Sequential estimation Since the blocks of the data covariance matrix can be separately inverted, the blocks of the estimation (A'V-1A)can be formed separately can combined later Also since the parameters to be estimated can be often divided into those that effect all data (such as station coordinates and those that effect data a one time or over a limited period of time(clocks and atmospheric delays) it is possible to separate these estimations(shown next page) Sequential estimation Sequential estimation with division of global and local parameters V is covariance matrix of new data (uncorrelated with priori parameter estimates), vxa is covariance matrix of prior parameter estimates with estimates xa and x, are local parameter estimates, x* are new global parameter estimates AVA+V AIIJAV-ly+v-x A, VA A VA A, V† 03/17/03 12.540 Lec 11 17 Sequential estimation • Since the blocks of the data covariance matrix can be separately inverted, the blocks of the estimation (ATV-1A) can be formed separately can combined later. • Also since the parameters to be estimated can be often divided into those that effect all data (such as station coordinates) and those that effect data a one estimations (shown next page). time or over a limited period of time (clocks and atmospheric delays) it is possible to separate these 9 03/17/03 12.540 Lec 11 18 Sequential estimation • Sequential estimation with division of global and local parameters. V parameter estimates), Vxg is covariance matrix of prior parameter xg and xl are local parameter estimates, xg + are new global parameter estimates. y x g È Î Í ˘ ˚ ˙ = A g A l I 0 È Î Í ˘ ˚ ˙ xg xl È Î Í ˘ ˚ ˙ x g + xl È Î Í ˘ ˚ ˙ = A g T V-1 A g + Vxg -1 ( ) A g T V-1 A l A l T V-1 A g A l T V-1 A l È Î Í Í ˘ ˚ ˙ ˙ -1 A g T V-1 y + Vxg -1 xg A l T V-1 y È Î Í ˘ ˚ ˙ is covariance matrix of new data (uncorrelated with priori estimates with estimates