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Homework 20: Viterbi Decoder for the Graz Weather Model

[Points: 8; Issued: 2004/06/04; Deadline: 2004/06/28; Tutor: Alexander Rudolf Gruber; Infohour: 2004/06/21, 12:00-13:00, Seminarraum IGI; Einsichtnahme: 2004/07/05, 12:00-13:00, Seminarraum IGI; Download: pdf; ps.gz]

• Make an umbrella sequence'' of length using the MATLAB commands
    >> rand('state',YOUR_MATRIKELNUMMER);
>> x = 0.5+0.5*sign(rand(5,1)-0.5);

Take the numbers in vector x as time sequence according to for no umbrella'' at day , and for umbrella'' at day .
• Manually find the most likely weather sequence'' for the five days based on the HMM weather model in the tutorial Hidden Markov Models:
 and

using the Viterbi algorithm.

Present your Viterbi decoding of the weather sequence graphically, using trellis plots as figs. 5-7 in the HMM tutorial. State the values for the variables and used in the Viterbi algorithm for and .

• Write a MATLAB function for the Viterbi decoding of the weather sequence from your umbrella sequence. This Viterbi decoder is for discrete emission probabilities (no umbrella'' or umbrella''). You may relate to the Viterbi decoder function (with continuous emission probabilities) requested in homework Hidden Markov Models''.

Verify your result for the most likely weather sequence found above.