  The Kalman filter is indispensable for state estimation across diverse fields
but faces computational challenges with higher dimensions. Approaches such as
Riccati equation approximations aim to alleviate this complexity, yet ensuring
properties like bounded errors remains challenging. Yamada and Ohki introduced
low-rank Kalman-Bucy filters for continuous-time systems, ensuring bounded
errors. This paper proposes a discrete-time counterpart of the low-rank filter
and shows its system theoretic properties and conditions for bounded mean
square error estimation. Numerical simulations show the effectiveness of the
proposed method.
