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StateTransitionMatrix Class

An extended state transition matrix, if consider parameters are not used then it functions as a normal state transition matrix: mapping the value of the state parameters from one time to another time.

The state transition matrix represents the transformation from the state at one time to the state at another time. This can be used as an alternative to propagating a state in time with NumericalPropagator, but is more often used in order to find the time-varying covariance of the state. This is because the construction of a StateTransitionMatrix entails the linearization of the state, and in most cases calculating the derivatives of the state transition matrix takes as long or longer as calculating the derivatives of the state.

To find the covariance of a state over time a StateTransitionMatrix is propagated with a NumericalPropagator and the resulting data is used to create the covariance information for the same period using PopulateCovarianceCollection(Matrix, DateMotionCollectionMatrix, TransitionType).

Inheritance Hierarchy

Namespace:  AGI.Foundation.Propagators
Assembly:  AGI.Foundation.Models (in AGI.Foundation.Models.dll) Version: 19.1.398.0 (19.1.398.0)
Syntax
public class StateTransitionMatrix : PropagationStateElement

The StateTransitionMatrix type exposes the following members.

Constructors
  NameDescription
Public methodStateTransitionMatrix
Initializes a new instance.
Protected methodStateTransitionMatrix(StateTransitionMatrix, CopyContext)
Initializes a new instance as a copy of an existing instance.
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Properties
  NameDescription
Public propertyConsiderDimension
Gets the summed dimension of all of the consider parameters.
Public propertyDimension
Gets the number of parameters (per Order) within this element.
(Overrides PropagationStateElementDimension.)
Public propertyIdentification
Gets or sets the string identifying this instance in the overall output.
(Inherited from PropagationStateElement.)
Public propertyIncludeHighestDerivativeInOutput
Gets or sets whether to include the derivative computed at each step with the output. If this is true, the output converted from the raw state will contain the derivative associated with the Order of the differential equation.
(Inherited from PropagationStateElement.)
Public propertyInitialConsiderTransitionMatrix

Gets or sets the optional user-specified initial consider transition matrix. In general this should be left null and the default value will be used instead. The default initial state takes the form of a StateDimension by ConsiderDimension zero matrix.

Public propertyInitialStateTransitionMatrix

Gets or sets the optional user-specified initial state transition matrix. In general this should be left null and the default value will be used instead. The default initial state takes the form of a StateDimension by StateDimension identity matrix.

Public propertyIntegrationDynamicMatrix

Gets a DynamicMatrix which is parameterized on the value of the StateTransitionMatrix during integration.

This matrix is only valid while the NumericalPropagator is running.

Public propertyIsFrozen
Gets a value indicating whether this object is frozen. A frozen object cannot be modified and an ObjectFrozenException will be thrown if an attempt is made to do so.
(Inherited from DefinitionalObject.)
Public propertyLinearDimension

Gets the linear dimension of the StateTransitionMatrix

The StateTransitionMatrix takes the form of a square matrix of dimensions L x L, where L is equal to N, the total dimension of the state parameters (StateDimension) plus Q, the total dimension of the consider parameters (ConsiderDimension). The StateTransitionMatrix's dimension as far as the propagation state is concerned is L squared, and that is what the Dimension property returns. This property returns the value of L.

Public propertyNumberOfConsiderParameters
Gets the number of consider parameters that have been added to this StateTransitionMatrix.
Public propertyNumberOfStateParameters
Gets the number of state parameters and derivatives that have been added to this StateTransitionMatrix.
Public propertyOrder
Gets the order of the differential equation corresponding to this element.
(Overrides PropagationStateElementOrder.)
Public propertyStateDimension
Gets the summed dimension of all of the state parameters.
Public propertyStateParameter
Gets or sets a parameter which represents the state during propagation. In general, users should never need to explicitly set this property. It should only be set when multiple NumericalPropagator objects are running in the same EvaluatorGroup, such as when elements of a state require additional instances of a NumericalPropagator inside their implementation in order to produce their values. In such cases, it may be necessary to distinguish between the state of the exterior propagator and the state of the interior propagator. In these cases, it is up to the user to ensure that both the state and all of its elements are configured with the same parameter. Otherwise, the state will throw an exception when creating its propagator.
(Overrides PropagationStateElementStateParameter.)
Public propertyTransitionType
Gets or sets whether this StateTransitionMatrix is operating in epoch or piecewise mode. By default this is set to EpochTransition, which means that the state transition matrix at each time step transforms the state from the epoch state to the state at that time step.
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Methods
  NameDescription
Public methodAddConsiderParameter
Adds a consider parameter to the StateTransitionMatrix. Consider parameters can be used when calculating covariance for a state parameter. The transitions are not actually calculated for a consider parameter, however the values of the consider parameter do affect those of the state parameters. For example, if you weren't interested in examining how the uncertainty of the coefficient of drag evolved over time, but were interested in how it's uncertainty affected the uncertainty of the state parameters, then you would add it as a consider parameter.
Public methodAddStateParameter

Adds a state parameter to the StateTransitionMatrix. The state parameters added here make up the state represented by the state transition matrix. The stateDerivative of the stateParameter is needed in order to calculate the derivative of the state transition matrix so that it can be integrated.

