Appendix C: Building up of the covariance matrix

A covariance matrix is created for the data contained in each orbit. To each abscissa record is assigned a flag F(J), which tests as .TRUE. for data from FAST, and as .FALSE. for data from NDAC. Abscissae are calculated using the mechanism described in Sect. 6, giving for each record a value ABSC(J). Each record is in addition identified by its star number, HIP(J). The covariance matrix is called CV and is stored in vector form as described above. The standard error on the abscissa residual is given by SRES(J) and the correlation coefficient with the same measurement as reduced by the other consortium by CCOR(J). The function ABSCCORR(F(J),LE,DIS) returns the correlation coefficient ACOR, which applies to data obtained within one consortium (F(J)) with a given dataset length of N5 and an abscissae distance of DIS between two stars. Then, given N abscissa records for current orbit:

    I1 = 0
    DO K = 1, N
C
C  diagonal element
C
      I1 = I1 + K
      CV(I1) = SRES(K) * SRES(K)
      DO L = K-1, 1, -1
        L1 = K*(K-1)/2 + L
        IF(HIP(L) .EQ. HIP(K)) THEN
C
C  same observation, different consortium
C
          CV(L1) = CCOR(K)*SRES(K)*SRES(L)
        ELSE
          DIS = ABS( ABSC(K) - ABSC(L) )
          ACOR = ABSCCORR(F(L),N5,DIS)
          IF(F(L) .EQ. F(K)) THEN
C
C  same consortium
C
            CV(L1) = ACOR*SRES(K)*SRES(L)
          ELSE 
C
C  different consortia, secondary correlation
C
            CV(L1) = CCOR(K)*ACOR*SRES(K)*SRES(L)
            END IF
          END IF
        END DO