I wanted to know how accurate a simple stellar observation can be. I decided to check my stellar derived locations against the GPS location for the same point. I knew that some degree of accuracy can be achieved with stellar observations but how close is it really to actual position? Is the location within walking distance or seeing distance? I decided to make the observations and see how close I would get. I wanted to know what kind of accuracies I should expect from normal observations. Of course the controllable variables, such as the time of observation, logging the time of observation and higher precision instruments, can help get higher accuracies but I wanted this to be more along the lines of using the equipment that I use everyday. Which is pretty good but it is not in the geodetic range of high precision instruments. I strongly recommend a good stop watch and a method to set your data collector to the exact time (Fig.2).. Time is one of the most important variables and the closer you can get to the actual moment of observation the better your chances are to get accurate results.

I knew that one observation wasn’t going to suffice to verify results accurately. I would have to take a series of observations through the night and repeat the same procedure over a period of a few nights to get enough data to be able to eliminate poor readings, instrument error and any other anomalies. I have a high precision GPS unit and for the purpose of this experiment I am assuming the latitude and longitude that the unit provides will be accurate enough to compare with my stellar observations.

I began by setting up a baseline that I could use through the night and stable enough to use on other nights. I set three points using my GPS unit and established position at each point. I knew I wanted to plot my positions on a map so I set my mapping plane to the right system and used the coordinates provided to establish locations for each of my points. I then used my total station to survey through the points and adjusted my GPS results. I did need a bearing and it did help to establish one but it is not as critical as the actual geodetic location which is what I was going to use to check my stellar observations. After all I am not doing this to see if the North Star is in the north, but rather to see how close I can determine my position with the means available to me. This method has been used for a long time and the formulas used to calculate a position has obviously been refined over time to become very accurate. But how accurate can you expect to be with a reasonable number of observations? So in this experiment I determine my position and convert that position to state plane coordinates and compare the results to my base position established by GPS. The results give me a bearing and distance to each observed position from the base GPS position. For me this helps me visualize the results much better than comparing latitudes and longitudes.

I know that the methods I am using are making a lot of assumptions. For instance I am assuming that the conversion from lat/long to state plane coordinates that my GPS unit is providing is accurate. It is close but accurate? Also to simplify the experiment I calculated an approximate length per second of latitude to be used to convert my differences in latitude to feet. This is also not an accurate conversion but was just used to simplify the results. The length I used is close for my area and will give me a consistent conversion. . However, all that being said the experiment still validates itself for visualizing results since I am applying the same procedures and formulas throughout the experiment. So if any data are flawed due to one of the steps than they are all flawed similarly hence the results although possibly not accurate to the real world are still hopefully accurate within themselves.

I decided that from my base point I would make all my observations using the same backsight point. Knowing the bearing of that line and also knowing my latitude from GPS I was able to turn to the approximate position of Polaris at any time. This became very crucial as you will see later.

The next step was to get an accurate ephemeris. Not as easy as one would think. Mostly because, well, with GPS who needs Polaris? So it is getting scarcer but I found a good one here  (Fig.3) and here (Fig. 4)that gives me all the data I need. I then used the formula and tables that were provided in "Surveying" 8th ed. Moffitt/Bouchard (Fig. 5) to prepare a spreadsheet that I could use for every observation. I have provided it here (Fig. 6)  if anyone wants to give it a try. Just enter the required data in the green boxes and it should work. I set the observation angle to zenith since that is the normal state of my total station. The spreadsheet will convert the zenith angle to altitude for the calculations. The example provided is based on the example in Moffitt/Bouchard (Fig.5).and includes the same data to show it works. I used that form and modified it to work with my experiment. I already knew my longitude from the reported position from my GPS unit. I entered that value and converted to time for the offset from Greenwich. I think this helped tremendously. The modified spreadsheet is here. (Fig. 12)..One big difference is that in this spreadsheet you will need to enter your longitude value. I used my GPS value for all my observations. I think this helped in that the time offset is calculated exactly from the longitudinal offset rather than the local time zone.

