This technical note is concerned with the remote estimation problem for measurement-delay systems with multiplicative noise and periodic coefficients. The multiplicative noise in every communication channel is described by an independent and identically distributed (i.i.d) Bernoulli process. The quality of the estimation achieved by an admissible filter is measured by a performance criterion described by the Cesaro limit of the mean square of the deviation between the remote signal and the estimated signal. The filter is designed in terms of the unique periodic solution of a Lyapunov equation together with the periodic stabilizing solution of a Riccati equation. In the end, we supply a numerical example to show the effectiveness of our proposed estimation approach.