Table of contents
CSPICE_GFPOSC determines the time intervals for which a coordinate of
an observer-target position vector satisfies a numerical constraint.
Given:
target name of the target body.
[1,c1] = size(target); char = class(target)
or
[1,1] = size(target); cell = class(target)
Optionally, you may supply the integer ID code for the object
as an integer string. For example both 'MOON' and '301'
are legitimate strings that indicate the Moon is the
target body.
The target and observer define a position vector
that points from the observer to the target.
frame name of the reference frame in which to perform state look-ups
and coordinate calculations.
[1,c2] = size(frame); char = class(frame)
or
[1,1] = size(frame); cell = class(frame)
The SPICE frame subsystem must recognize the `frame' name.
abcorr describes the aberration corrections to apply to the state
evaluations to account for one-way light time and stellar
aberration.
[1,c3] = size(abcorr); char = class(abcorr)
or
[1,1] = size(abcorr); cell = class(abcorr)
This routine accepts the same aberration corrections as does
the routine cspice_spkezr. See the header of cspice_spkezr for
a detailed description of the aberration correction options.
For convenience, the options are listed below:
'NONE' Apply no correction.
'LT' "Reception" case: correct for
one-way light time using a Newtonian
formulation.
'LT+S' "Reception" case: correct for
one-way light time and stellar
aberration using a Newtonian
formulation.
'CN' "Reception" case: converged
Newtonian light time correction.
'CN+S' "Reception" case: converged
Newtonian light time and stellar
aberration corrections.
'XLT' "Transmission" case: correct for
one-way light time using a Newtonian
formulation.
'XLT+S' "Transmission" case: correct for
one-way light time and stellar
aberration using a Newtonian
formulation.
'XCN' "Transmission" case: converged
Newtonian light time correction.
'XCN+S' "Transmission" case: converged
Newtonian light time and stellar
aberration corrections.
The `abcorr' string lacks sensitivity to case, and to
embedded, leading and trailing blanks.
obsrvr name of the observing body.
[1,c4] = size(obsrvr); char = class(obsrvr)
or
[1,1] = size(obsrvr); cell = class(obsrvr)
Optionally, you may supply the ID code of the object as
an integer string. For example, both 'EARTH' and '399' are
legitimate strings to supply to indicate the
observer is the Earth.
crdsys name of the coordinate system for which the coordinate of
interest is a member.
[1,c5] = size(crdsys); char = class(crdsys)
or
[1,1] = size(crdsys); cell = class(crdsys)
coord name of the coordinate of interest in `crdsys'.
[1,c6] = size(coord); char = class(coord)
or
[1,1] = size(coord); cell = class(coord)
The supported coordinate systems and coordinate names are:
crdsys coord Range
------------------ ------------------- -----------
'RECTANGULAR' 'X'
'Y'
'Z'
'LATITUDINAL' 'RADIUS'
'LONGITUDE' (-Pi,Pi]
'LATITUDE' [-Pi/2,Pi/2]
'RA/DEC' 'RANGE'
'RIGHT ASCENSION' [0,2Pi)
'DECLINATION' [-Pi/2,Pi/2]
'SPHERICAL' 'RADIUS'
'COLATITUDE' [0,Pi]
'LONGITUDE' (-Pi,Pi]
'CYLINDRICAL' 'RADIUS'
'LONGITUDE' [0,2Pi)
'Z'
'GEODETIC' 'LONGITUDE' (-Pi,Pi]
'LATITUDE' [-Pi/2,Pi/2]
'ALTITUDE'
'PLANETOGRAPHIC' 'LONGITUDE' [0,2Pi)
'LATITUDE' [-Pi/2,Pi/2]
'ALTITUDE'
Limit searches for coordinate events in the GEODETIC and
PLANETOGRAPHIC coordinate systems to `target' bodies with
axial symmetry in the equatorial plane, i.e. equality
of the body X and Y radii (oblate or prolate spheroids).
relate describes the constraint relational on the selected coordinate
of the observer-target vector.
[1,c7] = size(relate); char = class(relate)
or
[1,1] = size(relate); cell = class(relate)
The result window found by this routine indicates the time
intervals where the constraint is satisfied.
