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This is a response to a message from Paul Hirose-

>George Huxtable wrote:
>>
>> [Using the newly updated values for B(F) and L(F) as Lat and Long, rework
>> the calculated altitudes and azimuths, in 7.2.2, 7.2.3, and 7.2.4, and
>> obtain a new intercept p from (observed alt. - calculated alt.). For this
>> to be possible, the original values for dec., GHA, and observed altitude of
>> the body must have been retained.]
>
>George, that algorithm sounds identical to the direct computation
>method in my 1998 Nautical Almanac (the newest one I have). The
>paragraph that begins "If d exceeds about 20 nautical miles..." is
>reproduced verbatim in the Almanac.
>
>It includes a fully worked reduction, which makes clear that some
>values are retained: "The table shows the intermediate values of the
>calculation for the second iteration. In each iteration the quantities
>Ho, GHA, Dec and t do not change."
>
>Computation of standard deviations and error ellipses are not
>mentioned in the Almanac.

====================

Paul is correct. The same algorithm is in the Nautical Almanac, under- "11.
Position from intercept and azimuth by calculation"

This is followed by "12. Example of direct computation". This example, in
the almanac, is different from, and better-chosen than, the example used to
illustrate the method in the AstronavPC booklet.

In the almanac, the first-chosen value for lat and long is "improved" by
the initial operation, but the change made exceeds the chosen criterion of
20 nautical miles. Therefore a complete reiteration is needed, in which new
values for intercepts and azimuths are calculated. By following the steps
in the example, it's reasonably clear what needs to be done.

In contrast, in the example shown in the AstronavPC booklet, first-chosen
values for lat and long are such that the first operation of "improvement"
is all that's needed, as the resultant change in position is less than 20
miles. As a result, no reiteration is shown, so that example fails to give
any guidance about how to reiterate, in cases where that's needed.

As Paul says, the Almanac does not proceed to deducing an error ellipse,
but the AstronavPC booklet does.

George.

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01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
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