Smoothing for a linear system driven by a marked point process with a rate that depends on the state of the system is considered. A linear combination of the states is observed in additive white Gaussian noise. A smoother that uses estimation and detection is simulated on a computer and its mean squared error (MSE) is compared with the theoretical MSE of the optimal linear smoother and filter. The falso alarm rate is shown to depend strongly on the region of support of the mark distribution. When false alarms are low, the estimation/detection scheme has lower MSE than the optimal linear smoother.