Iterative Least Square For GPS Navigation

1028 Words3 Pages

Methodology
4.1 Iterative Least Square for GPS navigation
This chapter describes an experimental of using Iterative Least Square (ILS) with the application of GPS navigation base on Matlab programming software. The psuedorange and satellite position of a GPS receiver at fix location for a period of 812 seconds is provided.
The following is a brief illustration of the principles of GPS. For more information see previous chapter. The Global positioning System (GPS) is a satellite-base navigation system that provides a user with proper equipment access to positioning information. The most commonly used approaches for GPS positioning are the Iterative Least Square (ILS) and the Kalman Filter (EKF) methods. Both of them are based on psuedorange equation:

(4.1)

In which Xs and Xu represent the position of the satellite and receiver, respectively. is the clock bias of receiver. is a measurement given by receiver for each satellites i.

There are 4 unknowns: the coordinate of receiver position X and clock bias b. The Iterative Least Square (ILS) can be used to calculate these unknowns. The following is a brief illustration of process of Iterative Least Square in flowchart as shown in Figure 11. In the appendix, the Iterative Least Square method on Matlab functions is presented.

Figure 11 Show flowchart of process of Iterative Leart Square for GPS navigation.

The following flowchart shows the data relation and algotithm for estimate the position of user. The first step for GPS positioning is using the position of satellite and pseudorange from GPS receiver data to estimate the position of user. The simulation results for GPS satellite position are shown in T...

... middle of paper ...

... (4.11)

7. Computing the covarince matrix of

(4.13)

Figure 16 Block diagram of system, measurement model, and discrete-time Kalman filter.

The relation of the filter to the system is illustrated in the block diagram of figure 16. The basic steps of the computational procedure for the discrete-time Kalman estimator are as follows:
1. Compute using , and
2. Compute using (compute in step 1), , and
3. Compute using (compute in step 2) and (from step 1)
4. Compute successive value of recursively using the computed values of (from step 2), the given initial estimate , and the input data .
In above steps describes step for calculate the position of user by using the Extended Kalman Filter Algorithm. In the appendix, Extended Kalman Filter Algorithm on Matlab functions is presented.

Open Document