Roundoff noise in signal estimation and minimization of total real estimator output noise

Statistical analysis of error due to roundoffs in the arithmetic in signal estimation is given. The convenience of modeling this error by an equivalent roundoff noise source is shown. Matrix relations for computing the roundoff noise in nonrecursive and recursive estimators implemented with fixed point and floating point arithmetic are derived. The derived relations are verified by a statistical simulation procedure. Furthermore, relations for determining estimator coefficients which ensure minimum total real estimator output noise are derived. The basic performances and advantages of the doubly optimized estimators are shown and verified by characteristic examples. The proposed new classes of estimators ensure lower total output noise (5-30%), which was the aim of the optimization. The doubly optimized recursive estimator shows significantly greater robustness than the standard estimator, in relation to the finite accuracy of the coefficients