Protected methodCheckForSameDefinition(DefinitionalObject)
Checks to determine if another instance has the same definition as this instance and returns if it does. Derived classes MUST override this method and check all new fields introduced by the derived class for definitional equivalence. It is NOT necessary to check base class fields because the base class will already have done that. When overriding this method, you should NOT call the base implementation because it will return for all derived-class instances. Derived classes should check the type of other to preserve the symmetric nature of IsSameDefinition(Object).
(Inherited from PropagationStateElement.)
Protected methodCheckForSameDefinition(PropagationStateElement)
Checks to determine if another instance has the same definition as this instance and returns if it does. Derived classes MUST override this method and check all new fields introduced by the derived class for definitional equivalence. It is NOT necessary to check base class fields because the base class will already have done that. When overriding this method, you should NOT call the base implementation because it will return for all derived-class instances. Derived classes should check the type of other to preserve the symmetric nature of IsSameDefinition(Object).
(Overrides PropagationStateElementCheckForSameDefinition(PropagationStateElement).)
Protected methodCheckForSameDefinition(StateTransitionMatrix)
Checks to determine if another instance has the same definition as this instance and returns if it does. Derived classes MUST override this method and check all new fields introduced by the derived class for definitional equivalence. It is NOT necessary to check base class fields because the base class will already have done that. When overriding this method, you should NOT call the base implementation because it will return for all derived-class instances. Derived classes should check the type of other to preserve the symmetric nature of IsSameDefinition(Object).
Public methodClone
Clones this object using the specified context.
(Overrides DefinitionalObjectClone(CopyContext).)
Protected methodComputeCurrentDefinitionHashCode
Computes a hash code based on the current properties of this object. Derived classes MUST override this method and compute a hash code that combines: a unique hash code seed, the base implementation result, and the hash codes of all new fields introduced by the derived class which are used in the CheckForSameDefinition(DefinitionalObject) method.
(Overrides PropagationStateElementComputeCurrentDefinitionHashCode.)
Public methodEnumerateDependencies
Enumerates the dependencies of this object by calling EnumerateT(T) for each object that this object directly depends upon. Derived classes which contain additional dependencies MUST override this method, call the base implementation, and enumerate dependencies introduced by the derived class.
(Overrides DefinitionalObjectEnumerateDependencies(DependencyEnumerator).)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodFreeze
Freezes this object. Further attempts to modify it will result in an ObjectFrozenException.
(Inherited from DefinitionalObject.)
Protected methodFreezeAggregatedObjects
Called by Freeze to also freeze any objects that are considered to be a part of this object. Derived classes which contain additional aggregated objects MUST override this method, call the base implementation, and freeze aggregated objects introduced by the derived class. The objects that need to be frozen in this method are frequently created in this object's constructor and are not settable via properties.
(Overrides DefinitionalObjectFreezeAggregatedObjects.)
Public methodGetConsiderParameter
Gets the consider parameter at the specified index which has been added to this StateTransitionMatrix.
Public methodGetConverter
Gets an instance of an output type which can convert the output of propagation back into the native type of this state element. This method is also responsible for configuring the state parameter and the state input indices on any parameterized geometry types used by this element. Each parameterized geometry type will have a static configuration method which will allow it to configure itself in a particular EvaluatorGroup.
(Overrides PropagationStateElementGetConverter(EvaluatorGroup, MotionInt32).)
Public methodGetDefinitionHashCode
Gets a hash code representing the definition of this object.
(Inherited from DefinitionalObject.)
Public methodGetDerivatives
This is used by the NumericalPropagatorDefinition to obtain an instance of a state element evaluator that can compute the derivatives of this element of the state during propagation. It cannot be used outside of a NumericalPropagator as the geometry for the propagation state will be unavailable.
(Overrides PropagationStateElementGetDerivatives(EvaluatorGroup).)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetStateDerivative
Gets the state derivative at the specified index which has been added to this StateTransitionMatrix.
Public methodGetStateParameter
Gets the state parameter at the specified index which has been added to this StateTransitionMatrix.
Public methodGetStateUpdater

Creates an object that will update the state of the StateTransitionMatrix in between propagation steps, if necessary.

If TransitionType is PiecewiseTransition then the matrices produced during propagation represent the transition matrices from the previous time step to their own time step. This means that at the beginning of each propagation step the value of the state transition matrix must be reset to the identity matrix.

If TransitionType is EpochTransition then the matrices produced during propagation represent the transition matrices from the epoch to their own time step, and this reset is not necessary.

(Overrides PropagationStateElementGetStateUpdater(EvaluatorGroup).)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodIndexOfConsiderParameter
Searches for the specified considerParameter and returns the index which can be used to access it via GetConsiderParameter(Int32) or RemoveConsiderParameterAt(Int32).
Public methodIndexOfStateDerivative
Searches for the specified stateDerivative and returns the index which can be used to access it via GetStateDerivative(Int32) or RemoveStateParameterAt(Int32).
Public methodIndexOfStateParameter
Searches for the specified stateParameter and returns the index which can be used to access it via GetStateParameter(Int32) or RemoveStateParameterAt(Int32).
Public methodIsSameDefinition
Determines if this object has the same definition as another object.
(Inherited from DefinitionalObject.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodStatic memberPopulateCovarianceCollection
Transforms an initial covariance matrix forward in time using the given collection of state transition matrices.
Public methodRemoveConsiderParameterAt
Removes the consider parameter at the given index.
Public methodRemoveStateParameterAt
Removes the state parameter at the given index, as well as its derivative.
Protected methodThrowIfFrozen
Throws ObjectFrozenException if this object IsFrozen. This method should be called from any method or property that modifies this object.
(Inherited from DefinitionalObject.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

If consider parameters are used, then this class represents information in the following form:

If the cumulative dimension of the state elements is N, and the cumulative dimension of the consider parameters is M, then Φ is an ordinary state transition matrix: an NxN matrix equal to the partials of the state at time tj with respect to the state at time ti. Θ is an NxM matrix equal to the partials of the state at time tj with respect to the consider parameters at time ti, and the zero and identity matrices are size MxN and MxM, respectively. The complete consider covariance matrix is a square matrix with a dimension of N+M.

See Also