A Simple Navigation Problem

1. A Simple Navigation Problem By Marc Sobel, (Statistics) Iyad Obeid and John Montney (Computer and Electrical Engineering)

2. New Model • Discrete time points t=1,….,n • Observe only angles:

3. Equations: • 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:

4. Assumption • Assumption: Assume that the update step is a mixture of distributions:

5. Prediction Equation Using equation (3) in equation the prediction equation:

6. Update Equation • Using equation (4) in equation (2):

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

8. Specify Weights • We put:

9. Component mixture update • We have the update:

10. Change components • Change components from Im to Im’.