This paper proposes a linear estimation theory based direction of arrival (DOA) estimator to guarantee high-performance and computational efficiency. To do this, state-space system is derived from the linear prediction relation of the sinusoidal acoustic signal. Since it contains uncertain measurement matrix, the recently developed non-conservative robust Kalman filter (NCRKF) can be applied to compensate the performance degradation by the uncertain measurement matrix. However, unfortunately, the statistical information used in NCRKF scheme may not be precise in actual situation and it leads to the performance degradation. Therefore, in this paper, constrained NCRKF (CNCRKF) is presented to develop practical DOA estimator. It adopts constraint condition derived from the relation between target states to solve the performance degradation problem by the incorrect statistical information. The performance of the proposed solution is demonstrated by the computer simulation.