About the Cover

The watercolor portrait of Carl Friedrich Gauss was made by J.C.A. Schwartz in 1803 (photo courtesy of Axel Wittmann, copyright owner). This is the decade when Gauss first used the least squares method to determine orbits of asteroids and comets. The 1963 picture of Rudolf Kalman in his office at the Research Institute for Advanced Studies was taken after he first published papers describing the Kalman filter (photo courtesy of Rudolf Kalman, copyright owner). The GPS IIF spacecraft is the latest operational version of the spacecraft series (picture courtesy of The Boeing Company, copyright owner). The GPS ground system uses a Kalman filter to track the spacecraft orbits and clock errors of both the spacecraft and ground monitor stations. A least squares fit is used to compute the navigation message parameters that are uplinked to the spacecraft and then broadcast to user receivers. GPS receivers typically use a Kalman filter to track motion and clock errors of the receiver. The plot shows the root-mean-squared user range error (URE) for 29 GPS satellites operational in 2005. Those URE values were computed using smoothed GPS orbit and clock estimates as the “truth” reference (see Example 9.6 of Chapter 9).