Navigation and surveillance applications require tracking constant input/bias targets. When the target’s trajectory follows a constant input/bias constraint,model mismatching caused by conventional track-ing algorithms can be handled by a delayed update filter (DUF). The statistical convergence and stability properties of the delayed update filter were studied to insure the rationality of its steady-state analysis. A steady-state filter gain was then designed for a constant-gain DUF to reduce the computations without much performance loss. Simulations demonstrate the potential of the constant-gain DUF,and the CGDUF is nearly 60% faster than the DUF without much loss in steady-state tracking accuracy. Navigation and surveillance applications require tracking constant input / bias targets. When the target’s trajectory follows a constant input / bias constraint, model mismatching caused by conventional track-ing algorithms can be handled by a delayed update filter (DUF). properties of the delayed update filter were studied to insure the rationality of its steady-state analysis. A steady-state filter gain was then designed for a constant-gain DUF to reduce the computations without much performance loss. Simulations demonstrate the potential of the constant -gain DUF, and the CGDUF is nearly 60% faster than the DUF without much loss in steady-state tracking accuracy.