cspice_gfposc |
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## AbstractCSPICE_GFPOSC determines the time intervals for which a coordinate of an observer-target position vector satisfies a numerical constraint. ## I/OGiven: Parameters- All parameters described here are declared in the header file SpiceGF.h. 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. Arguments- target name of the target body. 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. [1,c1] = size(target); char = class(target) or [1,1] = size(target); cell = class(target) 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 spkezr_c. See the header of spkezr_c 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. 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. [1,c4] = size(obsrvr); char = class(obsrvr) or [1,1] = size(obsrvr); cell = class(obsrvr) crdsys name of the 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: Coordinate System (crdsys) Coordinates (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. The result window found by this routine indicates the time intervals where the constraint is satisfied. [1,c7] = size(relate); char = class(relate) or [1,1] = size(relate); cell = class(relate) 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. See the discussion of relate above for further information. [1,1] = size(refval); double = class(refval) 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: when relate is set to ABSMAX or ABSMIN and adjust is set to a positive value, ## ExamplesAny 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. Example(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. MAXWIN = 1000; TIMFMT = 'YYYY-MON-DD HR:MN:SC.###### (TDB) ::TDB ::RND'; % % Load kernels. % cspice_furnsh( 'standard.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 = ## ParticularsThis routine provides a simple interface for conducting searches for observer-target vector coordinate value events. This routine determines a set of one or more time intervals within the confinement window when the selected coordinate of the observer-target 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 distance 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 convergence tolerance used by this routine is set by the parameter SPICE_GF_CNVTOL. 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 in seconds ) 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 affect 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. Longitude and Right Ascension ============================= The cyclic nature of the longitude and right ascension coordinates produces branch cuts at +/- 180 degrees longitude and 0-360 longitude. Round-off error may cause solutions near these branches to cross the branch. Use of the SPICE routine wncond_c 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. ## Required ReadingFor important details concerning this module's function, please refer to the CSPICE routine gfposc_c. MICE.REQ GF.REQ SPK.REQ CK.REQ TIME.REQ WINDOWS.REQ ## Version-Mice Version 1.0.1, 13-NOV-2014, EDW (JPL) Edited I/O section to conform to NAIF standard for Mice documentation. -Mice Version 1.0.2, 05-SEP-2012, EDW (JPL) Edit to comments to correct search description. Header updated to describe use of cspice_gfstol. -Mice Version 1.0.1, 10-JUN-2009, EDW (JPL) Minor header edit "cosin" -> "cos". -Mice Version 1.0.0, 15-APR-2009, EDW (JPL) ## Index_EntriesGF position coordinate search |

Wed Apr 5 18:00:32 2017