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# A Simple Navigation Problem PowerPoint PPT Presentation

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:.

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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:

• We put:

### Component mixture update

• We have the update:

### Change components

• Change components from Im to Im’.