Kalman filtering represents formidable computational linear algebra requirements for each new input measurement vector. The air-to-air missile guidance problem is addressed for which an extended Kalman filter (EKF) is required because the measurements are nonlinear in Cartesian coordinates. An explicit formulation is used. At the outset, we discretize the system dynamics and measurement model and incorporate a discrete-time EKF. A factorized L D LT algorithm is used to propagate the covariance matrices between sample times. A simulation analysis of the number of data bits required in the computations is provided. Comparison with other EKF algorithms shows that this method requires only 18 bit accuracy (compared to 32-40 bits for other methods). Quantitative position, velocity and acceleration estimates obtained for a highly maneuverable target are presented. A high-accuracy floating point optical processor is presented that is capable of computing the full EKF to allow a new measurement update each msec.