Supported values of `relate' and corresponding meanings are
shown below:
'>' Separation is greater than the reference
value refval.
'=' Separation is equal to the reference
value refval.
'<' Separation is less than the reference
value refval.
'ABSMAX' Separation is at an absolute maximum.
'ABSMIN' Separation is at an absolute minimum.
'LOCMAX' Separation is at a local maximum.
'LOCMIN' Separation is at a local minimum.
The caller may indicate that the region of interest
is the set of time intervals where the quantity is
within a specified measure of an absolute extremum.
The argument `adjust' (described below) is used to
specify this measure.
Local extrema are considered to exist only in the
interiors of the intervals comprising the confinement
window: a local extremum cannot exist at a boundary
point of the confinement window.
The `relate' string lacks sensitivity to case, and to leading
and trailing blanks.
refval reference value used together with `relate' argument to
define an equality or inequality to satisfy by the selected
coordinate of the observer-target vector.
[1,1] = size(refval); double = class(refval)
See the discussion of `relate' above for further information.
The units of `refval' correspond to the type as defined
by `coord', radians for angular measures, kilometers for
distance measures.
adjust value used to modify searches for absolute extrema.
[1,1] = size(adjust); double = class(adjust)
When `relate' is set to 'ABSMAX' or 'ABSMIN' and `adjust'
is set to a positive value, cspice_gfposc finds times
when the observer-target vector coordinate is within `adjust'
radians/kilometers of the specified extreme value.
For `relate' set to 'ABSMAX', the result window contains
time intervals when the observer-target vector coordinate has
values between ABSMAX - adjust and ABSMAX.
For `relate' set to `ABSMIN', the result window contains
time intervals when the observer-target vector coordinate has
values between ABSMIN and ABSMIN + adjust.
`adjust' is not used for searches for local extrema,
equality or inequality conditions.
step time step size to use in the search.
[1,1] = size(step); double = class(step)
`step' must be short enough to for a search using this step
size to locate the time intervals where coordinate
function of the observer-target vector is monotone increasing
or decreasing. However, `step' must not be *too* short, or
the search will take an unreasonable amount of time.
For coordinates other than LONGITUDE and RIGHT ASCENSION,
the step size must be shorter than the shortest interval,
within the confinement window, over which the coordinate
is monotone increasing or decreasing.
For LONGITUDE and RIGHT ASCENSION, the step size must
be shorter than the shortest interval, within the
confinement window, over which either the sin or cos
of the coordinate is monotone increasing or decreasing.
The choice of `step' affects the completeness but not
the precision of solutions found by this routine; the
precision is controlled by the convergence tolerance.
See the discussion of the parameter SPICE_GF_CNVTOL for
details.
`step' has units of TDB seconds.
nintvls value specifying the number of intervals in the internal
workspace array used by this routine.
[1,1] = size(nintvls); int32 = class(nintvls)
`nintvls' should be at least as large as the number of
intervals within the search region on which the specified
observer-target vector coordinate function is monotone
increasing or decreasing. It does no harm to pick a value of
`nintvls' larger than the minimum required to execute the
specified search, but if chosen too small, the search will
fail.
cnfine a SPICE window that confines the time period over which the
specified search is conducted.
[2m,1] = size(cnfine); double = class(cnfine)
`cnfine' may consist of a single interval or a collection
of intervals.
In some cases the confinement window can be used to
greatly reduce the time period that must be searched
for the desired solution. See the -Particulars section
below for further discussion.
See the -Examples section below for a code example
that shows how to create a confinement window.
In some cases the observer's state may be computed at
times outside of `cnfine' by as much as 2 seconds. See
-Particulars for details.
the call:
[result] = cspice_gfposc( target, frame, abcorr, obsrvr, ...
crdsys, coord, relate, refval, ...
adjust, step, nintvls, cnfine )
returns:
result the SPICE window of intervals, contained within the
confinement window `cnfine', on which the specified
constraint is satisfied.
