Stochastic processes satisfying the stochastic differential equations \[ \begin{aligned} dx(t) &= A(t,\zeta (t))x(t)dt+B(t,\zeta (t))dW(t),\quad t\geq 0,\\ dy(t) &= H(t,\zeta (t))x(t)dt+G(t,\zeta (t))dV(t),\quad t\geq 0,\end{aligned} \] are considered. In these equations \(\zeta (t)\) is a Markov process with a finite number of states, \(W(t)\) and \(V(t)\) are jointly noncorrelated stochastic processes with orthogonal increments. A stochastic equation for the determination of an estimate \(\hat x(t)\) of the state of the process \(x(t)\) on the basis of observations of the stochastic process \(y(t)\) and a stochastic equation for determining the matrix \(D(t)\) of the second moments of the error of estimation \(\tilde x(t) = x(t)-\hat x(t)\) are obtained, and the problem of constructing optimal estimations with minimal variance is considered. The case of homogeneous system with fixed coefficients, where \(\zeta (t)\) is a homogeneous Markov ergodic process with a finite number of states, is considered and asymptotic behavior of the matrix \(D(t)\) is investigated.