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:.

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A Simple Navigation Problem

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A simple navigation problem

A Simple Navigation Problem

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


New model

New Model

  • Discrete time points t=1,….,n

  • Observe only angles:


Equations

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

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


Prediction equation

Prediction Equation

Using equation (3) in equation the prediction equation:


Update equation

Update Equation

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


Weights

Weights

  • We have that,

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


Specify weights

Specify Weights

  • We put:


Component mixture update

Component mixture update

  • We have the update:


Change components

Change components

  • Change components from Im to Im’.


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