Estimation fusion for linear equality constrained systems

The state of many dynamic systems evolves subject to some equality constraints. For example, in ground target tracking [1-3], if we treat roads as curves without width, the road networks can be described by equality constraints. In an airport, an aircraft moves on the runways or taxiways. In the quaternion-based attitude estimation problem, the attitude vector must have a unit norm [4]. In a compartmental model with zero net inflow [5], mass is conserved. In undamped mechanical systems, such as one with Hamiltonian dynamics, the energy conservation law holds. Likewise, in electric circuit analysis, Kirchhoff’s current and voltage laws hold.