estimation
#
This module contains the functionality for managing the inputs and outputs of an estimation.
Functions#

Function to simulate observations. 

Function to compute the azimuth angle, elevation angle and range at a ground station. 

Function to propagate system covariance through time. 

Function to propagate system formal errors through time. 
Function for creating an 
 simulate_observations(simulation_settings: List[tudat::simulation_setup::ObservationSimulationSettings<double>], observation_simulators: List[tudatpy.kernel.numerical_simulation.estimation.ObservationSimulator], bodies: tudatpy.kernel.numerical_simulation.environment.SystemOfBodies) tudat::observation_models::ObservationCollection<double, double, 0> #
Function to simulate observations.
Function to simulate observations from set observation simulators and observation simulator settings. Automatically iterates over all provided observation simulators, generating the full set of simulated observations.
 Parameters
observation_to_simulate (List[
ObservationSimulationSettings
]) – List of settings objects, each object providing the observation time settings for simulating one type of observable and link end set.observation_simulators (List[
ObservationSimulator
]) – List ofObservationSimulator
objects, each object hosting the functionality for simulating one type of observable and link end set.bodies (
SystemOfBodies
) – Object consolidating all bodies and environment models, including ground station models, that constitute the physical environment.
 Returns
Object collecting all products of the observation simulation.
 Return type
 compute_target_angles_and_range(bodies: tudatpy.kernel.numerical_simulation.environment.SystemOfBodies, station_id: Tuple[str, str], target_body: str, observation_times: List[float], is_station_transmitting: bool) Dict[float, numpy.ndarray[numpy.float64[m, 1]]] #
Function to compute the azimuth angle, elevation angle and range at a ground station.
Function to compute the azimuth angle, elevation angle and range at a ground station. This functions is provided as a function of convenience, to prevent users having to manually define the relevant settings for this oftenneeded functionality. This function takes an observing station and a target body as input, and provides the observed angles and current range (without correction for aberrations, with correction for light time) as observed at that station
 Parameters
bodies (SystemOfBodies) – System of bodies that defines the full physical environment
station_id (tuple[ str, str]) – Identifier for the observing station, as a pair of strings: the body name and the station name.
target_body (str) – Name of body which is observed by ground station
observation_times (list[float]) – List of times at which the ground station observations are to be analyzed
is_station_transmitting (Bool) – Boolean defining whether the observation times define times at which the station is transmitting to, or receiving from, the ground station. This has an impact on the whether the lighttime is computed forward or backward in time from the ground station to the target
 Returns
Dictionary with the required output. Key defines the observation time, the value is an array of size three containing entry 0  elevation angle, entry 1  azimuth angle, entry 2  range
 Return type
dict[float,numpy.ndarray[numpy.float64[3, 1]]]
 propagate_covariance(initial_covariance: numpy.ndarray[numpy.float64[m, n]], state_transition_interface: tudatpy.kernel.numerical_simulation.estimation.CombinedStateTransitionAndSensitivityMatrixInterface, output_times: List[float]) Dict[float, numpy.ndarray[numpy.float64[m, n]]] #
Function to propagate system covariance through time.
Function to propagate the covariance of a given system through time. The system dynamics and numerical settings of the propagation are prescribed by the state_transition_interface parameter.
