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We consider the standard Kalman filtering problem in which the dimension of the output (measurement) vector is p, while the dimension of the state-space for the process model is n. The usual approach to determination of the steady-state gain matrix involves solving an algebraic Riccati equation consisting of n(n+1)/2 quadratically nonlinear equations. In this article, we present an alternate equation for the optimal gain matrix, itself, continuing only np quadratically nonlinear components. Numerical results comparing the efficiency of the new equation with the standard approach are also given

A reduced dimensionality method for the steady-state Kalman filter