The 2nd Space Operations Squadron last month put into play an optimization scheme for the GPS satellite constellation that will bring better accuracy to GPS users worldwide.  Prior to now, GPS was only required to have 24 satellites operating in 24 specific orbital slots.  Of course there have been many more than 24 satellites on orbit for over 12 years.  Because of the 24 satellite requirement though, their orbital positions were determined by optimizing constellation performance on only those 24 slots.  That has now changed.  There is a new 24+3 constellation slot definition that allows GPS satellite orbital positions to be optimized based on a 27 satellite  constellation rather than 24.  This means that your GPS receiver’s positioning accuracy will get better – for free!  I’m not covering the specifics of the satellite moves for this Nog, those are covered in articles linked above.  Here, I’m focusing on the end user’s gain based on this change.

Remember that your position accuracy depends generally on two things: the orientation of the the GPS satellites at a given time and the accuracy of the the GPS signals themselves.  I know, I know, there are other factors involved in accuracy, but let’s just look at the big picture here : ).

The metric defining the orientation of the satellites is Dilution of Precision (DOP), the metric defining the accuracy of the satellite signals is User Range Error (URE).  Because the GPS orbital slot positions are changing based on this new optimization, we expect to see a change in DOP, not URE.  The new positions presumably have been chosen to optimize DOP – let’s see how much better the DOP will be when the satellites have completed their move.  There are several types of DOP, representing the effect of satellite orientation on different coordinates.  For example, Horizontal DOP (HDOP) represents how much satellite orientation affects your navigation positioning error on the surface of the Earth (2 dimensions).  Vertical DOP (VDOP) represents how the satellite orientation affects on your altitude positioning accuracy.

For my analysis, I’ll look at HDOP and VDOP values for the entire globe for today’s constellation, and for the constellation once all the satellite moves have been completed for the optimization.  I’ll call this the optimized constellation.  I’m also going to constrain the DOP calculations by requiring that each point on Earth not be able to see any GPS satellite below 10 degrees from the horizon.  This is a typical mask angle used for these types of analysis.  Note that clicking on each picture will bring up a full size version, for closer examination.

Horizontal DOP

Today’s average HDOP values are shown in Figure 1.  The HDOP average is taken over a 24 hour period from Jan 1, 2010 to Jan 2, 2010.  The color at each point on the grid represents the daily average HDOP for that grid point.

Figure 1 – Average HDOP, January 1, 2010

Now we’ll look at how HDOP changes with the new optimized constellation.  Figure 2 shows the average HDOP with the newly optimized constellation.

Figure 2 – Average HDOP, Optimized Constellation

The changes here aren’t too striking, but you’ll notice that the bands where the average HDOP is greater that 1.0 (the red bands) have shrunk a bit.  Let’s see if Vertical DOP is any better.

Vertical DOP

Today’s average VDOP values are shown in Figure 3.  Again, the VDOP average is taken over a 24 hour period from Jan 1, 2010 to Jan 2, 2010.  The color at each point on the grid represents the daily average VDOP for that grid point.

Figure 3 –Average VDOP,  January 1, 2010

Next is the average VDOP for the new, optimized constellation, shown in Figure 4.

Figure 4 – Average VDOP, Optimized Constellation

It appears that VDOP is getting improved more than HDOP – but by how much?

Let’s look at some numbers.

I’ll take a global average of all the HDOP and VDOP values and put them into a table:

	Optimized	January 1, 2010	Percent change
Average HDOP	0.9491	0.9759	-2.743%
Average VDOP	1.651	1.699	-2.855%

Table 1 – DOP Percentage Changes

So the VDOP change is slightly better than the HDOP improvement and both changes reflect roughly a 3% increase in DOP performance.

