Re: looking for a problem's name and possibly algorithm

[Francesco Potortì]

>
>On 06/29/2012 02:41 PM, Francesco Potortì wrote:
>> Dear all,
>> 
>> I have a problem which I am sure is very common, but I don't know how it
>> is usually named.
>> 
>> I have a system with a small number of states (N < 100), which evolves
>> in discrete time.  I have a state vector indicating the likelihood of
>> the system to be in any of its possible states.  For each time step,
>> there can be one of a number of events (M) or no events.  For each
>> event, or the no-event situation, I have a transition matrix with which
>> I multiply the state vector to get a new state vector.
>> 
>> So the system evolves at each time step by multiplying the likelihood
>> state vector by a transition matrix depending on the event happening at
>> that time step.  At each time, I declare that the system is in state S
>> where S is the index of the state vector with the highest number.
>> 
>> This may be made more complex by adding some memory: the currect state
>> vector does not depend only on the immediately past one, but on a small
>> number of past ones.
>> 
>> What is the official name of such a model, and what are the functions
>> that I may find useful in Octave's or Octave-forge's arsenal?
>> 
>> Until now, I ma just doing matrix multiplication, and that looks enough,
>> but onenever knows what's around...
>> 
>
>Hi,
>
>to me this sounds like some sort of stochastic process. You might have a
>look at Poisson processes and similar stuff. Some people in the image
>processing community also use quite similar models. There they are
>sometimes referred to as diffusion or osmotic processes. For example,
>Gaussian smoothing can be interpreted in such a way.

The state of the system in fact represents the position of a person in
an environment, and the events are generated by the person moving inside
a triggering sensors.  The states are positions inside the environment,
the likelihood vector shows a guess of the person's position in the
environment, and the evolution of the system and the vector is driven by
the movements of the person.

So, if the person's movements are deterministic, I do not think that I
can call this a stochastic process.  Yet, I don't know the person's
position for sure, and I must guess it from the triggered events (which
may not be reliable).

Does this process of guessing have a sandard name?

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