[2n,1] = size(result); double = class(result)
If the search is for local extrema, or for absolute
extrema with `adjust' set to zero, then normally each
interval of `result' will be a singleton: the left and
right endpoints of each interval will be identical.
If no times within the confinement window satisfy the
constraint, `result' will return with cardinality zero.
All parameters described here are declared in the Mice include file
MiceGF.m. See that file for parameter values.
SPICE_GF_CNVTOL
is the convergence tolerance used for finding endpoints
of the intervals comprising the result window.
SPICE_GF_CNVTOL is used to determine when binary
searches for roots should terminate: when a root is
bracketed within an interval of length SPICE_GF_CNVTOL,
the root is considered to have been found.
The accuracy, as opposed to precision, of roots found
by this routine depends on the accuracy of the input
data. In most cases, the accuracy of solutions will be
inferior to their precision.
Any numerical results shown for these examples may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.
1) Find the time during 2007 for which the latitude of the
Earth-Sun vector in IAU_EARTH frame has the maximum value,
i.e. the latitude of the Tropic of Cancer.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: gfposc_ex1.tm
This meta-kernel is intended to support operation of SPICE
example programs. The kernels shown here should not be
assumed to contain adequate or correct versions of data
required by SPICE-based user applications.
In order for an application to use this meta-kernel, the
kernels referenced here must be present in the user's
current working directory.
The names and contents of the kernels referenced
by this meta-kernel are as follows:
File name Contents
--------- --------
de421.bsp Planetary ephemeris
pck00009.tpc Planet orientation and
radii
naif0009.tls Leapseconds
\begindata
KERNELS_TO_LOAD = ( 'de421.bsp',
'pck00009.tpc',
'naif0009.tls' )
\begintext
End of meta-kernel
Example code begins here.
function gfposc_ex1()
MAXWIN = 1000;
TIMFMT = 'YYYY-MON-DD HR:MN:SC.###### (TDB) ::TDB ::RND';
%
% Load kernels.
%
cspice_furnsh( 'gfposc_ex1.tm' );
%
% Store the time bounds of our search interval in
% the cnfine confinement window.
%
et = cspice_str2et( { '2007 JAN 01', '2008 JAN 01'} );
cnfine = cspice_wninsd( et(1), et(2) );
%
% The latitude varies relatively slowly, ~46 degrees during the
% year. The extrema occur approximately every six months.
% Search using a step size near half that value (180 days).
% For this example use ninety days (in units of seconds).
%
step = 90.*cspice_spd;
adjust = 0.;
refval = 0.;
%
% Search for the date on which the `crdsys' system
% coordinate `coord' satisfies the `relate' constraint.
%
%
% Perform this search using the geometric position
% of the bodies; set the aberration correction to 'NONE'.
%
targ = 'SUN';
obsrvr = 'EARTH';
frame = 'IAU_EARTH';
abcorr = 'NONE';
relate = 'ABSMAX';
crdsys = 'LATITUDINAL';
coord = 'LATITUDE';
nintvls= MAXWIN ;
result = cspice_gfposc( targ, frame, abcorr, obsrvr, ...
crdsys, coord, relate, refval, ...
adjust, step, nintvls, cnfine );
%
% List the beginning and ending times in each interval
% if result contains data.
%
for i=1:numel(result)/2
[left, right] = cspice_wnfetd( result, i );
output = cspice_timout( [left,right], TIMFMT );
if( isequal( left, right) )
disp( ['Event time: ' output(1,:)] )
else
disp( ['From : ' output(1,:)] )
disp( ['To : ' output(2,:)] )
end
end
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
Event time: 2007-JUN-21 17:54:13.172475 (TDB)
2) A minor modification of the program listed in Example 1; find
the time during 2007 for which the latitude of the Earth-Sun
vector in IAU_EARTH frame has the minimum value, i.e. the
latitude of the Tropic of Capricorn.
Use the meta-kernel from the first example.
Example code begins here.
function gfposc_ex2()
MAXWIN = 1000;
TIMFMT = 'YYYY-MON-DD HR:MN:SC.###### (TDB) ::TDB ::RND';
%
% Load kernels.
%
cspice_furnsh( 'gfposc_ex1.tm' );
%
% Store the time bounds of our search interval in
% the cnfine confinement window.