How do these changes in DOP affect what we really care about though – our GPS positioning error?  Using the same methodology as above, I’ll now look at navigation accuracy for the January 2010 constellation and the optimized constellation.  To complete a navigation accuracy analysis, I need User Range Error (URE) information for each satellite. I’ll use the GPS User Range Errors from January 1, 2010 for both the current and the optimized constellations.  The green bars in Figure 5 show the values I’m using for each satellite.  Because PRN 1 (SVN 49) is a critical piece of this optimization, I’m including it in the analysis, with a URE of two (2) meters.  I’ve also included a receiver error value of two (2) meters in the following accuracy analysis.

Figure 5 – GPS User Range Error values: Dec 30, 2009 – Jan 01, 2010

Horizontal Accuracy

Figure 6 shows the average horizontal accuracy for January 1, 2010.   The color at each grid point is the average horizontal navigation error over 24 hours, for the constellation on January 1, 2010.  I tend to use navigation accuracy and navigation error interchangeably – to me, they mean the same thing.

Figure 6 – Average Horizontal Navigation Accuracy, January 1, 2010

With the new constellation, we do see some improvements.  Figure 7 shows the horizontal accuracy using the optimized constellation.

Figure 7 – Average Horizontal Navigation Accuracy,  Optimized Constellation

Vertical Accuracy

The vertical navigation accuracy plots show improvement as well.  Figure 8 shows the average vertical navigation error for January 1, 2010.

Figure 8 – Average Vertical Navigation Accuracy, January 1, 2010

Figure 9 shows the improved average vertical accuracy with the optimized constellation.

Figure 9 – Average Vertical Navigation Accuracy, Optimized Constellation

Table 2 shows the percent improvement in average accuracy with this change in constellation orientation.

	Optimized	January 1, 2010	Percent change
Average Horizontal Accuracy (meters)	2.244	2.291	-2.05%
Average Vertical Accuracy (meters)	3.949	4.027	-1.93%

Table 2 Average Accuracy Percent Change

The changes aren’t eye-dropping – you do get an overall accuracy improvement, but you may not notice it.  But hey, it’s free right?

Number of Satellites Visible

One last piece of analysis.  Typically you might equate the number of GPS satellites available to your receiver with better accuracy.  This does make some sense, but it’s important to remember that quality trumps quantity – fewer satellites oriented optimally are better than more satellites oriented sub-optimally.  This is shown in the following figures.  Figure 10 shows the minimum number of GPS satellites you’d see over 24 hours at a given location with the current constellation.

Figure 10 – Minimum number of GPS satellites visible over 1 day, January 1, 2010

Figure 11 below shows the same plot but with the optimized constellation.

Figure 11- Minimum number of GPS satellites visible over 1 day, Optimized constellation

Note that the scale starts at four (4) satellites visible and goes up to nine (9). So far so good – it looks like we have larger minimums over the globe, except at the poles.  Also note that the two areas that had a minimum of 4 satellites available  currently (in red in Figure 10)have been eliminated in the optimized constellation.

What about the maximum number of satellites available?

Figure 12 – Maximum number of GPS satellites visible over 1 day, January 1, 2010

Figure 12 shows the maximum number of satellites visible over one day for the current constellation.  Note the scale on this graph has changed – it starts at ten (10) and goes up to fifteen (15).  Figure 13 shows the same plot, but for the optimized constellation.

Figure 13 -  Maximum number of GPS satellites visible over 1 day, Optimized constellation

The maximum number of visible satellites has gone down in most cases.  This is counter intuitive, but it echoes the idea that the orientation is what’s important, not the sheer number of satellites visible.

All in all the new optimized GPS constellation will improve average DOP and navigation accuracy, but not substantially so.  Another way to approach this analysis is to look at the maximum errors of today’s constellation versus the optimized constellation.  This may (or may not!) show more improvement, but those maximum errors only occur rarely in any case.  What we usually have is the average case as we cruise about with our GPS receivers.  Thanks for the optimization 2SOPs, we’ll take it!

Remember fresh batteries.

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