I am interested in using Hidden Markov Models in the context of multi-sensors sequences in vegetation remote sensing.

The observation labels are the same as the state labels.

Each observation at a given time $t$ is classified and I want to use HMM in order to reduce classification errors.

For example, the states could be : FOREST, CROP, SOIL, WATER.

I have an associated transition matrix between those states.

Thanks to a sensor, I can observe a sequence of observations from which I want to infer the most likely sequence of hidden states.

Sequence of observations : FFFWFFFF

--> Sequence of states : FFFFFFFF

Now, each observation comes from a given sensor (or maybe ground data) and I am able to assign a given weight or confidence in this observation.

As a limiting case, let's imagine I'm 100% positive that the fourth observation is water because I was on the ground, and that the transitions from/to water are null.

I would like the algorithm to output :

--> Sequence of states : WWWWWWWW

I was thinking about using the following states:

  • etc.

and computing a new transition matrix but this does not seem right.

Thank you for your help!

  • $\begingroup$ It seems like you already know your states, so there is nothing hidden or latent. I am not sure you need to model your problem with a HMM. You can calculate the most likely sequence by using the viterbi algorithm. So you can calculate the transition matrix, and then since you know when you are at a given state, you can calculate the conditional emission probabilities. $\endgroup$
    – Zhubarb
    Jan 10, 2018 at 15:43

1 Answer 1


I think you can model your problem with the original states, where each state has multiple emissions (the different sensors), and there are missing emissions (where a sensor hasn't measured a particular state). Maybe you can find a software library that allows for both circumstances, or you might be able to implement this with a flexible probabilistic programming language such as rstan. If you already have the transition probabilities and measurement probabilities, your problem is only decoding, the Viterbi algorithm. A recent book on text processing has a good chapter on the Hidden Markov Model, you can find it here: https://web.stanford.edu/~jurafsky/slp3/9.pdf.

  • $\begingroup$ Thanks for your answer! However I don't know the probability that an observaiton is measured by a given sensor... For example, I could have only observations from Sensor 1 in a sequence and mixed observations in another. I don't know how I can untangle this. $\endgroup$
    – thomas
    Jan 10, 2018 at 15:48
  • $\begingroup$ So you don't know any of these probabilities? That would maybe make it easier to implement, although harder to measure. You do need some kind of prior on this. Let's say you think all three types are equally likely? Does that differ in each of the states? $\endgroup$
    – Gijs
    Jan 10, 2018 at 16:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.