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Hydrodynamic Modeling Of Sailing Yachts

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This modified VA is obtained with a minimal modification of the normal VA (substituting bj (xt ) by [bj (xt )]γt ). 92) is independent of the specific form of the observation probabilities bi (xt ), and is applicable to both discrete and continuous density HMMs. 71) with diagonal covariance matrices, it is also possible to apply a specific weight γj,t for each feature xt (j ) (j = 1, . . 94) c In case of uncertain values we can consider that x is a random variable and, therefore, P (c|x) is a random variable too.

In the case of an ASR system, this observation sequence can be obtained from a sequence of feature vectors X = x1 , . . , xT submitted to a VQ process. However, the VQ process involves a loss of information that can reduce the system performance. This problem can be solved by forcing the HMM to work directly with the vectors x = (x(1), . . , x(p)) of the continuous p-dimensional representation space Rp . 70) vk ∈V (si ) where each P (x|vk , si ) is a log-concave or an elliptically symmetric pdf and cik = P (vk |si ) is the pdf weight (the sum of the pdf weights over k must be 1).

N ; k = 1, . . 33) (i = 1, . . 34) These probabilities must verify M k=1 bi (vk ) = 1 5. A matrix of initial states, in which each element is the probability of having a certain state as initial state = {πi } with πi = P (q1 = si ) (i = 1, . . 36) As can be seen, the model is fully defined by matrices A, B y . Thus, from now on, the model will be noted as the set of parameters λ = (A, B, ). As previously mentioned, the model generates a sequence of observations O = (o1 , o2 , . . , oT ) and a hidden sequence of states Q = (q1 , q2 , .

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