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A Simple Navigation Problem

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A Simple Navigation Problem

By Marc Sobel, (Statistics) Iyad Obeid and John Montney (Computer and Electrical Engineering)

- Discrete time points t=1,….,n
- Observe only angles:

- Divide up the data into k non-sparse groups. G1,….,Gk. Define weights 0th generation weights π1,0,….,πk,0 Define two equations:Let Z’s be states and O’s be observations:

- Assumption: Assume that the update step is a mixture of distributions:

Using equation (3) in equation the prediction equation:

- Using equation (4) in equation (2):

- We have that,
- Now, it follows as usual with w(i) denoting the weight from the I’th component:

- We put:

- We have the update:

- Change components from Im to Im’.