Table of contents
CSPICE_GFRR determines the time intervals for which a specified constraint
on the observer-target range rate is met.
Given:
target the scalar string naming the target body.
help, target
STRING = Scalar
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 string `target' is case-insensitive, and leading
and trailing blanks in `target' are not significant.
The target and observer define a position vector which
points from the observer to the target; the time derivative
length of this vector is the "range rate" that serves as
the subject of the search performed by this routine.
abcorr the scalar string indicating the aberration corrections to apply
to the state evaluations to account for one-way light time and
stellar aberration.
help, abcorr
STRING = Scalar
This routine accepts the same aberration corrections as does
the Icy 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 the scalar string naming the observing body.
help, obsrvr
STRING = Scalar
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 earth.
relate the string or character scalar describing the constraint
relational operator on observer-target range rate.
help, relate
STRING = Scalar
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:
'>' Range rate is greater than the reference
value `refval'.
'=' Range rate is equal to the reference
value `refval'.
'<' Range rate is less than the reference
value `refval'.
'ABSMAX' Range rate is at an absolute maximum.
'ABSMIN' Range rate is at an absolute minimum.
'LOCMAX' Range rate is at a local maximum.
'LOCMIN' Range rate 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 distance of an absolute extremum.
The argument `adjust' (described below) is used to
specify this distance.
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, leading
and trailing blanks.
refval the scalar double precision reference value used together with
`relate' argument to define an equality or inequality to satisfy
by the observer-target range rate.
help, refval
DOUBLE = Scalar
See the discussion of `relate' above for further information.
The units of 'refval' are km.
adjust a scalar double precision value used to modify searches for
absolute extrema: when `relate' is set to 'ABSMAX' or 'ABSMIN'
and `adjust' is set to a positive value, cspice_gfrr finds times
when the observer-target vector coordinate is within `adjust'
kilometers/seconds of the specified extreme value.
help, adjust
DOUBLE = Scalar
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 range rate has
values between ABSMIN and ABSMIN + adjust.
`adjust' is not used for searches for local extrema,
equality or inequality conditions.
step the scalar double precision time step size to use in the search.
help, step
DOUBLE = Scalar
`step' must be short enough 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.
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.
`step' has units of seconds.
nintvls a scalar integer value specifying the number of intervals in the
internal workspace array used by this routine.
help, nintvls
LONG = Scalar
`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 scalar double precision window that confines the time period
over which the specified search is conducted.
help, cnfine
STRUCT = cspice_celld(2*N)
`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:
cspice_gfrr, target, abcorr, obsrvr, relate, refval, $
adjust, step, nintvls, cnfine, result
returns:
result the scalar double precision window of intervals, contained
within the confinement window `cnfine', on which the specified
constraint is satisfied.
help, result
STRUCT = cspice_celld(2*R)
If `result' is non-empty on input, its contents
will be discarded before cspice_gfrr conducts its
search.
`result' must be declared and initialized with sufficient
size to capture the full set of time intervals
within the search region on which the specified constraint
is satisfied.
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 be returned with a
cardinality of zero.
SPICE_GF_CNVTOL
is the convergence tolerance used for finding endpoints
of the intervals comprising the result window.
SPICE_GF_CNVTOL is also used for finding intermediate
results; in particular, SPICE_GF_CNVTOL is used for
finding the windows on which the specified coordinate
is increasing or decreasing. 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.
See Icy include file IcyGF.pro for declarations and descriptions of
parameters used throughout the GF system.
Any numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.
1) Determine the time windows from January 1, 2007 UTC to
April 1, 2007 UTC for which the sun-moon range rate satisfies the
relation conditions with respect to a reference value of
0.3365 km/s radians (this range rate known to occur within the
search interval). Also determine the time windows corresponding
to the local maximum and minimum range rate, and the absolute
maximum and minimum range rate during the search interval.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: gfrr_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.
