The paper is devoted to the algorithms of real-time process estimation in stochastic differential systems. The hidden state under estimation belongs to a class the Markov jump processes (MJPs), which can be treated as a continuous-time Markov chain with values in the abstract space of the random vectors. The available statistical information includes continuous indirect noisy observations and processes with counting components. The filtering problem is to find the state estimate based on the observations available up to the current moment. The paper introduces the essential analytical properties of the investigated MJPs. The key feature is a martingale representation of any function of the MJP via the solution to a linear stochastic differential system (SDS) with a martingale on the right-hand side (RHS). It allows us to treat the investigated stochastic observation systems as linear non-Gaussian ones and apply the Kalman–Bucy algorithm to obtain the best linear filtering estimate. The paper also presents an analog of the Kushner–Stratonovich equation, describing the evolution of the conditional probability density function (pdf), given the available observations, to calculate the optimal non-linear estimate. The estimation performance is illustrated by the numerical example related to the computer network.