Mathematical transformation between two GNSS models
Budget: $30 – $250 CAD
This relatively simple project is strictly mathematical. Main task is to find an algorithm or method of transforming Klobuchar parameters to NeQuick parameters and vice versa. Both Klobuchar and NeQuick ionospheric models are available online, as well as can be modeled from links 1. for Klobuchar model and 2. for NeQuick model.
You have two functions: Klobuchar model is a function of 8 parameters, and NeQuick model is a function of 3 parameters. Your task will be to find the forward and inverse algorithm, method or solution of how to transform between models.
Firstly, we will define the criteria of the sameness. E.g. to minimize square
position differences calculated by both models (least squares method). For this, we will select some constellation of navigation satellites. Start with the GPS satellites only, and then we will see. Then we will find some method how to uniformly distribute the investigated user positions on the globe. For the first attempts we will use from 10 to 20 points and then we will see. For this navigation satellite constellation and user positions we will calculate the position errors caused by the ionosphere modeled by the Klobuchar and Nequick models. First attempts for parameter transformation will be done by brute force method. Then we will see how to continue.
1. https://www.gps.gov/technical/icwg/IS-GPS-200N.pdf
2. https://www.gsc-europa.eu/sites/default/files/sites/all/files/Galileo_Ionospheric_Model.pdf
Other sources are also available.
You have two functions: Klobuchar model is a function of 8 parameters, and NeQuick model is a function of 3 parameters. Your task will be to find the forward and inverse algorithm, method or solution of how to transform between models.
Firstly, we will define the criteria of the sameness. E.g. to minimize square
position differences calculated by both models (least squares method). For this, we will select some constellation of navigation satellites. Start with the GPS satellites only, and then we will see. Then we will find some method how to uniformly distribute the investigated user positions on the globe. For the first attempts we will use from 10 to 20 points and then we will see. For this navigation satellite constellation and user positions we will calculate the position errors caused by the ionosphere modeled by the Klobuchar and Nequick models. First attempts for parameter transformation will be done by brute force method. Then we will see how to continue.
1. https://www.gps.gov/technical/icwg/IS-GPS-200N.pdf
2. https://www.gsc-europa.eu/sites/default/files/sites/all/files/Galileo_Ionospheric_Model.pdf
Other sources are also available.