1. A method comprising: implementing a likelihood function using a processor, the likelihood function P = ∑ k = 1 K ⁢ ⁢ ∑ j = 1 J ⁢ ⁢ { - ( O k ⁡ ( j ) - μ _ o s ⁡ ( k ) ⁡ ( j ) ) 2 σ o s ⁡ ( k ) 2 ⁡ ( j ) } for a sequence of LPC cepstra observation vectors being utilized to estimate a mean for a distribution of target vocal tract resonances where K is the number of frames in the training signal, J is the number of orders in the LPC cepstra observation vectors o k , μ o s(k) (j)=F n [z 0 (k)]+F n ′[z 0 (k)][α k μ T −Z 0 (k)]+μ r s(k) and σ o s(k) (j) is the jth element along the diagonal matrix: Σ o s(k) =Σ r s(k) +F n ′[z 0 (k)]Σ z (k)(F n ′[z 0 (k)]) Tr where Σ r s(k) is a covariance of a residual model, Σ z (k) is a covariance of a distribution of vocal tract resonance trajectories, F n ⁡ [ z 0 ⁡ ( k ) ] = 2 n ⁢ ∑ p = 1 P ⁢ ⁢ e - π ⁢ ⁢ n ⁢ b p ⁡ ( k ) f s ⁢ cos ⁡ ( 2 ⁢ π ⁢ ⁢ n ⁢ f p ⁡ ( k ) f s ) is for an nth LPC cepstral order for a Taylor series expansion point z 0 (k), f s is a sampling frequency of a speech signal, f p is a vocal tract resonance frequency and b p is a corresponding vocal tract resonance bandwidth, μ T is a vector of means of target vocal tract resonances, α k is a filter parameter vector, μ r s(k) is a mean of the residual model, F n ′[z 0 (k)] is the derivative of F n [z 0 (k)] with respect to a vocal tract resonance dimension, wherein utilizing a likelihood function comprises: forming a plurality of partial derivatives of the likelihood function, the plurality of partial derivatives comprising a separate partial derivative δ ⁢ ⁢ P δ ⁢ ⁢ μ T ⁡ ( l o , f o ) for each combination of a speech unit l o and a dimension f 0 that can be formed from a plurality of speech units and a multi-dimensional target vocal tract resonance vector, each partial derivative being taken with respect to a dimension of a mean target vocal tract resonance vector for a speech unit; setting each of the plurality of partial derivatives equal to zero δ ⁢ ⁢ P δμ T ⁡ ( l o , f o ) = 0 to form a system of equations ∑ f ⁢ ⁢ ∑ l ⁢ ⁢ A ⁡ ( l , f ; l o , f o ) ⁢ μ T ⁡ ( l , f ) = ∑ k = 1 K ⁢ ⁢ { ∑ j = 1 J ⁢ ⁢ F ′ ⁡ [ z o ⁡ ( k ) , j , f o ] σ o s ⁡ ( k ) 2 ⁡ ( j ) ⁢ d k ⁡ ( j ) } ⁢ a k ⁡ ( l o ) ⁢ ⁢ where A ⁡ ( l , f ; l o , f o ) = ∑ k = 1 K ⁢ ∑ j = 1 J ⁢ F ′ ⁡ [ z o ⁡ ( k ) , j , f ] ⁢ F ′ ⁡ [ z o ⁡ ( k ) , j , f o ] σ o s ⁡ ( k ) 2 ⁡ ( j ) ⁢ a k ⁡ ( l o ) ⁢ a k ⁡ ( l ) ⁢ ⁢ and ⁢ d k ⁡ ( j ) = o k ⁡ ( j ) - F ⁡ [ z o ⁡ ( k ) , j ] + ∑ f ⁢ ⁢ F ′ ⁡ [ z o ⁡ ( k ) , j , f ] ⁢ z o ⁡ ( k , f ) - μ r s ⁡ ( k ) ⁡ ( j ) with each equation in the system having a different combination of (f o , l 0 ); and solving the system of equations to identify a mean for a distribution of target vocal tract resonances for each speech unit of the plurality of speech units.