BatchEstimatorInv
BatchEstimatorInv — A batch least squares estimator
Description
A batch least squares estimator is a method for obtaining an estimate for a parameter vector, x0, such that a performance index, which is a function of that parameter, J = J(x0), is minimized. For our application, x0 typically includes the spacecraft position and velocity at a specific epoch and the performance index is a weighted sum of the squares of the measurement residuals.
See Also: TrackingFileSet, RunEstimator
Fields
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| AbsoluteTol | Absolute Weighted RMS convergence criteria tolerance
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| DataFilters |
Defines filters to be applied to the data. One or more filters of either type (AcceptFilter, RejectFilter) may be specified. Rules specified by data filters on a BatchEstimatorInv are applied to determine what data is accepted or rejected from the computation of the state update.
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| EstimationEpoch | Estimation Epoch. This is the epoch associated with the "solve-fors." As of R2016A, this epoch comes from the participants defined in the Measurements field. In later releases, additional options will be allowed.
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| EstimationEpochFormat | Estimation Epoch format. This is the desired input format for the EstimationEpoch field. For release R2016A, the only allowed value is 'FromParticipants' which means that the EstimationEpoch comes from the participants defined in the Measurements field. In later releases, additional options will be allowed.
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| FreezeIteration | Specifies which iteration to freeze the selection of measurements that are edited out
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| FreezeMeasurementEditing | Allows the selection of measurements that are edited out to be frozen
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| InversionAlgorithm | Algorithm used to invert the normal equations
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| MatlabFile | File name for the output MATLAB file. Leaving this parameter unset means that no MATLAB file will be output.
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| MaxConsecutiveDivergences | Specifies maximum number of consecutive diverging iterations allowed before batch estimation processing is stopped
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| MaximumIterations | Specifies maximum number of iterations allowed for batch estimation
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| Measurements | Specifies a list of measurements used for batch estimation
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| OLSEAdditiveConstant | Additive constant used for outer loop sigma editing (OLSE)
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| OLSEInitialRMSSigma | Initial predicted root-mean-square value used for outer loop sigma editing (OLSE)
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| OLSEMultiplicativeConstant | Multiplicative constant used for outer loop sigma editing (OLSE)
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| OLSEUseRMSP | Flag used to specify editing algorithm used for outer loop sigma editing (OLSE) for iterations greater than 1. See Behavior of Outer Loop Sigma Editing (OLSE) in the Remarks section for details.
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| Propagator | Propagator object used for batch estimation
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| RelativeTol | Relative Weighted RMS convergence criteria tolerance
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| ReportFile | Specifies the name of estimation report file
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| ReportStyle | Specifies the type of estimation report. The
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| ResetBestRMSIfDiverging |
If set true and the estimation process has diverged, then the Best RMS is reset to the current RMS.
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| ShowAllResiduals | Allows residuals plots to be shown
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| ShowProgress | Allows detailed output of the batch estimator to be shown in the message window
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| UseInitialCovariance | If set true, a priori error covariance term is added to the estimation cost function. This option should be set to true when estimating with an applied Spacecraft.OrbitErrorCovariance, Spacecraft.CdSigma, Spacecraft.CrSigma, or ErrorModel.BiasSigma. See the Remarks section below for some restrictions on the use of this field.
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Remarks
Navigation Requires Use of Fixed Step Numerical Integration
GMAT navigation requires use of fixed stepped propagation. The BatchEstimatorInv resource has a Propagator field containing the name of the Propagator resource that will be used during the estimation process. As shown in the Note below, there are some hard restrictions on the choice of error control specified for the ForceModel resource associated with your propagator.
Note
For batch estimation, the ErrorControl parameter
specified for the ForceModel resource associated
with the BatchEstimatorInv
Propagator must be set to 'None.' Of
course, when using fixed step control, the user must choose a step
size, as given by the Propagator
InitialStepSize field, for the chosen orbit regime and
force profile, that yields the desired accuracy.
Behavior of Convergence Criteria
GMAT has four input fields, RelativeTol, AbsoluteTol, MaximumIterations, and MaxConsecutiveDivergences that are used to determine if the estimator has converged after each new iteration. Associated with these input fields are the two convergence tests shown below:
Absolute Weighted RMS convergence criteria
Weighted RMScurrent <= AbsoluteTol
Relative Weighted Root Mean Square (RMS) convergence criteria
|RMSP – RMSB|/ RMSB <= RelativeTol
where
RMSB = smallest Weighted RMS achieved during the current and previous iterations
RMSP = predicted Weighted RMS of next iteration
Batch estimation is considered to have converged when either or both of the above criteria is met within MaximumIterations iterations or less.
Batch estimation is considered to have diverged when number of consecutive diverging iterations is equal to or greater than MaxConsecutiveDivergences or the number of iterations exceeds MaximumIterations.
