In this paper, a new modeling and filtering approachfor rigid body attitude estimation is investigated. Incontrast to the current state-of-the art where the process modelisdrivenbygyroscope measurements, weproposeanalternativemodeling formulation where the process model is fed by themagnetometer measurements. The resulting dynamic modeltakes the form of a descriptor system, also known as singularsystem.Basedonthismodelandusingthequaternionformalismwe derive a recursive filter whose performance is validatedthrough numerical and experimental tests.