Equality-constrained bilinear state estimation

This paper generalizes the recently introduced bilinear formulation of the weighted least squares (WLS) state estimation problem to those cases in which equality constraints must be explicitly considered. This leads to augmented equation systems in which both state variables and Lagrange multipliers get updated throughout the three stages arising in the bilinear approach (two linear filters with a nonlinear transformation in between). The proposed formulation prevents the ill-conditioning typically arising when exact-injection constraints are handled as virtual measurements with huge weights, while the excellent convergence speed of the bilinear scheme, which for practical purposes reaches the optimal solution in a single iteration, is fully preserved.