Suppose, for example, that I'll always be applying the algorithm on the last five measurements; sort of a souped-up moving average. Then the x-values will always be (again, shifting and scaling as needed):

(22)

The values of the sums are:

(23)

The determinant is:

(24)

and the inverse is:

(25)

or:

(26)

Of course, it's a constant matrix, so we can encode it as such, using whatever scaling we find to be appropriate.

Now let's look at the terms in U. These, you'll recall, do involve the measured values of the y's, so we can hardly compute them in advance. On the other hand, u₁ depends only on the y's, not the x's. We can compute this one recursively, using the equivalent of a moving average (or, more properly, sum). Just add the one new data point and drop the oldest one.

Let me make this last point crystal clear. Suppose the last measurement I've processed was y_k. After I've processed that data, the value of u₁ will be:

(27)