Stages List

Select the Stages property, and click where indicated to display a List window that lets you define one or more LS stages, with the following parameters:

LS Parameters
Parameter Description
StartTime/StopTime Define the time period during which measurements are taken.
DataFrequency Specify the time to elapse between measurements. The greater this interval, the fewer measurements are available for the LS calculations.
NumMeasurements This read-only field indicates how many measurements are available, based on the selected time period and data frequency (see above).
EstimateBCoeff Allows LS to estimate a correction to the nominal ballistic coefficient. When transferred to the satellite, the correction is transformed to a correction in Cd if the ForceModel.Drag.SpecMethod of the satellite is set to Mass Area Cd or directly transferred if the ForceModel.Drag.SpecMethod of the satellite is set to Ballistic Coefficient.
EstimateCR Allows LS to estimate a correction to the nominal CR value. When transferred to the satellite's initial state, the nominal CR value is adjusted by this amount.
EstimateMeasBias Allows LS to estimate measurement biases. When enabled, and for each stage, a "mean" measurement bias will be estimated for each tracker and measurement type present in the measurements whenever the corresponding tracker MeasurementStatistics Estimate flag is enabled. In the first stage where a particular tracker/measurement bias is estimated the "Constant" bias estimate in the MeasurementStatistics will be used as the initial LS estimate. In subsequent stages the LS solution estimate from the most recent stage containing that tracker/measurement bias will be used. Note that the Transfer to Satellite does not transfer the measurement biases. These need to be transferred by user to the "Constant" bias estimate in the MeasurementStatistics.
EstimateTransBias Allows LS to estimate transponder biases. When enabled, and for each stage, a "mean" bias will be estimated for each Transponder present in the measurement list whenever the corresponding Transponder Estimates flag is enabled. In the first stage, the Transponder model "Constant" bias will be used as the initial state estimate. In subsequent stages the most recent stage estimate will be used. Note that the Transfer to Satellite does NOT transfer the transponder bias LS estimate; this need to be done manually.
MaxIterations The maximum number of tries to achieve convergence. If this number is reached before convergence occurs, LS processing stops. Convergence is defined to occur when the relative difference between the residual RMS from the current iteration and residual RMS from the previous iteration is smaller than the RMSConvergenceCriteria. See Tip, below.
RMSConvergenceCriteria Stop iterating when the following ratio:
(where RMSi is the current weighted RMS and RMSi-1 is the previous weighted RMS) is less than or equal to the user-entered value.
SigmaEdit This boolean attribute, if set to true, will exclude observations for which the observation residual exceeds the specified N-sigma level relative to the unweighted RMS of all accepted observations of the specified measurement type computed the previous iteration.

Specifically:

If | Δyji | ≥ N RMSi-1 then exclude the measurement.

where:

     Δyji = iteration i, jth observation residual

     N = N-sigma level specified below by the satellite residual sigma attribute "MeasurementProcessing.ResidualEditing.NominalSigma"

     RMSi-1 = the unweighted RMS of all accepted observations of measurement type "y" used in the i-1 iteration solution. Note the RMS includes observations from all trackers, and that no N-sigma level editing is applied during the first iteration.

If this attribute is false, sigma editing is not applied, and all residuals are considered (provided that they pass the min/max elevation criteria). This attribute is useful when working with noisy or sparse data.
Sigma When sigma editing is True, enter the value of N to be used in the sigma editing equation shown above.
InitialEdit Only applicable when SigmaEdit is true. When true InitialEdit allows residuals to be edited out on first iteration by making an initial pass through the data to compute the initial measurement RMS.
StateCorrection Select among
  • Pos and Vel - Least Squares solves for satellite position and velocity (default).


  • Position Only - Least squares corrects position only; velocity does not change.


  • Velocity Only - Least Squares corrects velocity, holding position fixed.


  • Neither Pos nor Vel – Position and velocity are both held constant to their nominal values. If selected, at least one of the EstimateBCoeff, EstimateCr, and EstimateMeasBias settings should be set to True. Otherwise, LS has no states to estimate.

Use the Add... button to add new LS stages to the list. If an item in the list is selected, the new stage is added after that one; if nothing is selected, the new stage is added at the beginning. When you add a new stage to the list, the default LS fit time span will be set on the basis of the scenario's DefaultTimes.Intervals.TimeSpan attribute.

Use the Remove button to delete stages from the list. To change the position of a given stage in the list, select it and use the Up or Down button.

Tip: When processing maneuvers in Least Squares, you may need to turn the CheckForDivergence attribute off and increase MaximumIterations. A least squares stage can be defined to include all data up to the time of the maneuver. A second stage can be defined to include tracking data after the maneuver. Least squares will automatically include the maneuver when transitioning between stages, and the starting state for the second stage will be properly formed.

ODTK 6.5