arXiv:2610.34095v1 Announce Type: new Abstract: This paper deals with the optimal state estimation problem for discrete-time Markov jump linear systems in the sense of linear minimum mean-square error where the noises corrupting the system are mode-dependent and need not be Gaussian. An orthogonal projection extension-based equation (OPEBE) is established, which can decompose a random vector into several parts where the random vector contains conditional expectation of another random vector. Using the OPEBE and some results obtained in this paper, an optimal linear filter for the system under consideration is proposed. The computational and storage load of the proposed filter does not increase with time. Also, the proposed filter is finite-dimensionally computable and has a recursive structure. Computer simulations are provided to verify the effectiveness and performance of the proposed optimal linear filter.