Influence of a priori pole coordinate errors on the errors of UT1 determined from NEOS Intensives.

Simplified case

Expression for delay may be approximately written in the form:

tau = alpha ( M b ) P s + d

where tau -- delay, M -- matrix of diurnal rotation and wobble, P -- matrix of precession and nutation, b -- baseline vector, s -- source unit vector, alpha = 1/c * 1/(1 + 1/c (V_earth + v_2) s, d -- other terms. Since we a looking for small correction for rotation matrix M, we can re-write the expression above in the form

tau = alpha ( m x b ) P s = alpha m ( b x P s)

where m -- vector of perturbation rotation and "x" denotes vector product. Partial derivatives delta tau/ delta m_i are then

delta tau/ delta m_i = alpha ( b x P s) e_i

where e_i -- unit vector. Imagine that we estimate only one parameter: m_3 (UT1). Then the LSQ estimate:

Delta Y_e = ( sum delta X/delta Y * Delta X ) / sum (delta X/delta Y)**2

We can express delta m_3(est) as

delta m_3(est) = 1/alpha sum ( beta_3 * delta tau )/ sum (beta_3**2)

having neglected term d, where beta_i stands for (b x P s) e_i Contribution of the errors in a priori polar motion to delay can be expressed as

Delta tau = alpha ( beta_1 Delta X + beta_2 Delta Y )

This error propagates to the estimates of UT1 as

delta m_3 = (sum beta_1 beta_3)/( sum beta_3**2 ) * Delta X + (sum beta_2 beta_3)/( sum beta_3**2 ) * Delta Y

Rigorous approach

We can lift simplifying conditions. Contribution of the errors in polar motion to the estimates of UT1 can be written in this form:

Delta m_3 = k_1 Delta X + k_2 Delta Y

where k_1 and k_2 are session-dependent admittance coefficient which are expressed in the following form:

k_i = ( N**-1 sum A(T) w Delta tau/Delta m_i )_{m_3}

Here N -- normal matrix, A -- matrix of equations of conditions, w -- vector of weights and the symbols _{m_3} denotes the components of the vector which corresponds to the parameter m_3 (UT1). Coefficients k_1 and k_2 were found numerically from two LSQ solutions which used partial derivatives of delay on pole coordinates in the right parts of equations of conditions instead of the difference between observed and predicted delay. Admittance for X pole (green) and for Y pole (blue) coordinates is shown in this figure.

Conclusions

Admittance is roughly -+0.5 for WETTZELL/NRAO20 baseline and about 0.2 for WETTZELL/KOKEE baseline. Median formal error of determination of UT1 from NEOS Intensive experiments for 1999 is at the level of 1.1 nrad. Comparison of UT1 series derived from analysis of 24 hours VLBI experiments with UT1 derived from Intensives, shows that the formal error should be scaled by factor 1.7, and the actual errors are at the level of 1.8 nrad. Provided the errors in X and Y component of polar motion are uncorrelated, combined admittance of polar motion errors is at the level of 0.3 for the baseline WETTZELL/KOKEE. IF to put the goal to have the the contribution of systematic errors in determination of UT1 at the baseline WETTZELL/KOKEE 10% of the overall budget ( 0.2 * 1.7 nrad ) the errors in polar motion should not exceed 0.2 * 1.7 / 0.3 = 1 nrad = 0.2 mas.
Back to Leonid Petrov's discussion page.

Last update: 14-MAY-2001 19:14:07