Data covariance matrix In practice in GPS (as well as many other fields), the data covariance matrix is somewhat arbitrarily chosen Largest problem is temporal correlations in the measurements. Typical gps data set size for 24- hours of data at 30 second sampling is 8X2880=23000 phase measurements. Since the inverse of the covariance matrix is required fully accounting for correlations requires the inverse of 23000X23000 matrix To store the matrix would require, 4Gbytes of memory Even if original covariance matrix is banded (ie correlations over a time short compared to 24-hours), 03/1703 12540Lec11 Data covariance matrix Methods on handling temporal correlations If measurements correlated over say 5-minute period, then Use full rate data, but artificially inflate the noise on each measurement so that equivalent to say 5-minute sampling(ie, sqrt(10)higher noise on the 30-second sampled values (GAMIT method) When looking a GPS results, always check the data noise assumptions(discussed more near end of course) Assuming a valid data noise model can be developed what can we say about noise in parameter estimates? 03/703 12540Lec1103/17/03 12.540 Lec 11 5 Data covariance matrix • In practice in GPS (as well as many other fields), the data covariance matrix is somewhat arbitrarily chosen. • Largest problem is temporal correlations in the measurements. Typical GPS data set size for 24- hours of data at 30 second sampling is 8x2880=23000 phase measurements. Since the inverse of the correlations requires the inverse of 23000x23000 matrix. • To store the matrix would require, 4Gbytes of memory • correlations over a time short compared to 24-hours), covariance matrix is required, fully accounting for Even if original covariance matrix is banded (ie., the inverse of banded matrix is usually a full matrix 03/17/03 12.540 Lec 11 6 Data covariance matrix • use samples every 5-minutes (JPL method) measurement so that equivalent to say 5-minute sampling (ie., (GAMIT method) assumptions (discussed more near end of course). • what can we say about noise in parameter estimates? Methods on handling temporal correlations: – If measurements correlated over say 5-minute period, then – Use full rate data, but artificially inflate the noise on each sqrt(10) higher noise on the 30-second sampled values – When looking a GPS results, always check the data noise Assuming a valid data noise model can be developed, 3