%
et = cspice_str2et( { '2007 JAN 01', '2008 JAN 01'} );
cnfine = cspice_wninsd( et(1), et(2) );
%
% The latitude varies relatively slowly, ~46 degrees during the
% year. The extrema occur approximately every six months.
% Search using a step size near half that value (180 days).
% For this example use ninety days (in units of seconds).
%
step = 90.*cspice_spd;
adjust = 0.;
refval = 0.;
%
% Search for the date on which the `crdsys' system
% coordinate `coord' satisfies the `relate' constraint.
%
%
% Perform this search using the geometric position
% of the bodies; set the aberration correction to 'NONE'.
%
targ = 'SUN';
obsrvr = 'EARTH';
frame = 'IAU_EARTH';
abcorr = 'NONE';
relate = 'ABSMIN';
crdsys = 'LATITUDINAL';
coord = 'LATITUDE';
nintvls= MAXWIN ;
result = cspice_gfposc( targ, frame, abcorr, obsrvr, ...
crdsys, coord, relate, refval, ...
adjust, step, nintvls, cnfine );
%
% List the beginning and ending times in each interval
% if result contains data.
%
for i=1:numel(result)/2
[left, right] = cspice_wnfetd( result, i );
output = cspice_timout( [left,right], TIMFMT );
if( isequal( left, right) )
disp( ['Event time: ' output(1,:)] )
else
disp( ['From : ' output(1,:)] )
disp( ['To : ' output(2,:)] )
end
end
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
Event time: 2007-DEC-22 06:04:32.635539 (TDB)
3) Find the time during 2007 for which the Z component of the
Earth-Sun vector in IAU_EARTH frame has value 0, i.e. crosses
the equatorial plane (this also defines a zero latitude).
The search should return two times, one for an ascending
passage and one for descending.
Use the meta-kernel from the first example.
Example code begins here.
function gfposc_ex3()
MAXWIN = 1000;
TIMFMT = 'YYYY-MON-DD HR:MN:SC.###### (TDB) ::TDB ::RND';
%
% Load kernels.
%
cspice_furnsh( 'gfposc_ex1.tm' );
%
% Store the time bounds of our search interval in
% the cnfine confinement window.
%
et = cspice_str2et( { '2007 JAN 01', '2008 JAN 01'} );
cnfine = cspice_wninsd( et(1), et(2) );
%
% The latitude varies relatively slowly, ~46 degrees during the
% year. The extrema occur approximately every six months.
% Search using a step size near half that value (180 days).
% For this example use ninety days (in units of seconds).
%
step = 90.*cspice_spd;
adjust = 0.;
refval = 0.;
%
% Search for the date on which the `crdsys' system
% coordinate `coord' satisfies the `relate' constraint.
%
%
% Perform this search using the geometric position
% of the bodies; set the aberration correction to 'NONE'.
%
targ = 'SUN';
obsrvr = 'EARTH';
frame = 'IAU_EARTH';
abcorr = 'NONE';
relate = '=';
crdsys = 'RECTANGULAR';
coord = 'Z';
nintvls= MAXWIN ;
result = cspice_gfposc( targ, frame, abcorr, obsrvr, ...
crdsys, coord, relate, refval, ...
adjust, step, nintvls, cnfine );
%
% List the beginning and ending times in each interval
% if result contains data.
%
for i=1:numel(result)/2
[left, right] = cspice_wnfetd( result, i );
output = cspice_timout( [left,right], TIMFMT );
if( isequal( left, right) )
disp( ['Event time: ' output(1,:)] )
else
disp( ['From : ' output(1,:)] )
disp( ['To : ' output(2,:)] )
end
end
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
Event time: 2007-MAR-21 00:01:25.500673 (TDB)
Event time: 2007-SEP-23 09:46:39.579484 (TDB)
4) Find the times between Jan 1, 2007 and Jan 1, 2008
corresponding to the apoapsis on the Moon's orbit around the
Earth (note, the cspice_gfdist routine can also perform this search).
Use the meta-kernel from the first example.
