1. A method comprising: representing, by use of a processor, state transition probabilities between a plurality of states that are statistical Markov model states and output probabilities associated with a plurality of previous states that are previous statistical Markov model states, wherein each of the plurality of states is represented by an integer state indicator i that indicates a current basic state, and a history indicator comprising a real number in the form h 1 h 2. .. h n created as a concatenation of previous state indicators h, with more recent previous state indicators h having more numerical significance, to provide a signal history without excessive computational burden, the state transition probabilities between the plurality of previous states depend on a sequence of previous states of the plurality of previous states and the output probabilities associated with each of the plurality of states depend on the sequence of previous states; calculating a state transition probability for the plurality of states by minimizing an expression tr(Ã i T D T Ã i G)−2tr(DÃ i P α,i ) subject to constraints that 1 T Ã i φ(h)≦0 and Ã i φ(h)≧0, wherein A |i is chosen so that A i φ(h)≈ā(h), 1 T A i φ(h)=1, A i φ(h)≧0, ∀hε[0,1), 1 is a vector of all ones, D = [ I - 1 T ] , G = ∫ 0 1 ⁢ φ ⁡ ( h ) ⁢ φ T ⁡ ( h ) ⁢ dh ⁢ ⁢ and ⁢ ⁢ P a , i = ∫ 1 1 ⁢ φ ⁡ ( h ) ⁢ b i ⁡ ( h ) T ⁢ dh , where G is a Grammian, P a,i is a cross correlation, φ(h) is a basis function, A i is a state transition probability matrix, Ã i denotes a first s−1 rows of A i , ā(h) is a histogram-based estimate state transition probability, and b i (h) T =ā 1i (h)−e s , e s =[0, 0,. .. 1] T ; and using the calculated state transition probability to generate an output signal for use in signal analysis that includes pattern recognition or pattern detection.