Markov Models and Applications . Henrik Schiøler, Hans-Peter Schwefel . Mm1 Discrete time Markov processes Mm2 Continuous time Markov processes Mm3 M/M/1 type models Mm4 Advanced queueing models Mm5 Hidden Markov Models and their application (hps).
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Henrik Schiøler, Hans-Peter Schwefel
Note: slide-set will be complemented by formulas, mathematical derivations, and examples on the black-board!
Problem 2: Find ’most likely’ state sequence for an observation o=[o1,...,oT] in a given HMM.
Problem 3: Find ’most likely’ HMM model for an observation o=[o1,...,oT].
Hidden Markov Models: Given is the following 3-state hidden Markov model with parameters pi1=[0.2,0.3,0.5], P=[0.2,0.4,0.4; 0.5,0.1,0.4; 0.2,0.2,0.6]. The observations are coin-toss results (Heads=1, Tails=2) with B=[0.8,0.2;0.5,0.5;0.1,0.9].
Localisation with HMMs: Consider a 5mx5m squared room in which 3 access points are placed in the three corners (0,5), (5,5), (5,0). Use a grid with 1mx1m elements to discretize this geographic space. A mobile device is moving through the room and the Access Points measure received signal strength which follows a path-loss model RSSI[dB] = Round(- 6 log10 (d/d0)+13+N), with d0=0.1m. The Noise N is assumed to be Normal distributed with standard deviation sigma=2.
Write Matlab functions to