ESTIMATION OF RANDOM STATES IN GENERAL LINEAR-MODELS

When studying the problem of state estimation in linear models, one usually assumes that the state vector is an unknown vector of constants, thereby attributing the statistical behavior of the measurements entirely to the measurement noise. In addition, it is also common to assume invertibility of various matrices. There are, however, situations in which the state vector is genuinely random and no matrices are invertible, making the aforementioned assumptions unwarranted. In this note, we formulate an estimate, called the generalized Fisher estimate, and show how to calculate it without assuming invertibility of any of the matrices involved and also allowing the state vector to be random. The result subsumes all of the usual Fisher-type estimates as special cases. This problem was originally addressed by the author in [2] and an incorrect solution was given there; this note provides a correction to that result.