  We consider the two-line fitting problem. True points lie on two straight
lines and are observed with Gaussian perturbations. For each observed point, it
is not known on which line the corresponding true point lies. The parameters of
the lines are estimated. This model is a restriction of the conic section
fitting model because a couple of two lines is a degenerate conic section. The
following estimators are constructed: two projections of the adjusted least
squares estimator in the conic section fitting model, orthogonal regression
estimator, parametric maximum likelihood estimator in the Gaussian model, and
regular best asymptotically normal moment estimator. The conditions for the
consistency and asymptotic normality of the projections of the adjusted least
squares estimator are provided. All the estimators constructed in the paper are
equivariant. The estimators are compared numerically.
