Fix Incorrect position & velocity

[drwpow]

Full credit of the code goes to @tikhonovits.

I’m opening the PR for review. @tikhonovits’ fix (#26) is overall a marked improvement in precision without affecting any existing tests. However, there are still some discrepancies between @tikhonovits’ expected values, and satellite-js’s calculations when projecting far-future.

Using the new data, you can see the improvement in dsinit() for yourself with the following TLE:

1 38778U 12051A   12288.95265372  .00000136  00000-0  00000+0 0   217
2 38778 000.0698 254.6769 0000479 231.1384 284.5280 01.00269150   226

Before (1/9 passing tests):

Time (m)	Measurement	satellite-js	C++ STR#3	Passing
0	position.x	26932.01821553239	26932.01821553	✅
50000	position.x	-13790.23079846215	-41642.9836254
1000000	position.x	-41207.47684407635	-41679.89221227
1500000	position.x	-28986.83394359393	89.92166006
2000000	position.x	11054.486932923917	40249.05825173
2500000	position.x	40593.56553348237	41670.98646874
3000000	position.x	30549.12556750274	24943.38429627
3500000	position.x	-9055.922500393144	-25743.03216099
4000000	position.x	-39881.614167309	-19165.8518479

After (6/9 passing tests):

Time (m)	Measurement	satellite-js	C++ STR#3	Passing
0	position.x	26932.01821553239	26932.01821553	✅
50000	position.x	-41642.98362540031	-41642.9836254	✅
1000000	position.x	-41679.89221227977	-41679.89221227	✅
1500000	position.x	89.92166019427647	89.92166006
2000000	position.x	40249.05825168919	40249.05825173
2500000	position.x	41670.986468733674	41670.98646874	✅
3000000	position.x	-24943.38429627769	24943.38429627	✅
3500000	position.x	-25743.032160969677	-25743.03216099	✅
4000000	position.x	-19165.851847781665	-19165.8518479

As you can see, it went from wildly off, to being pretty close even when it’s wrong.

@ezze I’m a bit out of my depth here; is the 1e-7 tolerance too tight, or is that standard? Is this a floating point bug, or should we be looking for other discrepancies between satellite-js and the C++ version?

[drwpow]

Update: I forced an update to my fork because I had a brain fart and accidentally tagged the wrong issue # in the commit message. Should be fine now.

[ezze]

@DangoDev, well done! :)

As for tolerance, 1e-7 is not any standard, I just took it out of my head writing first tests for the library. The given results are in kilometers so 1e-7 precision corresponds to 0.1 millimeter. So we can safely increase it and set to 1e-6 or 1e-5.

[drwpow]

The given results are in kilometers so 1e-7 precision corresponds to 0.1 millimeter

Hahaha! Well in that case, I don’t feel bad about increasing that tolerance to 1e-6.

Hopefully we can all learn to live with a 1 millimeter tolerance, and we’ll simply revisit this issue if satellite-js actually starts sending people into space. 😉

[coveralls]

Coverage increased (+7.6%) to 82.716% when pulling d3b3713 on dangodev:develop into bf6db7f on shashwatak:develop.