This paper considers the problem of continuous state estimation in the presence of random switches. There are three random chains X=(X1, ..., XN), R=(R1, ..., RN), , and Y=(Y1, ..., YN), where the continuous Y is observed, while the continous X and the discrete R are hidden. The problem is to estimate X and R from Y. In the classical models R is Markovian, X is linear Markovian conditionally on R, and Y1, ..., YN are independent conditionally on (R,X). Neither exact filtering nor smoothing is possible with reasonable complexity in such models and the different research works mainly concern different approximate algorithms. More recently, another class of models, in which exact filtering and smoothing with polynomial complexity in time are feasible, has been proposed. In the latter models the distribution of the triplet (X, R, Y) is defined by a Markov distribution of (R, Y), and then X is linear Markovian conditionally on (R, Y). Subsequently, two extensions of these models have been specified. In the first one, the Markovianity of (R, Y) is extended to the « partial » Markovianity, in which (R, Y) is Markovian with respect to R, but may not be with respect to Y. In the second one, (R, Y) remains Markovian and X is assumed to be linear conditionally on (R, Y), but is not assumed Markovian. The aim of this paper is to propose a new model admitting both these extensions simultaneously. In the new model proposed the distribution of Y conditional on R can be of the « long dependence » kind, and it is the same for the distribution of X conditional on (R, Y). We show that the Kalman-like exact filtering is computable with polynomial complexity in time in the new proposed model.