Example code begins here.
function gfposc_ex4()
MAXWIN = 1000;
TIMFMT = 'YYYY-MON-DD HR:MN:SC.###### (TDB) ::TDB ::RND';
%
% Load kernels.
%
cspice_furnsh( 'gfposc_ex1.tm' );
%
% Store the time bounds of our search interval in
% the cnfine confinement window.
%
et = cspice_str2et( { '2007 JAN 01', '2008 JAN 01'} );
cnfine = cspice_wninsd( et(1), et(2) );
%
% This search requires a change in the step size since the
% Moon's orbit about the earth (earth-moon barycenter) has
% a twenty-eight day period. Use a step size something
% less than half that value. In this case, we use twelve
% days.
%
step = 12.*cspice_spd;
adjust = 0.;
refval = 0.;
%
% Search for the date on which the `crdsys' system
% coordinate `coord' satisfies the `relate' constraint.
%
%
% Perform this search using the geometric position
% of the bodies; set the aberration correction to 'NONE'.
%
targ = 'MOON';
obsrvr = 'EARTH';
frame = 'J2000';
abcorr = 'NONE';
relate = 'LOCMAX';
crdsys = 'SPHERICAL';
coord = 'RADIUS';
nintvls= MAXWIN ;
result = cspice_gfposc( targ, frame, abcorr, obsrvr, ...
crdsys, coord, relate, refval, ...
adjust, step, nintvls, cnfine );
%
% List the beginning and ending times in each interval
% if result contains data.
%
for i=1:numel(result)/2
[left, right] = cspice_wnfetd( result, i );
output = cspice_timout( [left,right], TIMFMT );
if( isequal( left, right) )
disp( ['Event time: ' output(1,:)] )
else
disp( ['From : ' output(1,:)] )
disp( ['To : ' output(2,:)] )
end
end
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
Event time: 2007-JAN-10 16:26:18.784521 (TDB)
Event time: 2007-FEB-07 12:39:35.055710 (TDB)
Event time: 2007-MAR-07 03:38:07.308330 (TDB)
Event time: 2007-APR-03 08:38:55.191516 (TDB)
Event time: 2007-APR-30 10:56:49.819340 (TDB)
Event time: 2007-MAY-27 22:03:28.834302 (TDB)
Event time: 2007-JUN-24 14:26:23.617432 (TDB)
Event time: 2007-JUL-22 08:43:50.113902 (TDB)
Event time: 2007-AUG-19 03:28:33.515939 (TDB)
Event time: 2007-SEP-15 21:07:13.940711 (TDB)
Event time: 2007-OCT-13 09:52:30.791223 (TDB)
Event time: 2007-NOV-09 12:32:50.039258 (TDB)
Event time: 2007-DEC-06 16:54:31.199770 (TDB)
5) Find times between Jan 1, 2007 and Jan 1, 2008 when the
latitude (elevation) of the observer-target vector between
DSS 17 and the Moon, as observed in the DSS 17 topocentric
(station) frame, exceeds 83 degrees.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: gfposc_ex5.tm
This meta-kernel is intended to support operation of SPICE
example programs. The kernels shown here should not be
assumed to contain adequate or correct versions of data
required by SPICE-based user applications.
In order for an application to use this meta-kernel, the
kernels referenced here must be present in the user's
current working directory.
The names and contents of the kernels referenced
by this meta-kernel are as follows:
File name Contents
--------- --------
de421.bsp Planetary ephemeris
pck00009.tpc Planet orientation and
radii
naif0009.tls Leapseconds
earthstns_itrf93_050714.bsp SPK for DSN Station
Locations
earth_topo_050714.tf Topocentric DSN stations
frame definitions
earth_latest_high_prec.bpc High precision earth PCK
\begindata
KERNELS_TO_LOAD = ( 'de421.bsp',
'pck00009.tpc',
'naif0009.tls',
'earthstns_itrf93_050714.bsp',
'earth_topo_050714.tf',
'earth_latest_high_prec.bpc' )
\begintext
End of meta-kernel
Example code begins here.
function gfposc_ex5()
MAXWIN = 1000;
TIMFMT = 'YYYY-MON-DD HR:MN:SC.###### (TDB) ::TDB ::RND';
%
% Load kernels.
