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Richard,

If you want a "real life" example, let's take
our observations with Bill on Lake Michigan.
The 10' systematic error in these observations
can be explained
a) by anomalous dip
b) by 1 min watch error.
Can you tell from the data alone, which was the case?
I could not.
Now suppose that the watch was correct but the longitude
was unknown...
How would you detect the anomalous dip
in these observations based on the observations alone,
and any amount of mathematical statistics, no matter how sophisticated?

Alex.

On Tue, 10 Apr 2012, Richard B. Langley wrote:

>
> Thanks, Alex, but I was not talking about ordinary averaging but the
> use of parametric least squares, which is able to estimate the value
> of a bias along with the parameters of interest. So, if we have a
> series of observations for which we can assume that the bias was
> reasonably constant, then by simultaneously processing the complete
> set, one should be able to get a single estimate of position and the
> value of the bias (dip).
> -- Richard
>
> On 10-Apr-12, at 9:49 AM, Alexandre E Eremenko wrote:
>
>> Dear Richard,
>>
>> Unfortunately, no statistical method, including least squares
>> can help with dip. The reason is that dip can deviate from its
>> normal value for relatively long periods.
>> For example, if our much discussed observation with Bill B on lake
>> Michigan is explained by the dip (which a majority on the list seems
>> to believe), this anomalous dip persisted for several hours,
>> and was almost constant. (This is an extreme example of course).
>> What averaging (or least square) helps to eliminate is a
>> SUM of MANY small INDEPENDENT errors.
>> The error of the dip is not a "random" error but a "systematic" one.
>> And the only way to eliminate it is the use of some dip-meter device.
>>
>> However, we know that dip-meters were rarely used.
>> (Western manuals almost never mention the device,
>> Soviet ones do mention, and recommend, and it was a standard
>> equipment,
>> but the same manuals recognize that "people do not use it").
>>
>> This only shows that navigators did not care about anomalous dip.
>> That high accuracy in celestial navigation was not needed,
>> and that large variations of the dip are probably rare.
>>
>> Alex.
>>
>> On Tue, 10 Apr 2012, Richard B. Langley wrote:
>>
>>>
>>> Warning: academic exercise follows ;-)
>>>
>>> Perhaps if one has sufficient redundant observations and uses least
>>> squares to estimate position, one could include dip as an additional
>>> quantity estimated simultaneously from the (biased) observations. The
>>> same procedure is used to process GPS measurements where one of the
>>> "nuisance" parameters is the offset of the receiver's clock from GPS
>>> System Time, which is generally unknown.
>>>
>>> -- Richard Langley
>>>
>>> On 10-Apr-12, at 1:31 AM, Antoine Couëtte wrote:
>>>
>>>> Still, your observations once again point out that DIP is definitely
>>>> one "weak link" in the accuracy computation chain, since even under
>>>> (quite) good conditions, dip standard deviation was already close to
>>>> 0.15/0.20 arc minute.
>>>>
>>>
>>> -----------------------------------------------------------------------------
>>> | Richard B. Langley                            E-mail:
>>> lang---ca         |
>>> | Geodetic Research Laboratory                  Web: http://www.unb.ca/GGE/
>>> |
>>> | Dept. of Geodesy and Geomatics Engineering    Phone:    +1 506
>>> 453-5142   |
>>> | University of New Brunswick                   Fax:      +1 506
>>> 453-4943   |
>>> | Fredericton, N.B., Canada  E3B
>>> 5A3                                        |
>>> |        Fredericton?  Where's that?  See: http://
>>> www.fredericton.ca/       |
>>> -----------------------------------------------------------------------------
>>>
>>>
>>>
>>>
>>>
>>> : http://fer3.com/arc/m2.aspx?i=118883
>>>
>>>
>
> -----------------------------------------------------------------------------
> | Richard B. Langley                            E-mail:
> lang---ca         |
> | Geodetic Research Laboratory                  Web: http://www.unb.ca/GGE/
>  |
> | Dept. of Geodesy and Geomatics Engineering    Phone:    +1 506
> 453-5142   |
> | University of New Brunswick                   Fax:      +1 506
> 453-4943   |
> | Fredericton, N.B., Canada  E3B
> 5A3                                        |
> |        Fredericton?  Where's that?  See: http://
> www.fredericton.ca/       |
> -----------------------------------------------------------------------------
>
>
>
>
>
> : http://fer3.com/arc/m2.aspx?i=118885
>
>
>

   

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