Suddenly, I realized the answer. It is simpler than anything above, yet formally it seems more complicated, because a full inverse covariance matrix of the unknown filter is implicitly supplied. But they are not prior estimates of P and A because the phases of P 0 and A 0 are irrelevant, washing out in the squaring. If we specify large values for ,the overall problem becomes more linear, so P 0 and A 0 give a way to impose uniqueness in a nonlinear case where uniqueness is otherwise unknown. We will come to understand P 0 and A 0 better as we study more examples.
Simple theory offers some indications, however.
It seems natural that P 0 should have the spectrum that we believe to be appropriate for P . We have little idea about what to expect for A , except that its spectrum should be roughly inverse to P . To begin with, I think of P 0 as a low-pass filter, indicating that data is normally oversampled. Likewise, A 0 should resemble a high-pass filter. It is a small, additional, theoretical dataset that has no missing values.