A recursive estimation procedure for certain nonlinear regression problems-Scalar single parameter case

Many problems of current interest (e. g. in space engineering) are formulated as parameter estimation in a prescribed nonlinear regression model when the number of observations is large. It is important that a proposed method of estimation be such that (i) the computations can be performed quickly in a recursive fashion as more data becomes available, and (ii) that the successive estimates possess desirable asymptotic statistical properties. It is the purpose of this paper to present such a procedure for scalar observations and a single unknown parameter. The vector multi-parameter case is of greater interest, but a good deal of insight into these more general problems is gained from our present considerations. They appear to have some independent interest in the field of mathematical statistics.