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,..., x_k, giving information at different times about how the probe's position compares with its planned trajectory. Let X_k be the matrix [X₁ ... X_k]. The matrix Gk = X_k X_k^T is computed as the radar data are analyzed. When X_k+1 arrives, a new G_k+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 G_k and G_k+1, and describe what must be computed in order to update G_k to form G_k+1.

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The probe Galileo was launched October 18, 1989, and arrived near Jupiter in early December 1995.