Parameter steepest slope method

Identification of the Parameters of a Model by the Steepest Slope Method... 

If the WSS surface is seen as similar to a geographical section with hills and valleys (at least for the two-parameter surface), the steepest-descent method would appear to follow the path of a round ball moving towards the minimum. When translated to a computer algorithm, some of the disadvantages become more apparent. The basic approach is to calculate the slope of the surface at the point of the initial (or current) parameter values. This can be calculated as dWSS/ dP over some small increment for each of the parameters P. By combining each of these partial derivatives over all the parameters, the direction of movement towards the minimum can be calculated. The second part of the problem is the distance h to move in thespecified direction. This must be determined by finding the minimum WSS in the direction calculated from the slope. This means extra calculations of the WSS, which makes this process less efficient, especially as it approaches the minimum. The new parameter value is calculated with the help of Eq. (19) ... 

To determine the direction of the steepest ascent, all estimated slopes along the variable axes are used. This means that even variables with a minor influence are used for maximum profit. We cannot be sure that variables associated with small linear coefficients are without any influence. If they have a small influence, this is picked up by the model parameter, and the method of steepest ascent will pay account for even such small influences. 

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