There have been several new results to do with an old topic, the Cramer-Rao lower bound (CRLB). Specifically, it has been shown that for a wide class of parameter estimation problems (e.g. for objects with deterministic dynamics) the matrix CRLB with measurement origin uncertainty in addition to measurement noise, is simply that without measurement origin uncertainty times a scalar "information reduction factor" (IRF). Conversely, there has arisen a neat expression for the CRLB for state estimation of a stochastic dynamic nonlinear system (i.e. objects with a stochastic motion); but this is only valid without measurement origin uncertainty. This paper can be considered a marriage of the two topics: the clever Riccati-like form from the latter is preserved, but it includes the IRF from the former.