This article regards a piecewise linear discrete time filtering problem with small observation noise. It is possible to separate the time intervals of linearity of the model and we can then approximate, over such an interval, the optimal filter by the corresponding Kalman-Bucy filter. When separating the intervals of linearity, the problem is to decide
wich filter must be applied. Likelihood ratio and quadratic variation tests are proposed for this purpose. We present and compare the performance of both tests numerically, based on simulation results.

keywords: sate estimation, Kalman-Bucy filter, likelihood ratio test, quadratic variation test.