 Parameters
initial_covariance (numpy.ndarray[numpy.float64[m, n]]) – System covariance matrix (symmetric and positive semidefinite) at initial time. Dimensions have to be consistent with estimatable parameters in the system (specified by state_transition_interface)
state_transition_interface (
CombinedStateTransitionAndSensitivityMatrixInterface
) – Interface to the variational equations of the system dynamics, handling the propagation of the covariance matrix through time.output_times (List[ float ]) – Times at which the propagated covariance matrix shall be reported. Note that this argument has no impact on the integration timesteps of the covariance propagation, which always adheres to the integrator settings that the state_transition_interface links to. Output times which do not coincide with integration time steps are calculated via interpolation.
 Returns
Dictionary reporting the propagated covariances at each output time.
 Return type
Dict[ float, numpy.ndarray[numpy.float64[m, n]] ]
 propagate_formal_errors(initial_covariance: numpy.ndarray[numpy.float64[m, n]], state_transition_interface: tudatpy.kernel.numerical_simulation.estimation.CombinedStateTransitionAndSensitivityMatrixInterface, output_times: List[float]) Dict[float, numpy.ndarray[numpy.float64[m, 1]]] #
Function to propagate system formal errors through time.
Function to propagate the formal errors of a given system through time. Note that in practice the entire covariance matrix is propagated, but only the formal errors (variances) are reported at the output times. The system dynamics and numerical settings of the propagation are prescribed by the state_transition_interface parameter.
 Parameters
initial_covariance (numpy.ndarray[numpy.float64[m, n]]) – System covariance matrix (symmetric and positive semidefinite) at initial time. Dimensions have to be consistent with estimatable parameters in the system (specified by state_transition_interface)
state_transition_interface (
CombinedStateTransitionAndSensitivityMatrixInterface
) – Interface to the variational equations of the system dynamics, handling the propagation of the covariance matrix through time.output_times (List[ float ]) – Times at which the propagated covariance matrix shall be reported. Note that this argument has no impact on the integration timesteps of the covariance propagation, which always adheres to the integrator settings that the state_transition_interface links to. Output times which do not coincide with integration time steps are calculated via interpolation.
 Returns
Dictionary reporting the propagated formal errors at each output time.
 Return type
Dict[ float, numpy.ndarray[numpy.float64[m, 1]] ]
 estimation_convergence_checker(maximum_iterations: int = 5, minimum_residual_change: float = 0.0, minimum_residual: float = 0.0, number_of_iterations_without_improvement: int = 2) tudatpy.kernel.numerical_simulation.estimation.EstimationConvergenceChecker #
Function for creating an
EstimationConvergenceChecker
object.Function for creating an
EstimationConvergenceChecker
object, which is required for defining the convergence criteria of an estimation. Parameters
maximum_iterations (int, default = 5) – Maximum number of allowed iterations for estimation.
minimum_residual_change (float, default = 0.0) – Minimum required change in residual between two iterations.
minimum_residual (float, default = 0.0) – Minimum value of observation residual below which estimation is converged.
number_of_iterations_without_improvement (int, default = 2) – Number of iterations without reduction of residual.
 Returns
Instance of the
EstimationConvergenceChecker
class, defining the convergence criteria for an estimation. Return type
Classes#
Class containing a consolidated set of estimatable parameters. 

