILS) and Kalman Filter (EKF) methods. Both are based on the pseudo-orange equation: (4.1) Where Xs and Xu represent the position of the satellite and the receiver, respectively. is the receiver clock bias. is a measurement provided by the receiver for each satellite i. There are 4 unknowns: the position coordinate of the receiver X and the clock bias b. To calculate these unknowns you can use the Iterative Least Square (ILS) method. Below is a brief illustration of the iterative least squares process in the flowchart, as shown in Figure 11. The appendix presents the iterative least squares method on Matlab functions. Figure 11 Shows flowchart of iterative Leart Square process for GPS navigation. The following flowchart shows the relationship between the data and the algorithm to estimate the user's location. The first step in GPS positioning is to use the satellite position and pseudorange from the GPS receiver data to estimate the user's location. The simulation results for the GPS satellite position are shown in T...... in the center of the sheet...... (4.11)7. Calculation of the covariance matrix of (4.13). Figure 16 Block diagram of the system, measurement model and discrete-time Kalman filter. The relationship of the filter to the system is illustrated in the block diagram of Figure 16. The basic steps of the calculation procedure for the discrete-time Kalman estimator are as follows:1. Calculate using , and2. Calculate using (calculate in step 1), and3. Calculate using (calculate in step 2) and (from step 1)4. Calculate the next value of recursively using the calculated values ​​of (from step 2), the initial estimate provided, and the input data. The steps above describe the step to calculate the user's location using the extended Kalman filter algorithm. The extended Kalman filter algorithm on Matlab functions is presented in the appendix.