sarkit.sicd.projection.r_rdot_to_dem_surface

r_rdot_to_dem_surface(look, scp, projection_set, ecef2dem_func, hae_min, hae_max, delta_dist_dem, *, delta_dist_rrc=10.0, delta_hd_lim=0.001, bistat_max_npts=9999, **kwargs)

Project along a contour of constant range and range rate to a surface described by a Digital Elevation Model.

Parameters:

look{+1, -1}

+1 if SideOfTrack = L, -1 if SideOfTrack = R

scp(3,) array_like

SCP position in ECEF coordinates (m)

projection_setProjectionSetsLike

Center of Aperture projection set for a single point

ecef2dem_funccallable()

A function that returns an ndarray of DEM offset heights from an ndarray of positions with ECEF (WGS 84 cartesian) X, Y, Z components in meters in the last dimension

Note

SICD v1.4.0 volume 3 decomposes this into two steps:

1. Convert ECF To DEM Coords

2. Get Surface Height HD

hae_min, hae_maxfloat

WGS-84 HAE values (m) that bound DEM surface points

delta_dist_demfloat

Max horizontal distance between surface points (m) for which the surface is well approximated by a straight line

delta_dist_rrcfloat, optional

Max distance between adjacent points along R/Rdot contour (m)

delta_hd_limfloat, optional

Height difference threshold for determining if a point on the R/Rdot contour is on DEM surface (m)

Deprecated since version 1.7.0: delta_hd_lim was removed from SICD v1.5 volume 3 “Projection to a DEM Surface”. This argument has no effect.

bistat_max_nptsint, optional

Threshold for number of bistatic contour points to compute, above which an exception is raised. This is an implementation detail to prevent infinite loops that is not in the document.

Returns:

sndarray

Set of point(s) where the R/Rdot contour intersects the DEM surface with ECEF (WGS 84 cartesian) X, Y, Z components in meters in the last dimension. Ordered by increasing WGS-84 HAE.

Other Parameters:

**kwargs

Keyword-only arguments for intermediate r_rdot_to_constant_hae_surface calls

Raises:

RuntimeError

If number of bistatic contour points exceeds bistat_max_npts without computing a point above hae_max.

Examples

Example of a monostatic collect over the Grand Canyon with layover. ecef2dem_func is defined using 3 arc-second SRTM via Open Topo Data’s free public API and a hard-coded, approximate geoid height.

>>> import itertools
>>> import json
>>> import urllib.request
>>> import numpy as np
>>> import sarkit.wgs84
>>> import time

>>> geoid_height = -23.43  # from www.unavco.org

>>> def height_above_srtm90(ecf):
...     llh = sarkit.wgs84.cartesian_to_geodetic(ecf)
...     max_pts_api = 100
...     haes = []
...     for ll_strs in itertools.batched(
...         (f"{lat:.5f},{lon:.5f}" for lat, lon in llh[:, :2]), max_pts_api
...     ):
...         url = f"https://api.opentopodata.org/v1/srtm90m?locations={'|'.join(ll_strs)}"
...         with urllib.request.urlopen(url) as f:
...             resp = json.load(f)
...             time.sleep(1.05)  # opentopodata is rate limited
...             assert resp["status"] == "OK"
...             height_above_geoid = np.array([x["elevation"] for x in resp["results"]])
...             haes.append(height_above_geoid + geoid_height)
...     dem_hae = np.concatenate(haes)
...     return llh[:, -1] - dem_hae

The DEM surface contour of the canyon wall intersects the R/Rdot contour in 3 places:

>>> import sarkit.sicd.projection as sicdproj

>>> pset = sicdproj.ProjectionSetsMono(
...     t_COA=0.611,
...     ARP_COA=[-2.5413e6, -5.1217e6, 4.6498e6],
...     VARP_COA=[7.0914e3, -1.3727e3, 2.3637e3],
...     R_COA=1128574,
...     Rdot_COA=-1.3197e3,
... )
>>> scp_llh = [ 36.238989, -112.387843, 1000]

>>> s = sicdproj.r_rdot_to_dem_surface(
...     look=-1,
...     scp=sarkit.wgs84.geodetic_to_cartesian(scp_llh),
...     projection_set=pset,
...     ecef2dem_func=height_above_srtm90,
...     hae_min=0,
...     hae_max=2000,
...     delta_dist_dem=90.0,
... )
>>> s_llh = sarkit.wgs84.cartesian_to_geodetic(s)
>>> with np.printoptions(precision=4):
...     print(s_llh)
[[  36.2442 -112.3905  650.9127]
 [  36.2433 -112.39    709.8588]
 [  36.234  -112.3858 1287.5452]]