Template class for observation viability calculators. 

Class hosting the functionality for simulating observations. 

Class collecting all products of the observation simulation. 

Class establishing an interface with the simulation's State Transition and Sensitivity Matrices. 

Class defining the convergence criteria for an estimation. 

Class for consolidating all inputs to the estimation. 

Class collecting all outputs from the estimation process. 
 class EstimatableParameterSet#
Class containing a consolidated set of estimatable parameters.
Class containing a consolidated set of estimatable parameters, linked to the environment and acceleration settings of the simulation. The user typically creates instances of this class via the
create_parameters_to_estimate()
factory function. indices_for_parameter_type(self: tudatpy.kernel.numerical_simulation.estimation.EstimatableParameterSet, parameter_type: Tuple[tudat::estimatable_parameters::EstimatebleParametersEnum, Tuple[str, str]]) List[Tuple[int, int]] #
Function to retrieve the indices of a given type of parameter.
Function to retrieve the index of all parameters of a given type from the parameter set. This function can be very useful, since the order of parameters within the parameter set does not necessarily correspond to the order in which the elements were added to the set.
 Parameters
parameter_type (Tuple[
EstimatableParameterTypes
, Tuple[str, str] ]) – help Returns
help
 Return type
 property constraints_size#
readonly
Total size of linear constraint that is to be applied during estimation.
 Type
 property initial_multi_arc_states_size#
readonly
Amount of initial state parameters in the set, which are treated in a multiarc fashion.
 Type
 property initial_single_arc_states_size#
readonly
Amount of initial state parameters in the set, which are treated in a singlearc fashion.
 Type
 property initial_states_size#
readonly
Amount of initial state parameters contained in the set.
 Type
 property parameter_set_size#
readonly
Size of the parameter set, i.e. amount of estimatable parameters contained in the set.
 Type
 property parameter_vector#
Vector containing the parameter values of all parameters in the set.
 Type
numpy.ndarray[numpy.float64[m, 1]]
 class ObservationViabilityCalculator#
Template class for observation viability calculators.
Template class for classes which conducts viability calculations on simulated observations. Instances of the applicable ObservationViabilityCalculators are automatically created from the given
ObservationSimulationSettings
objects during the simulation of observations (simulate_observations()
). The user typically does not interact directly with this class. is_observation_viable(self: tudatpy.kernel.numerical_simulation.estimation.ObservationViabilityCalculator, link_end_states: List[numpy.ndarray[numpy.float64[6, 1]]], link_end_times: List[float]) bool #
Function to check whether an observation is viable.
Function to check whether an observation is viable. The calculation is performed based on the given times and link end states. Note, that this function is called automatically during the simulation of observations. Direct calls to this function are generally not required.
 Parameters
link_end_states (List[ numpy.ndarray[numpy.float64[6, 1]] ]) – Vector of states of the link ends involved in the observation.
link_end_times (List[float]) – Vector of times at the link ends involved in the observation.
 Returns
True if observation is viable, false if not.
 Return type
 class ObservationSimulator#
Class hosting the functionality for simulating observations.
Class hosting the functionality for simulating a given observable over a defined link geometry. Instances of this class are automatically created from the given
ObservationSettings
objects upon instantiation of theEstimator
class.
 class ObservationCollection#
Class collecting all products of the observation simulation.
Class containing all products of the observation simulation. This class is instantiated via a call to the
simulate_observations()
function. property concatenated_observations#
readonly
Vector containing concatenated observation times. Concatenation takes place over the observations of all observables.
 Type
numpy.ndarray[numpy.float64[m, 1]]
 property concatenated_times#
readonly
Vector containing concatenated observation times. Concatenation takes place over the observation times of all observables.
 Type
numpy.ndarray[numpy.float64[m, 1]]
 class CombinedStateTransitionAndSensitivityMatrixInterface#
Class establishing an interface with the simulation’s State Transition and Sensitivity Matrices.
Class establishing an interface to the State Transition and Sensitivity Matrices. Instances of this class are instantiated automatically upon creation of
Estimator
objects, using the simulation information in the observation, propagation and integration settings that theEstimator
instance is linked to. full_state_transition_sensitivity_at_epoch(self: tudatpy.kernel.numerical_simulation.estimation.CombinedStateTransitionAndSensitivityMatrixInterface, time: float) numpy.ndarray[numpy.float64[m, n]] #
 Parameters
