  The problem of optimal linear estimation of functionals depending on the
unknown values of a random field $\zeta(t,x)$, which is mean-square continuous
periodically correlated with respect to time argument $t\in\mathbb R$ and
isotropic on the unit sphere ${S_n}$ with respect to spatial argument
$x\in{S_n}$. Estimates are based on observations of the field
$\zeta(t,x)+\theta(t,x)$ at points $(t,x):t\leq 0,x\in S_{n}$, where
$\theta(t,x)$ is an uncorrelated with $\zeta(t,x)$ random field, which is
mean-square continuous periodically correlated with respect to time argument
$t\in\mathbb R$ and isotropic on the sphere ${S_n}$ with respect to spatial
argument $x\in{S_n}$. Formulas for calculating the mean square errors and the
spectral characteristics of the optimal linear estimate of functionals are
derived in the case of spectral certainty where the spectral densities of the
fields are exactly known. Formulas that determine the least favourable spectral
densities and the minimax (robust) spectral characteristics are proposed in the
case where the spectral densities are not exactly known while a class of
admissible spectral densities is given.
