We propose a decentralized subset method for optimal processing and combining of uplink signals in a distributed MIMO (D-MIMO) network. We further propose the use of Kalman filters with the square-root implementation to estimate the received uplink signals. This square-root implementation is shown to be numerically stable when inverting the covariance matrix, as it always assures the covariance matrix to be symmetric and positive semi-definite. In the paper we also analyze the computational complexity and cost with different combining methods. We show that the Kalman filter implementation provides the same result as the MMSE method in terms of the spectral efficiencies and equivalent SINR. However, the Kalman filter implementation is shown to be very efficient as it provides the possibility to fully utilize  parallel computing of distributed hardware processors. Moreover, the processing can be decentralized and the estimates can be aggregated from local estimates to as many access points (APs) as needed to reach the desired performance target. A Kalman filter implementation has the flexibility to aggregate signals in different ways, allowing the fronthaul architecture to support connectivity of individual APs in any combination of parallel or serial manners.