Abstract: An analytical apparatus for optimally combining measurements from N individual rate sensing devices or gyros into a single rate estimate significantly improves performance over that of any individual component device. Kalman filtering is used to combine rate sensed devices optimally in the sense of minimizing the variance of the rate error. The Riccati differential equation (RDE) associated with combining a collection of rate sensed devices is completely and exactly solved to derive to the matrix RDE. This analytic solution serves as the key for understanding all of the theoretical properties of the optimal filter, and provides a complete characterization of the final virtual rate sensed performance. In addition, the analytic RDE solution allows many practical problems to be solved that have proved essential for developing successful filter implementations. A discrete-time minimum variance filter implementation combines sensor measurements optimally.

Abstract: An analytical apparatus for optimally combining measurements from N individual rate sensing devices or gyros into a single rate estimate significantly improves performance over that of any individual component device. Kalman filtering is used to combine rate sensed devices optimally in the sense of minimizing the variance of the rate error. The Riccati differential equation (RDE) associated with combining a collection of rate sensed devices is completely and exactly solved to derive to the matrix RDE. This analytic solution serves as the key for understanding all of the theoretical properties of the optimal filter, and provides a complete characterization of the final virtual rate sensed performance. In addition, the analytic RDE solution allows many practical problems to be solved that have proved essential for developing successful filter implementations. A discrete-time minimum variance filter implementation combines sensor measurements optimally.

Abstract: Periodic gain adjustment in plants of irreducible order, n, or for equalization of communications channels is effected in such a way that the plant (system) appears to be minimum phase by choosing a horizon time N>n of liftings in periodic input and output windows .rho..sub.u and .rho..sub.y, respectively, where N is an integer chosen to define the extent (length) of each of the windows .rho..sub.u and .rho..sub.y, and n is the order of an irreducible input/output plant. The plant may be an electrical, mechanical or chemical system, in which case output tracking (OT) is carried out for feedback control or a communication channel, in which case input tracking (IT) is carried out. Conditions for OT are distinct from IT in terms of zero annihilation, namely H.sub.s H.sup.+.sub.s =I for OT and H.sub.s.sup.+ H.sub.s =I of IT, where the OT conditions are intended for gain adjustments in the control system, and IT conditions are intended for equalization for communication channels.