A New Model for Navigation Problems Using Discrete Time Points and Mixture of Distributions
This paper presents a novel approach to a navigation problem involving discrete time points (t=1,…,n). It proposes a method to observe only angles, leading to the formulation of equations. The data is divided into k non-sparse groups (G1,…,Gk), with the definition of initial weights for these groups. The prediction and update equations are derived using a mixture of distributions, allowing for efficient state and observation handling. The paper details the weight specification and component mixture updates, offering a comprehensive framework for problem-solving in navigation contexts.
A New Model for Navigation Problems Using Discrete Time Points and Mixture of Distributions
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Presentation Transcript
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’.
