bcdev/beam — pull request #4 by pmar (2013-09-04 18:19:19+00:00)
Title: Fix for Envisat/Doris Orbit interpolation

Interpolation of Envisat Doris orbits in BEAM is broken. The used cubic convolution is not reliable enough to describe the orbit curvature, and introduces systematic errors. The errors introduced are on the level of meters, see the example below.

This fix - switching from cubic to Lagrange 8th order, and reorganizing sampling points - resolved the issue.

**Numerical example: **

BEAM would interpolate state vector with time stamp 02-NOV-2004 18:36:20.000000 to

```
time	02-NOV-2004 18:36:20.000000
x_pos	4220198.4853476295
y_pos	4275922.756203057
z_pos	3895159.210248456
x_vel	-1560.2717742116388
y_vel	-4085.961766792243
z_vel	6157.451537955331
```

While correct values are:
```
time	02-NOV-2004 18:36:20.000000
x_pos	4220202.108926475
y_pos	4275938.835178602
z_pos	3895139.0948149073
x_vel	-1560.2524478946987
y_vel	-4085.948159224766
z_vel	6157.466221932776
```

Numerical values have been validated with 'getorb' package, and internally developed matlab code, see 'more info' for more info.

**More info:**

For more info on the problem, and further discussion on the issue see the pull request I issued for integration into NEST: https://github.com/lveci/nest/pull/19

Also, note that the leap seconds are not checked because of this: https://github.com/ppolabs/jlinda/issues/19

**Context:**

Of course the impact of this error depends on the application, so perhaps it slipped un-noticed on your end. However, in interferometry and sar we were seeing some funny stuff.

Still it is good to keep things correct ;)