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Numerical rounding can affect the Kalman filter by introducing errors in the computation of state estimates and covariance matrices. The Kalman filter is a mathematical algorithm that requires calculations involving real-valued numbers, and many of these computations involve the addition, subtraction, multiplication, or division of small values. As a result, the computations can be susceptible to rounding errors, especially when dealing with large or small numbers.

When numerical rounding occurs, the values used in the Kalman filter may deviate from their true values, leading to inaccurate estimates of the state and covariance matrices. This can lead to poor performance of the filter, especially if the rounding errors accumulate over time. To minimize the impact of numerical rounding, it is important to use high-precision arithmetic when implementing the Kalman filter algorithm, and to carefully choose the data types used for representing the values involved in the calculations. Additionally, techniques such as scaling and rescaling can be used to reduce the effects of numerical rounding on the filter.