An on-line measurement of pipe length is considered. First, the acoustic pressure in a straight pipe is modeled by a linear dynamic system which includes some unknown parameters, that is, the parameters of pipe length and variances of transition and observation noises. Second, adequate candidates are introduced for the unknown parameters and then the posteriori probabilities of the candidates are calculated by using Kalman filters and Bayes' rule.
The increase of the number of the candidates, however, causes the measurement system to require much com-putational time for measuring the pipe length. Thus, determination of optimal candidates is considered using the probabilistic measure “divergence” together with an effective candidate-updating algorithm based on the Powell method.