Numerical techniques deterministic approach

Over the past ten years the numerical simulation of the behavior of complex reaction systems has become a fairly routine procedure, and has been widely used in many areas of chemistry, [l] The most intensive application has been in environmental, atmospheric, and combustion science, where mechanisms often consisting of several hundred reactions are involved. Both deterministic (numerical solution of mass-action differential equations) and stochastic (Monte-Carlo) methods have been used. The former approach is by far the most popular, having been made possible by the development of efficient algorithms for the solution of the "stiff" ODE problem. Edelson has briefly reviewed these developments in a symposium volume which includes several papers on the mathematical techniques and their application. [2]... 

In this paper the estimation problem is solved from a point of view which is essentially different from the stochastic approach of the conventional Kalman filter. The time-variant state estimation problem is re-phrased into a time-invariant parameter estimation problem, and least-squaxes techniques, which is derived under deterministic framwork, are then used. The advantage of using least-squaxes approach is that it does not require a pHori knowledge of the noise statistics, the initial values of the estimated state, and its corresponding error covariance. Close relations are found between the Kalman filter and the least-squaxes Alter. Finally, a numerical example is provided to illustrate the feasibility of the proposed method. 

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