649 Kalman Filter, read instructions, 1500-2000 words assignment

Below are the information for the Kalman filter assignment. The question 1 consist of a theoretical part where from the y and z positions and the y and z components of velocity, the state vector and measurement vector needs to be writen. For a kinematic propagation model, the matrices needs to be determined, measurement model, propagation covariance and measurement covariances as well. Every aspect needs to be mathematically developped (for an easy understanding) An example of the of what is required is given page 37 (slides 162 to 164) but it need further [login to view URL] the "Sensor & data fusion" ch4-6-2014" Question 2 consist of creating a Kalman filter in Matlab following the algorithm example given in page 28 (Slide 145) or page 48 (Slide 184) Justifying the use of that method over the algorithm 1 (The Matlab code must be also explained briefly). Then using the data given on the file [login to view URL] prove that it is working. Question 3 Add rate to the measurement vector previously found and justify teh revised filter design (including initialisation) and evaluate the effect of the change on the position estimates obtained with the data of SDF2013b.txt. Assume the range rate measurement model is R(dot) = - z(dot)sin alpha, where sin alpha =0.13100062 Question 4. The north-south motion can be approximated by simple harmonic motion with angular frequency omega = 2 Pi / Tday, where Tday = 86164 s (1 sidereal day). Use this to develop a model for a dynamics-based propagation model of the z and dz/dt components, modify the filter of part 3 with this change, and then use the new filter to re-process the data of SDF2013b.txt. Show and discuss the results.