I checked and recalibrated my total station. I set a tripod with prism over my backsight, then set up over my base point. Set all condition parameters in the total station, leveled the instrument, set my backsight to zero and waited for the stars to appear.

The First Observation:

Being the first set I decided that I would take a set of shots all through the night at regular intervals. This series of shots would take me almost completely through the culmination and elongation intervals of Polaris. I wanted to practice taking the shot and recording the time. I wasn’t as concerned with results at this point as I was with procedure. I took a series of shots approximately 20-30 minutes apart beginning at the moment I could first see Polaris with the naked eye. I started at almost 9:00 pm and continued until I couldn’t see it anymore which was around 7:00 am. I did not adjust the total station during this time and reset 0 at my backsight for every observation.

I did learn a lot on the first night. I worked out how to get my time and observation simultaneously (or almost). I realized I could set my tripods for more convenience in viewing. This turned out to be very important in that for the best results you don’t want any disturbance to the instrument. A slight lean against one of the legs at the wrong time can destroy any chance of getting a good observation.

And the most important lesson. It is extremely difficult to get the crosshairs on the star at night. It is a pinpoint of light but that light is as bright as the sun and it is against a very dark background. Although you would think that you could sight it exactly because it is so small it is hard to sight for just that reason. If you use the reticle lighting feature of the total station it can help a lot but it also has a tendency to be too bright with no adjustment (at least on mine) so it can help to see the crosshairs but can end up blanking out the star. I used a combination on the first night, switching between lit and not to get the observation. I eventually discarded this approach simply because I was adding vibration to the sighting by pushing buttons on the total station. I wanted to eliminate as many potential problems that I could to help my accuracies. One of those potential problems was making sure the total station was stable throughout the night. So I tried to eliminate all possible forms to vibration that could occur, from touching the tripod to pushing buttons on the data collector.

The final solution for this problem turns out to be time of sighting. Polaris can be sighted easily with a total station well before sunset and well after sunrise. When the sky actually begins to lighten, sighting becomes very easy. You can now see the crosshairs against the partially lit sky and still see Polaris well enough to sight. This is where having that bearing comes in handy. Since I know my latitude from GPS and I have a backsight line with a bearing I can approximate the location of Polaris, turn the gun to that point and be able to see the star even though it can’t be seen with the naked eye. The best observation times are at dusk and dawn. And for determining location it is best to schedule your observations when Polaris is in culmination at dawn or dusk. That will give you optimum viewing at the best time for location determination.

Amazingly my first observation put me within 35 feet of the GPS solution. Although this may have been a fluke it was very  encouraging. The results are a mixed bag. As I said I was working out procedural stuff on the first night so these results are more to test my procedure than provide good results. As a matter of fact I started getting farther away from my position as the night progressed. I did some research and although a majority of the shots were during elongation the errors were too big to account for that. I plotted the observations to see what they looked like and the image is here (Fig. 7). Something happened to the setup during the middle of the night. Possible problems: total station settled, I was leaning on the tripod (?), atmospherics affected the observation (temperature drop of 15 degrees), was not getting time of observation correct and even possibly my face against the gun to see the star might have caused a distortion. As you can see from the plots, early on I was getting circular results, then the distortion and then the later shots plotted circular again.

Not great results but I learned a lot. The next set would be better.

Summary of First set (Fig. 8).

The Second Observation:

This attempt was my first serious attempt in getting reliable data. I had modified my setup for easier viewing without disturbing the gun. I also decided to take shots again at night. I was still convinced I could get the shot at night. So I tried again. I also decided I would just take a set of shots, direct and reverse, over a shorter period of time. This time I started about 9:00pm and went to about 9:30pm. I would then compare the direct results and then average the direct and reverse and also do a comparison.

The results are shown here (Fig. 9) The first shot is direct, then the next eight are direct and reverse. The red data at the bottom are averages of direct/reverse for each of the four sets. The results again were very encouraging. My first average again put me about 35 feet away! The average of the averages calculates to 218.56 feet. The results were absolutely incredible. This is an average of a set of four observations taken over about half an hour with standard equipment.

