I have a binary sequence,how to calculate Gilbert-Elliott model probabilities in Matlab?

Hey, I have a very long sequence of 1's and 0's and I want to use hmmestimate to find the probabilities of the GE model. Can one show a simple example of how I can do it in Matlab?

I have checked the Matlab hmmestimate help page, but it didn't help, because I do not understand the meaning of 'states'. All I have is a binary sequence to start from, nothing else and I guess this sequence is the seq vector in the help page. Thanks!

Answer 1

[Walter Roberson]

Does every "0" correspond to one setting, and every "1" correspond to a different setting? Or are there combinations of 0's and 1's that, taken together, indicate the setting, such as (for example) 0 by itself indicating one setting, 10 indicating a second setting, and 11 indicating a third setting?

If there are only 2 settings then you have only two states, which you can give names to such as

hmmestimate(..., 'statenames', {'stop', 'go'});

Answer 2

[Filip]

I have only 2 states: packet came ('1') and packet lost ('0'). So what I want to do with the whole thing is to find the probabilities that channel goes from bad state to bad , good to good, bad to good and good to bad.So what would be the steps in that case with hmmestimate?

[Walter Roberson]

State 1: packet is not present. State 2: packet is present. "Came" or "lost" then map into those states. Two states, state numbers 1 and 2. 0 transits to state 1, 1 transits to state 2. hmm estimation should then have no trouble filling in the state transition probabilites.

Answer 3

[Filip]

Maybe my lack of understanding of difference between sequence and states is the problem. Matlab help says:

TR = estimate of the transition, E = emission probabilities of an HMM for sequence, SEQ, with known states, STATES.

What is the difference between sequence and states? I think that sequence is what I have (the record of successes and failures) and I think states are 2: success and failure. Am I right? If so, why does Matlab ask that input sequence and states must be the same length?

This is what I did:

ind_seq is my sequence of 1's and 0's, that's the only input that I have (packet losses and successes). Then I type:

[TR, E] = hmmestimate(ind_seq,'statenames',{'good' 'bad'})

and Matlab error message says:

Error using hmmestimate (line 65) Input sequence and states must be the same length.