PRO gfrr_ex1
MAXWIN = 2000
TIMFMT = 'YYYY-MON-DD HR:MN:SC.###'
TIMLEN = 41
relate = [ '=', '<', '>', 'LOCMIN', 'ABSMIN', 'LOCMAX', 'ABSMAX' ]
;;
;; Load kernels.
;;
cspice_furnsh, 'gfrr_ex1.tm'
;;
;; Store the time bounds of our search interval in
;; the cnfine confinement window.
;;
cspice_str2et, [ '2007 JAN 01', '2007 APR 01'], et
cnfine = cspice_celld( 2 )
cspice_wninsd, et[0], et[1], cnfine
;;
;; Search using a step size of 1 day (in units of seconds).
;; The reference value is .3365 km/s. We're not using the
;; adjustment feature, so we set 'adjust' to zero.
;;
step = cspice_spd();
adjust = 0.D0;
refval = .3365D0;
target = 'MOON'
abcorr = 'NONE'
obsrvr = 'SUN'
nintvls = MAXWIN
result = cspice_celld( MAXWIN*2)
for j=0, 6 do begin
print, 'Relation condition: ', relate[j]
;;
;; Perform the search. The SPICE window 'result' contains
;; the set of times when the condition is met.
;;
cspice_gfrr, target, abcorr, obsrvr, relate[j], refval, $
adjust, step, nintvls, cnfine, result
;;
;; List the beginning and ending times in each interval
;; if 'result' contains data.
;;
count = cspice_wncard( result )
if ( count eq 0 ) then begin
print, 'Result window is empty.'
endif else begin
for i= 0L, (count - 1L ) do begin
;;
;; Fetch the endpoints of the Ith interval
;; of the result window.
;;
cspice_wnfetd, result, i, left, right
cspice_timout, [left, right], TIMFMT, TIMLEN, timstr
print, 'Start time, drdt = ', timstr[0]
print, 'Stop time, drdt = ', timstr[1]
endfor
endelse
print, ' '
endfor
;;
;; It's always good form to unload kernels after use,
;; particularly in IDL due to data persistence.
;;
cspice_kclear
END
When this program was executed on a Mac/Intel/IDL8.x/64-bit
platform, the output was:
Relation condition: =
Start time, drdt = 2007-JAN-02 00:35:19.571
Stop time, drdt = 2007-JAN-02 00:35:19.571
Start time, drdt = 2007-JAN-19 22:04:54.897
Stop time, drdt = 2007-JAN-19 22:04:54.897
Start time, drdt = 2007-FEB-01 23:30:13.427
Stop time, drdt = 2007-FEB-01 23:30:13.427
Start time, drdt = 2007-FEB-17 11:10:46.538
Stop time, drdt = 2007-FEB-17 11:10:46.538
Start time, drdt = 2007-MAR-04 15:50:19.929
Stop time, drdt = 2007-MAR-04 15:50:19.929
Start time, drdt = 2007-MAR-18 09:59:05.957
Stop time, drdt = 2007-MAR-18 09:59:05.957
Relation condition: <
Start time, drdt = 2007-JAN-02 00:35:19.571
Stop time, drdt = 2007-JAN-19 22:04:54.897
Start time, drdt = 2007-FEB-01 23:30:13.427
Stop time, drdt = 2007-FEB-17 11:10:46.538
Start time, drdt = 2007-MAR-04 15:50:19.929
Stop time, drdt = 2007-MAR-18 09:59:05.957
Relation condition: >
Start time, drdt = 2007-JAN-01 00:00:00.000
Stop time, drdt = 2007-JAN-02 00:35:19.571
Start time, drdt = 2007-JAN-19 22:04:54.897
Stop time, drdt = 2007-FEB-01 23:30:13.427
Start time, drdt = 2007-FEB-17 11:10:46.538
Stop time, drdt = 2007-MAR-04 15:50:19.929
Start time, drdt = 2007-MAR-18 09:59:05.957
Stop time, drdt = 2007-APR-01 00:00:00.000
Relation condition: LOCMIN
Start time, drdt = 2007-JAN-11 07:03:58.991
Stop time, drdt = 2007-JAN-11 07:03:58.991
Start time, drdt = 2007-FEB-10 06:26:15.441
Stop time, drdt = 2007-FEB-10 06:26:15.441
Start time, drdt = 2007-MAR-12 03:28:36.404
Stop time, drdt = 2007-MAR-12 03:28:36.404
Relation condition: ABSMIN
Start time, drdt = 2007-JAN-11 07:03:58.991
Stop time, drdt = 2007-JAN-11 07:03:58.991
Relation condition: LOCMAX
Start time, drdt = 2007-JAN-26 02:27:33.762
Stop time, drdt = 2007-JAN-26 02:27:33.762
Start time, drdt = 2007-FEB-24 09:35:07.812
Stop time, drdt = 2007-FEB-24 09:35:07.812
Start time, drdt = 2007-MAR-25 17:26:56.148
Stop time, drdt = 2007-MAR-25 17:26:56.148
Relation condition: ABSMAX
Start time, drdt = 2007-MAR-25 17:26:56.148
Stop time, drdt = 2007-MAR-25 17:26:56.148
This routine determines if the caller-specified constraint
