When a deep space probe is launched, corrections may be necessary to place the probe on a precisely calculated trajectory. Radio telemetry provides a stream of vectors x1,,,,,,,,,,,,xk, giving information at different times about how the probe's position compares with its planned trajectory. Let Xk be the matrix [x1 xk]. The matrix Gk = XkXTk is computed as the radar data are analyzed. When xk+1 arrives, a new Gk+1 must be computed. Since the data vectors arrive at high speed, the computational burden could be severe. But partitioned matrix multiplication helps tremendously. Compute the column-row expansions of Gk and Gk+1, and describe what must be computed in order to update Gk to form Gk+1.
