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Vector state-scalar observation (VSSO) Kalman channel estimators for doubly-selective OFDM systems (DS-OFDM) result in complexity savings of 90% without any loss of performance, as compared to vector state-vector observation (VSVO) Kalman estimators. In this letter, we present the VSSO Kalman channel estimator for doubly-selective multiple-input multiple-output OFDM (DS-MIMO-OFDM) systems. Unlike the VSSO estimator in a DS-OFDM system, where all the pilot symbols had the same value, the pilot symbols need to be designed in a specific way to enable the feasibility of a VSSO estimator for a DS-MIMO-OFDM system. We derive a sufficient condition called as VSSO Kalman-filter condition (VSSO-KFC) that needs to be satisfied by the pilot-pattern design for the feasibility of the VSSO Kalman estimator. We comment, and compare, the proposed pilot pattern with that of Barhumi's and Dai's pilot pattern. A new scheme is introduced, based on the proposed pilot pattern and VSSO Kalman filter, that increases the spectral efficiency compared to a conventional system.