Sampling error results in large errors in sample covariance ÔfarÕ from observation location.  Results in inappropriate updates to state vector.  Simple example of how errors in Pb can affect state update in KF.  2-D state vector (x1 and y2), single ob only for x1 (x2 unobserved).  Heavy line is prior covariance (marginal distribution on axes).  Dot on x1 axis is value of ob, light solid is marginal distribution for ob. Dashed line is posterior covariance.  Note the true background x1 is uncorrelated with x2. Underestimating covariance causes ob not to be used enough, posterior covariance too similar to prior. Over-estimating correlations between state variables causes state vector to be incremented too much in that direction. Posterior variance is too small in x2 direction, x2 mean is biased.