%
cspice_furnsh( 'gfposc_ex5.tm' );
%
% Store the time bounds of our search interval in
% the cnfine confinement window.
%
et = cspice_str2et( { '2007 JAN 01', '2008 JAN 01'} );
cnfine = cspice_wninsd( et(1), et(2) );
%
% This search uses a step size of four hours since the
% time for all declination zero-to-max-to-zero passes
% within the search window exceeds eight hours.
%
% The example uses an 83 degree elevation because of its
% rare occurrence and short duration.
%
step = (4./24.)*cspice_spd;
adjust = 0.;
refval = 83*cspice_rpd;
%
% Search for the date on which the `crdsys' system
% coordinate `coord' satisfies the `relate' constraint.
%
%
% Perform this search using the geometric position
% of the bodies; set the aberration correction to 'NONE'.
%
targ = 'MOON';
obsrvr = 'DSS-17';
frame = 'DSS-17_TOPO';
abcorr = 'NONE';
relate = '>';
crdsys = 'LATITUDINAL';
coord = 'LATITUDE';
nintvls= MAXWIN ;
result = cspice_gfposc( targ, frame, abcorr, obsrvr, ...
crdsys, coord, relate, refval, ...
adjust, step, nintvls, cnfine );
%
% List the beginning and ending times in each interval
% if result contains data.
%
for i=1:numel(result)/2
[left, right] = cspice_wnfetd( result, i );
output = cspice_timout( [left,right], TIMFMT );
if( isequal( left, right) )
disp( ['Event time: ' output(1,:)] )
else
disp( ['From : ' output(1,:)] )
disp( ['To : ' output(2,:)] )
end
end
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
From : 2007-FEB-26 03:18:48.229281 (TDB)
To : 2007-FEB-26 03:31:29.734931 (TDB)
From : 2007-MAR-25 01:12:38.550572 (TDB)
To : 2007-MAR-25 01:23:53.909469 (TDB)
This routine determines a set of one or more time intervals
within the confinement window when the selected coordinate of
the observer-target position vector satisfies a caller-specified
constraint. The resulting set of intervals is returned as a SPICE
window.
Below we discuss in greater detail aspects of this routine's
solution process that are relevant to correct and efficient
use of this routine in user applications.
The Search Process
==================
Regardless of the type of constraint selected by the caller, this
routine starts the search for solutions by determining the time
periods, within the confinement window, over which the specified
coordinate function is monotone increasing and monotone
decreasing. Each of these time periods is represented by a SPICE
window. Having found these windows, all of the coordinate
function's local extrema within the confinement window are known.
Absolute extrema then can be found very easily.
Within any interval of these "monotone" windows, there will be at
most one solution of any equality constraint. Since the boundary
of the solution set for any inequality constraint is contained in
the union of
- the set of points where an equality constraint is met
- the boundary points of the confinement window
the solutions of both equality and inequality constraints can be
found easily once the monotone windows have been found.
Step Size
=========
The monotone windows (described above) are found using a two-step
search process. Each interval of the confinement window is
searched as follows: first, the input step size is used to
determine the time separation at which the sign of the rate of
change of coordinate will be sampled. Starting at
the left endpoint of an interval, samples will be taken at each
step. If a change of sign is found, a root has been bracketed; at
that point, the time at which the time derivative of the
coordinate is zero can be found by a refinement process, for
example, using a binary search.
Note that the optimal choice of step size depends on the lengths
of the intervals over which the coordinate function is monotone:
the step size should be shorter than the shortest of these
intervals (within the confinement window).
The optimal step size is *not* necessarily related to the lengths
of the intervals comprising the result window. For example, if
the shortest monotone interval has length 10 days, and if the
shortest result window interval has length 5 minutes, a step size
of 9.9 days is still adequate to find all of the intervals in the
result window. In situations like this, the technique of using
monotone windows yields a dramatic efficiency improvement over a
state-based search that simply tests at each step whether the
specified constraint is satisfied. The latter type of search can
miss solution intervals if the step size is longer than the
shortest solution interval.
