Non-Contact speed measurement is studied from the standpoint of statistical estimation and a new method is proposed.
Recorded waveform W(ξ) of natural irregularity of the surface of a strip is considered to be a sample function from some stochastic process and this process is stationary and gaussian in many cases.
Suppose the strip is moving at speed v. The signal X(t) obtained by observing the strip at ξ=0 is given by X(t)=W(vt). This means that the observation signal X(t) is a stochastic process with an unkown parameter v if the statistics of W(ξ) are known.
Therefore, if the observation data {X(t); 0≤t≤T} is given, it contains information about strip speed and non-contact speed measurement is made possible through applying the statistical estimation theory to the data.
The authors have studied on this problem and got the following results. (1) Maximum likelihood estimation is applied and an explicit expression of estimator is derived. (2) Error variance and bias of the setimator is examined and the estimator is probed to be fairly satisfactory in an ordinary measurement condition. (3) For the case where the statistics of W(ξ) are unkown or not stationary, a way of on-line determination of the statistics is discussed. And, it is shown that, when combined wtih the estimator derived in (1), it leads to a new non-contact speed measurement method which is applicable even if the statistics of irregularity are unknown. (4) This new method is analyzed and it is made clear that this is most naturally understood if one considers this to be a modified version of the method of obtaining v by using the formula W(vt)=vW′(vt) and that there is a possibility that strip speed is measured accuralety in a very short time by this method.

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