Behavior of Outer Loop Sigma Editing (OLSE)
GMAT has four input fields, OLSEMultiplicativeConstant, OLSEAdditiveConstant, OLSEUseRMSP, and OLSEInitialRMSSigma, that are used to 'edit' (i.e., reject or throw away) bad measurement data. There are plans to have both an inner loop and and outer loop iteration editing procedure. Currently, only the outer loop iteration editing procedure is implemented. This editing procedure is done on a per iteration basis. Data that is edited is not used to calculate the state vector estimate for the current iteration but the data is available as a candidate measurement for subsequent iterations. On the first outer loop iteration, data is edited if
|Weighted Measurement Residual| > OLSEInitialRMSSigma
where the Weighted Measurement Residual for a single given measurement is given by
(O-C)/NoiseSigma
and where NoiseSigma is the input noise (one sigma) for the measurement type associated with the given measurement. On subsequent outer loop iterations, the data is edited if
|Weighted Measurement Residual| > OLSEMultiplicativeConstant * RMS + OLSEAdditiveConstant
The editing algorithm above depends upon the user input value of OLSEUseRMSP. If OLSEUseRMSP = True, then RMS = WRMSP where WRMSP is the predicted weighted RMS calculated at the end of the previous iteration. Otherwise, If OLSEUseRMSP = False, then RMS = WRMS where WRMS is the actual weighted RMS calculated at the end of the previous iteration.
Behavior of Freezing Measurement Editing
GMAT has two input fields, FreezeMeasurementEditing and FreezeIteration, that are used to determine if and when to 'freeze' (i.e., no longer change) the selection of measurements which are edited out by the Outer Loop Sigma Editor. Freezing the measurement editing only takes place when FreezeMeasurementEditing is true.
If freezing is enabled, the selection of measurements to edit is locked after the iteration specified by FreezeIteration. If the value of FreezeIteration is 1, the estimator uses the value of OLSEInitialRMSSigma, as defined above, to determine which measurements are used to calculate the first iteration of the state vector deviation vector. Afterwards, the same measurements edited out by the initial RMS sigma filter are edited out for the remainder of the iterations. If the value of FreezeIteration is 2 or greater, the estimator uses the above defined outer loop sigma editing to determine the state vector deviation vector up to the iteration specified by FreezeIteration, at which point whichever measurements are edited out by the outer loop sigma editor stay edited out for the remainder of the iterations. Frozen measurements that are edited out will retain the edit flag the outer loop sigma editor used the iteration they were edited out.
Freezing measurement editing can be useful in situations where a solution takes an excessive number of iterations to converge and latter iterations are only editing a small amount of data. If this is the case, enabling the editing freeze on an appropriate iteration will generally force the solution to converge quickly after reaching the frozen iteration.
Propagator Settings
The BatchEstimatorInv resource has a Propagator field containing the name of the Propagator resource that will be used during the estimation process. The minimum step size, MinStep, of your propagator should always be set to 0.
UseInitialCovariance Restrictions
As mentioned in the Field spec above, if this field is set to true, then the a priori error covariance term is added to the estimation cost function. For the current GMAT release, there are some restrictions on the use of this field as given below.
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The user must input the a priori orbit state covariance in the EarthMJ200Eq coordinate system.
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If the user is solving for the Cartesian orbit state, e.g., Sat.SolveFors = {CartesianState}, then the input a priori orbit state covariance must be in terms of Cartesian elements. Likewise, if the user is solving for the Keplerian orbit state, e.g., Sat.SolveFors = {KeplerianState}, then the input a priori orbit state covariance must be in terms of Keplerian elements.
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If the user is solving for the Keplerian orbit state, e.g., Sat.SolveFors = {KeplerianState}, then the input a priori orbit state covariance must be expressed in terms in terms of spacecraft Mean Anomaly (MA) and not True Anomaly (TA). To be more specific, in this situation, the diagonal elements of the 6x6 orbit state error covariance are the variance of the SMA (km^2), eccentricity (dimensionless), INC (deg^2), RAAN (deg^2), AOP (deg^2), and MA (deg^2). Note that, in this case, we require the a priori covariance to be input in terms of MA even though, for the current release of GMAT, the associated orbit state can not be set using MA.
Interactions
| Resource | Description |
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| TrackingFileSet resource |
Must be created in order to tell the BatchEstimatorInv resource which data will be processed |
| Propagator resource | Used by GMAT to generate the predicted orbit |
| RunEstimator command |
Must use the RunEstimator command to actually process the data defined by the BatchEstimatorInv resource |
Examples
Below is an example of a configured batch estimator instance. In this example, estData is an instance of a TrackingFileSet and ODProp is an instance of Propagator.
Create BatchEstimatorInv bat;
bat.ShowProgress = true;
bat.Measurements = {estData}
bat.AbsoluteTol = 0.000001;
bat.RelativeTol = 0.001;
bat.MaximumIterations = 10;
bat.MaxConsecutiveDivergences = 3;
bat.Propagator = ODProp;
bat.ShowAllResiduals = On;
bat.OLSEInitialRMSSigma = 3000;
bat.OLSEMultiplicativeConstant = 3;
bat.OLSEAdditiveConstant = 0;
bat.InversionAlgorithm = 'Internal';
bat.EstimationEpochFormat = 'FromParticipants';
bat.EstimationEpoch = 'FromParticipants';
bat.ReportStyle = 'Normal';
bat.ReportFile = 'BatchEstimator_Report.txt';
BeginMissionSequence;
For a comprehensive example of reading in measurements and running the estimator, see the Chapter 14, Orbit Estimation using DSN Range and Doppler Data tutorial.