Having some knowledge of the relative geometry of the target and
observer can be a valuable aid in picking a reasonable step size.
In general, the user can compensate for lack of such knowledge by
picking a very short step size; the cost is increased computation
time.
Note that the step size is not related to the precision with which
the endpoints of the intervals of the result window are computed.
That precision level is controlled by the convergence tolerance.
Convergence Tolerance
=====================
As described above, the root-finding process used by this routine
involves first bracketing roots and then using a search process
to locate them. "Roots" are both times when local extrema are
attained and times when the coordinate function is equal to a
reference value. All endpoints of the intervals comprising the
result window are either endpoints of intervals of the
confinement window or roots.
Once a root has been bracketed, a refinement process is used to
narrow down the time interval within which the root must lie.
This refinement process terminates when the location of the root
has been determined to within an error margin called the
"convergence tolerance." The default convergence tolerance
used by this routine is set by the parameter SPICE_GF_CNVTOL (defined
in MiceGF.m).
The value of SPICE_GF_CNVTOL is set to a "tight" value so that the
tolerance doesn't become the limiting factor in the accuracy of
solutions found by this routine. In general the accuracy of input
data will be the limiting factor.
The user may change the convergence tolerance from the default
SPICE_GF_CNVTOL value by calling the routine cspice_gfstol, e.g.
cspice_gfstol( tolerance value );
Call cspice_gfstol prior to calling this routine. All subsequent
searches will use the updated tolerance value.
Setting the tolerance tighter than SPICE_GF_CNVTOL is unlikely to be
useful, since the results are unlikely to be more accurate.
Making the tolerance looser will speed up searches somewhat,
since a few convergence steps will be omitted. However, in most
cases, the step size is likely to have a much greater effect
on processing time than would the convergence tolerance.
The Confinement Window
======================
The simplest use of the confinement window is to specify a time
interval within which a solution is sought. However, the
confinement window can, in some cases, be used to make searches
more efficient. Sometimes it's possible to do an efficient search
to reduce the size of the time period over which a relatively
slow search of interest must be performed.
Practical use of the coordinate search capability would likely
consist of searches over multiple coordinate constraints to find
time intervals that satisfies the constraints. An
effective technique to accomplish such a search is
to use the result window from one search as the confinement window
of the next.
Certain types of searches require the state of the observer,
relative to the solar system barycenter, to be computed at times
slightly outside the confinement window `cnfine'. The time window
that is actually used is the result of "expanding" `cnfine' by a
specified amount "T": each time interval of `cnfine' is expanded by
shifting the interval's left endpoint to the left and the right
endpoint to the right by T seconds. Any overlapping intervals are
merged. (The input argument `cnfine' is not modified.)
The window expansions listed below are additive: if both
conditions apply, the window expansion amount is the sum of the
individual amounts.
- If a search uses an equality constraint, the time window
over which the state of the observer is computed is expanded
by 1 second at both ends of all of the time intervals
comprising the window over which the search is conducted.
- If a search uses stellar aberration corrections, the time
window over which the state of the observer is computed is
expanded as described above.
When light time corrections are used, expansion of the search
window also affects the set of times at which the light time-
corrected state of the target is computed.
In addition to the possible 2 second expansion of the search
window that occurs when both an equality constraint and stellar
aberration corrections are used, round-off error should be taken
into account when the need for data availability is analyzed.
Longitude and Right Ascension
=============================
The cyclic nature of the longitude and right ascension coordinates
produces branch cuts at +/- 180 degrees longitude and 0-360
right ascension. Round-off error may cause solutions near these
branches to cross the branch. Use of the Mice routine cspice_wncond
will contract solution windows by some epsilon, reducing the
measure of the windows and eliminating the branch crossing. A
one millisecond contraction will in most cases eliminate
numerical round-off caused branch crossings.
1) In order for this routine to produce correct results,
the step size must be appropriate for the problem at hand.
Step sizes that are too large may cause this routine to miss
roots; step sizes that are too small may cause this routine
to run unacceptably slowly and in some cases, find spurious
roots.