condition on the geometric event (range rate) is satisfied for
any time intervals within the confinement window `cnfine'. If one
or more such time intervals exist, those intervals are added
to the `result' 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
range rate 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 range rate
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 range rate 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
range rate 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 range rate 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 range rate 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 IcyGF.pro).
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.
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.
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 number of intervals `nintvls' is less than 1, the error
SPICE(VALUEOUTOFRANGE) is signaled by a routine in the call
tree of this routine.
4) If the size of the SPICE window `result' is less than 2 or not
an even value, the error SPICE(INVALIDDIMENSION) is signaled
by a routine in the call tree of this routine.
5) If the 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.
6) If an error (typically cell overflow) occurs during
window arithmetic, the error is signaled by a routine
in the call tree of this routine.
7) If the relational operator `relate' is not recognized, an
error is signaled by a routine in the call tree of this
routine.
8) If the aberration correction specifier contains an
unrecognized value, an error is signaled by a routine in the
call tree of this routine.
9) If `adjust' is negative, an error is signaled by a routine in
the call tree of this routine.
10) If `adjust' has a non-zero value when `relate' has any value other
than 'ABSMIN' or 'ABSMAX', an error is signaled by a routine
in the call tree of this routine.
11) 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.
12) If required ephemerides or other kernel data are not
available, an error is signaled by a routine in the call tree
of this routine.
13) If any of the input arguments, `target', `abcorr', `obsrvr',
`relate', `refval', `adjust', `step', `nintvls', `cnfine' or
`result', is undefined, an error is signaled by the IDL error
handling system.
14) If any of the input arguments, `target', `abcorr', `obsrvr',
`relate', `refval', `adjust', `step', `nintvls', `cnfine' or
`result', is not of the expected type, or it does not have the
expected dimensions and size, an error is signaled by the Icy
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.
- 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.
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 Icy routine cspice_furnsh) before this
routine is called.
2) This routine has the side effect of re-initializing the
range rate quantity utility package. Callers may themselves
need to re-initialize the range rate quantity utility
package after calling this routine.
ICY.REQ
GF.REQ
SPK.REQ
NAIF_IDS.REQ
TIME.REQ
WINDOWS.REQ
None.
J. Diaz del Rio (ODC Space)
E.D. Wright (JPL)
-Icy Version 1.0.2, 03-NOV-2021 (JDR)
Updated header to describe use of expanded confinement window.
Edited the header to comply with NAIF standard.
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections.
Removed reference to the routine's corresponding CSPICE header from
-Abstract section.
Added arguments' type and size information in the -I/O section.
-Icy Version 1.0.1, 05-SEP-2012 (EDW)
Edit to comments to correct search description.
Edits to Example section, proper description of "standard.tm"
meta kernel.
Header updated to describe use of cspice_gfstol.
-Icy Version 1.0.0, 16-FEB-2010 (EDW)
GF range rate search
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