Intersection of two paths given start points and bearings?

[vafonkin]

I spent about 2 weeks trying different approaches to get calculated distance between 2 GPS coordinates, intersection of two paths given start points and bearings, and calculate bearing to the giving point from current location and so far was able to calculate distance using "Flat Earth" approach by converting GPS coordinates to Cartesian and calculate distance in Cartesian.

What I was NOT able to complete is getting intersection and bearing.

I tried cordic library - this sounds like a valid approach - but even with that not able to get results.

My project does not require spherical earth - since all points a located within maximum 4km from each other and intersection point can be anywhere withing 4km by 4 km area.

Please advise if anyone was able successfully calculate intersection and bearing for Flat Earth model with any PIC controller, or this just a dead end road.

Thank you in advance.

[RF_Developer]

Flat, spherical or even spheroidal earth should be no problem. Its straightforward and well documented trigonometry, which the PIC is quite capable of, albeit sluggishly slowly. The CCS C float precision should be enough for what you want to do.

So, where is your problem? Is this a CCS C specific problem - in which case post what you've got - or is it that you simply don't know how to do the maths - in which case use Google.

RF Developer

[Mike Walne]

What is the required accuracy?

You may be able to get away with mainly integer maths.

Like RF developer says, you've not explained what your real problem is.

Mike

[vafonkin]

10 meters for required accuracy would be fine. I cannot compile/get valid results from following foxLocation function. It implements Haversine and PIC MCU appears cannot handle it. I tried to split code to smaller chuncks - does not help:

[RF_Developer]

It compiled OK for me on PCWH 4.130. Lots of code of course, and it would run like a dog, but it compiled OK.

I did a lot of this sort of thing with a radar project I was involved with in the 90's. There are many approaches, but I found that once I'd sorted out the spherical geometry (which you can get from the net) it was actually simpler to do all the math in spherical form. I had object methods to give me range and direction from point to point, and to project the lat long on to maps in various projections.

This points to the other relatively simple way to do this: project the points on to a vritual mercator map and then, once you've sussed the scale at a suitable point (and assumed it to be valid for the entire region of interest), simply do the crossing point math in straightforward planar geometry. That should be accurate enough for you, though doing it in spherical geometry would give you a better result (I was working over several tens of km). This approach is the virtual equivalent of doing it by hand on a paper navigational chart.

Anyway, it compiles for me. I cant say whether the results are right, and I know from experience that there are always all sorts of special cases to consider to make this sort of thing work over all possible combinations of input points.

RF Developer

Anyway,

[vafonkin]

Which PIC MCU processor do you use?

[RF_Developer]

No, which do YOU use? For the record, I compile the code for PIC18F4520 using PCWH 4.130. 34% of ROM was used, after all its full-on floating point, what do you expect?

RF Developer

[vafonkin]

16F886 ... obviously not enough of power.
Will move to new processor and test it out there.
Thanks a lot!
73!
KB1RLI

[dorinm]

try converting your coordinates in UTM, then it's straightforward and easy even for a 12f to do the mat;
UTM coordinates are in cm, so your 10km would be expressed in 1.000.000cm domain, always positive, so you would use unsigned32 or signed, either one won't overflow and produce correct result.

[vafonkin]

[vafonkin]

It appears triginimetric functions provide incorrect results starting with 4th decimal point. It cannot be used for navigation formula due to lack of precision.
.
I need to calculate intersection point given 2 gps locations and bearings, and I need to get bearing from current location to given point.

Area for calculation is small 4 by 4 km, precision should be not greater then 10 meters.

I am sure someone already done it and I will appreciate any help

If free help is not available I am willing to pay for solution.

[RF_Developer]

4th decimal place huh? In other words 6 or 7 significant places. Yes, that's about right for single length float precision, and CCS C doesn't have a double type. I don't know if other PIC Cs have a double type. If so, you'll have to use them. Either that or implement your own double length floating point... remembering that famously even Intel got that wrong on the first pentiums.

RF Developer.

[vafonkin]

I believe there are some approaches around:
1. Cordic
2. Lookup tables
3. Some other high math functions

It is probably possible to find intersection by solving simple line formula:

ax + by + c = 0
y = kx + d, где k=-(a/b), d=-(c/b)
k=tan(a)
d=y-tan(a)*x
b=1
k1x + d1 = y
k2x + d2 = y

I done it, however tan function badly degrades precision and introduces big errors i.e. instead of 0.013756 it returns 0.013744

[vafonkin]

I want to ask for a little help from community - I do not have a lot of processors available but want to get a test results for the following function for different PICs:

tan()
atan()
atan2()

For 89 decimal degree. You need to convert it to Rad to get result.

Can someone help me?

The purpose is to compare calculation precision.

Thanks a lot in advance!

[Ttelmah]

The only PIC's offering a higher maths precision, are the DsPIC's, which do offer a double type. The library for all the others is basically the same.

Best Wishes