This routine does not diagnose invalid step sizes, except
that if the step size is non-positive, an error is signaled
by a routine in the call tree of this routine.
2) Due to numerical errors, in particular,
- truncation error in time values
- finite tolerance value
- errors in computed geometric quantities
it is *normal* for the condition of interest to not always be
satisfied near the endpoints of the intervals comprising the
`result' window. One technique to handle such a situation,
slightly contract `result' using the window routine cspice_wncond.
3) If the output SPICE window `result' has insufficient capacity
to contain the number of intervals on which the specified
distance condition is met, an error is signaled
by a routine in the call tree of this routine.
4) If an error (typically cell overflow) occurs during
window arithmetic, the error is signaled by a routine
in the call tree of this routine.
5) If the relational operator `relate' is not recognized, an
error is signaled by a routine in the call tree of this
routine.
6) If the aberration correction specifier contains an
unrecognized value, an error is signaled by a routine in the
call tree of this routine.
7) If `adjust' is negative, an error is signaled by a routine in
the call tree of this routine.
8) If either of the input body names do not map to NAIF ID
codes, an error is signaled by a routine in the call tree of
this routine.
9) If required ephemerides or other kernel data are not
available, an error is signaled by a routine in the call tree
of this routine.
10) If the search uses GEODETIC or PLANETOGRAPHIC coordinates, and
the center body of the reference frame has unequal equatorial
radii, an error is signaled by a routine in the call tree of
this routine.
11) If any of the input arguments, `target', `frame', `abcorr',
`obsrvr', `crdsys', `coord', `relate', `refval', `adjust',
`step', `nintvls' or `cnfine', is undefined, an error is
signaled by the Matlab error handling system.
12) If any of the input arguments, `target', `frame', `abcorr',
`obsrvr', `crdsys', `coord', `relate', `refval', `adjust',
`step', `nintvls' or `cnfine', is not of the expected type, or
it does not have the expected dimensions and size, an error is
signaled by the Mice interface.
Appropriate SPK and PCK kernels must be loaded by the calling
program before this routine is called.
The following data are required:
- SPK data: the calling application must load ephemeris data
for the targets, observer, and any intermediate objects in
a chain connecting the targets and observer that cover the
time period specified by the window `cnfine'. If aberration
corrections are used, the states of target and observer
relative to the solar system barycenter must be calculable
from the available ephemeris data. Typically ephemeris data
are made available by loading one or more SPK files using
cspice_furnsh.
- If non-inertial reference frames are used, then PCK
files, frame kernels, C-kernels, and SCLK kernels may be
needed.
- In some cases the observer's state may be computed at times
outside of `cnfine' by as much as 2 seconds; data required to
compute this state must be provided by loaded kernels. See
-Particulars for details.
Such kernel data are normally loaded once per program
run, NOT every time this routine is called.
1) The kernel files to be used by this routine must be loaded
(normally using the Mice routine cspice_furnsh) before this
routine is called.
2) This routine has the side effect of re-initializing the
coordinate quantity utility package. Callers may
need to re-initialize the package after calling this routine.
MICE.REQ
GF.REQ
SPK.REQ
CK.REQ
TIME.REQ
WINDOWS.REQ
None.
J. Diaz del Rio (ODC Space)
E.D. Wright (JPL)
-Mice Version 1.1.0, 03-NOV-2021 (EDW) (JDR)
Updated header to describe use of expanded confinement window.
Edited the header to comply with NAIF standard. Added
example's meta-kernel.
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections.
Eliminated use of "lasterror" in rethrow.
Removed reference to the function's corresponding CSPICE header from
-Required_Reading section.
-Mice Version 1.0.1, 13-NOV-2014 (EDW)
Edited -I/O section to conform to NAIF standard for Mice
documentation.
-Mice Version 1.0.2, 05-SEP-2012 (EDW)
Edit to comments to correct search description.
Header updated to describe use of cspice_gfstol.
-Mice Version 1.0.1, 10-JUN-2009 (EDW)
Minor header edit "cosin" -> "cos".
-Mice Version 1.0.0, 15-APR-2009 (EDW)
GF position coordinate search
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