The independance of forward and backward estimation errors in the two-filter form of the fixed interval Kalman smoother

In this paper it is shown that the Fraser-Potter two-filter form of the fixed interval Kalman smoother can be derived without assuming that the forward and backward estimation errors are independent. In fact, it is shown that when the transformed process noise autocorrelation is nonsingular, the aforementioned independence is a conclusion rather than a hypothesis. Some additional conclusions pertinent to computations are also provided.