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A Simple Navigation ProblemPowerPoint Presentation

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)

New Model

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

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:

Assumption

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

Prediction Equation

Using equation (3) in equation the prediction equation:

Update Equation

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

Weights

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

Specify Weights

- We put:

Component mixture update

- We have the update:

Change components

- Change components from Im to Im’.

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