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"Andres Ruiz"  wrote:
>>   (It does require inverting 3x3 matrices, so it's not well suited to
>>   hand calculation.)
>>   If someone remembers seeing something like this, I would appreciate a
>>   reference.  Otherwise I'll write it up in more detail.
>
>   Now I am writing some articles to be published on my web page
>   under the name Navigational Algorithms.

That is indeed the first step I had in mind.

>   I am looking for some information about sight reduction with
>   matrices, I have find two articles:
...  
>   Watkins. R. and Janiczek. P. M., Sight Reduction with Matrices,
>   NAVIGATION, Journal of The Institute of Navigation, Vol. 25,
>   No. 4, Winter 1978-79, pp. 447-48.

Wolfgang K�berer has kindly supplied a copy of this article, and their
least squares method is the second step.  However I note they use
equally weighted least squares.  I believe the weight should be higher
for high altitude sights.  That's what the Kalman filter method would
suggest.

Paul Hirose  wrote:
>Have you read Kaplan's "navigation solution" paper at the USNO site?
>http://aa.usno.navy.mil/research/celnav.html
>
>His algorithm may give an error estimate. I can't remember. 

Yes, it uses an extended Kalman filter, so it does give an error
estimate but requires an estimated position.  The thing I think is
really neat about a Kalman filter is that it lets you update a
multi-dimensional state with a one-dimensional measurement.  I planned
to update a three-dimensional state (position in cartesian
coordinates).  Kaplan is using a four-dimensional state (latitude,
longitude, course, and speed) which I admit has more practical interest.

>It's used in
>the Navy's STELLA software, which unfortunately is not available to
>civilians. If you could create an open-source implementation of Kaplan's
>algorithm, that would be some accomplishment. If nobody else steps up, I
>may attempt that someday. I have experience in the related area of
>orbital element least-squares adjustment. 

The main technical obstacle is the calculation of all the partial
derivatives.  I would recommend using an unscented filter [1] which
eliminates that chore, but is otherwise similar to the Kalman filter.

>I don't believe that requiring an assumed position for a sight reduction
>is a significant problem in practice. And I suspect proficient
>navigators will pay little attention to a computer's error estimate.
>They will rely on their experience and intuition, based on the observing
>conditions and the way the LOPs look on the chart.

Alas, you're probably right.  

            - Jim Van Zandt

[1] http://citeseer.ist.psu.edu/julier97new.html

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