A bilinear approach to the parameter estimation of a general heteroscedastic linear system with application to conic fitting

Abstract

In this paper, we study the parameter estimation problem in a general heteroscedastic linear system, by putting the problem in the framework of the bilinear approach to low-rank matrix approximation. The ellipse fitting problem is studied as a specific example of the general theory. Despite the impression given in the literature, the ellipse fitting problem is still unsolved when the data comes from a small section of the ellipse. Although there are already some good approaches to the problem of conic fitting, such as FNS and HEIV, convergence in these iterative approaches is not ensured, as pointed out in the literature. Another limitation of these approaches is that they can’t model the correlations among different rows of the “general measurement matrix”. Our method, of employing the bilinear approach to solve the general heteroscedastic parameter estimation problem, overcomes these limitations: it is convergent and can cope with a general heteroscedastic problem. Experiments show that the proposed bilinear approach performs slightly better than other competing approaches