I liked the results but I still had a concern over the difference in each measurement. I wasn’t getting similar results or even similar differences between direct and reverse and I was still getting larger differences in later shots where the star may be moving towards elongation. I still was trying to spot the star at full night which also may have affected the results.

One more item concerning direct and reverse observations. The purpose for that exercise is to eliminate potential sighting errors and errors associated with the physical properties of the total station, theodolite or transit. This is a much used practice to increase accuracies however I find that doing this for stellar observation may lead to more error than eliminating errors. Here again depending on your total station, theodolite or transit you may have better results. My experience is that rotating the total station and inverting the scope may be adding some degree of error because in my case the movements are servo controlled. The vibration from the servos turning the gun (especially all the way around and over, and back again) seem like it probably isn’t helping matters any. I used direct/reverse for a lot of these observations but I am undecided as to benefit over well calibrated direct observations.

I recalibrated the total station, again. Checked all my setup items again. Reset my clock to NIST. I was ready. I would try again.

Summary of Second set (Fig. 9).

The Third Observation:

The third set of observations were made to substantiate earlier results and to test the prediction that observations on Polaris made at the periods of elongation (E-W) will be less accurate for determinations of position than observations made near culmination (N-S). As stated, observations made near elongation will be more accurate for determining North while observations made near culmination will be more accurate for determining latitude.

I took a set of 5 observations direct and reverse when Polaris was near it’s easterly elongation. The results shown here seem to bear out the hypothesis. None of the observations were very close on their own. I also noticed that as with my other observations that as time went by I would notice less and less accurate data. I am almost convinced that the first set of observations will be your best. If you want to do repetitions than I strongly suggest a complete check of the setup each time, including re-leveling, adjusting all the instrument settings and fresh back sight.

The results of the third observation are here (Fig. 10) The average of the first observation put me within 11 feet but still every observation on it’s own was not closer than 750 feet and extended out to over 6,000 feet.

No more observations at elongation unless I need a bearing.

Summary of Third set (Fig. 10).

The Fourth Observation:

This set was going to be my ultimate data set. I planned the observation for early morning near Polars’ upper culmination. I would take a series of direct and reverse shots continuously from about 4:30 am to about 6:18 am. I reset the zero on my backsight before each observation. I took 17 sets for a total of 34 shots. I did the same procedure for each shot. I wanted to see if I accumulated error as I took each observation even though I reset zero. The results for that are not conclusive. Although earlier sets were closer to my position I did not see a consistent increase in error over that period of time.

The results of the survey are here (Fig. 11) The first 34 lines are the observations. The averages for each set are shown below. The overall average using all observations was about 530 feet. Pretty good I think but I was hoping for better. Some observations were very close. Observation 5 is within 11 feet and Observation 23 is only 20 feet away. These types of results are very encouraging in that I think determination of latitude can be very accurate using Polaris.

Summary of Fourth set (Fig. 11).

Conclusion:

It is an extremely difficult experiment to perform in that there are so many variables that can affect the observation. I am planning to redo the test again at a later time but my approach will be to set up on consecutive days at dawn or dusk, only perform 4 observations on each day near culmination and re-setup the instrument before observation. I think this will be the best way to make the observations and to get the best results. I also strongly suggest someone to help with the stop watch. I managed to log the times myself but I am sure with an extra pair of hands it will make the whole procedure easier.

I felt most of the time that the errors were due to things that I could control with improved procedures and sighting. At one time solar or stellar observation was all there was to find your latitude and north. I think about the countless surveyors and navigators that relied solely on that technology to map this world. We take a lot for granted and even I couldn’t have done this experiment without the aid of computers and modern equipment. In the past the calculations were done manually, some times in the field while doing the survey. Maybe it didn’t seem unusual to them at the time but when I look at it now it seems phenomenal that they did this all the time with much less accurate instrumentation and still got it right (or almost).

In all I was very pleased with the results. The results were very close to my GPS values. I think stellar observations can be very accurate for determinations of latitude. Even my average for my best observations put me within 500 feet and at times much much closer. I was hoping I could average better at around 200 feet and I think I can but that will be another day and another experiment.