The Research Into The Problem Of Parameter's Estimate Of Linear System

The researth into the prob1em of signa1's parameter estimate has neverstopped. Up to now, this prob1em is a1ways studied with assumptiofl ofcondi tional invertibi l ity of design matrix.In this thesis, we first consider the performance comparison betweenoptima11y weighted LS estimate and 1inear unbiased minimum varianceestimate in the condition of design matrix invertibi 1 ity. Under acondition on noise variance matrix invertibi l ity, the difference betweentwo estimates error variances can be ca1cu1ated, and the two estimatescan converge to the same one under a certain condition.Second, we obtain general ized answers of weighted LS and optima1ly -weighted LS under a condition on singu1ar matrix, and discuss theperformance comparison between generalized optima11y weighted LSestimate and linear unbiased minimum variance estimate.Final1y, we present genera1ized Matrix Schwarz inequa1 ity.