time (float) – Time at which full concatenated state transition and sensitivity matrix are to be retrieved.
 Returns
Full concatenated state transition and sensitivity matrix at a given time.
 Return type
numpy.ndarray[numpy.float64[m, n]]
 state_transition_sensitivity_at_epoch(self: tudatpy.kernel.numerical_simulation.estimation.CombinedStateTransitionAndSensitivityMatrixInterface, time: float) numpy.ndarray[numpy.float64[m, n]] #
Function to get the concatenated state transition and sensitivity matrix at a given time.
Function to get the concatenated state transition and sensitivity matrix at a given time. Entries corresponding to parameters which are not active at the current arc are omitted.
 Parameters
time (float) – Time at which concatenated state transition and sensitivity matrix are to be retrieved.
 Returns
Concatenated state transition and sensitivity matrix at a given time.
 Return type
numpy.ndarray[numpy.float64[m, n]]
 property full_parameter_size#
readonly
Full amount of parameters w.r.t. which partials have been set up via State Transition and Sensitivity Matrices.
 Type
 class EstimationConvergenceChecker#
Class defining the convergence criteria for an estimation.
Class defining the convergence criteria for an estimation. The user typically creates instances of this class via the
estimation_convergence_checker()
factory function.
 class PodInput#
Class for consolidating all inputs to the estimation.
 __init__(self: tudatpy.kernel.numerical_simulation.estimation.PodInput, observations_and_times: tudatpy.kernel.numerical_simulation.estimation.ObservationCollection, parameter_size: int, inverse_apriori_covariance: numpy.ndarray[numpy.float64[m, n]] = array([], shape=(0, 0), dtype=float64), apriori_parameter_correction: numpy.ndarray[numpy.float64[m, 1]] = array([], dtype=float64)) None #
Class constructor.
Constructor through which the user can create instances of this class.
 Parameters
observations_and_times (ObservationCollection) – Total data structure of observations and associated times/link ends/type.
parameter_size (int) – Size of vector of estimated parameters.
inverse_apriori_covariance (numpy.ndarray[numpy.float64[m, n]], default = [ ]) – A priori covariance matrix (unnormalized) of estimated parameters.
apriori_parameter_correction (numpy.ndarray[numpy.float64[m, 1]], default = [ ]) – Correction to estimated parameter vector to be applied on first iteration.
 Returns
Instance of the
PodInput
class, defining the data and other settings to be used for the estimation. Return type
 define_estimation_settings(self: tudatpy.kernel.numerical_simulation.estimation.PodInput, reintegrate_equations_on_first_iteration: bool = True, reintegrate_variational_equations: bool = True, save_design_matrix: bool = True, print_output_to_terminal: bool = True, save_residuals_and_parameters_per_iteration: bool = True, save_state_history_per_iteration: bool = False) None #
Function to define specific settings for estimation process
Function to define specific settings for estimation process
 Parameters
reintegrate_equations_on_first_iteration (bool, default = True) – Boolean denoting whether the dynamics and variational equations are to be reintegrated on first iteration, or if existing values are to be used to perform first iteration.
reintegrate_variational_equations (bool, default = True) – Boolean denoting whether the variational equations are to be reintegrated during estimation.
save_design_matrix (bool, default = True) – Boolean denoting whether to save the partials matrix in the output.
print_output_to_terminal (bool, default = True) – Boolean denoting whether to print output to th terminal when running the estimation.
save_residuals_and_parameters_per_iteration (bool, default = True) – Boolean denoting whether the residuals and parameters from the each iteration are to be saved.
save_state_history_per_iteration (bool, default = False) – Boolean denoting whether the state history is to be saved on each iteration.
 Returns
Function modifies the object inplace.
 Return type
None
 set_constant_weight(self: tudatpy.kernel.numerical_simulation.estimation.PodInput, weight: float) None #
Function to set a constant weight matrix for all observables.
Function to set a constant weight matrix for all observables. The weights are applied to all observations managed by the given PodInput object.
 Parameters
constant_weight (float) – Constant weight factor that is to be applied to all observations.
 Returns
Function modifies the object inplace.
 Return type
None
 set_constant_weight_for_observable_and_link_ends(self: tudatpy.kernel.numerical_simulation.estimation.PodInput, observable_type: tudat::observation_models::ObservableType, link_ends: Dict[tudat::observation_models::LinkEndType, Tuple[str, str]], weight: float) None #
 set_constant_weight_per_observable(self: tudatpy.kernel.numerical_simulation.estimation.PodInput, weight_per_observable: Dict[tudat::observation_models::ObservableType, float]) None #
Function to set a constant weight matrix for a given type of observable.
Function to set a constant weight matrix for a given type of observable. The weights are applied to all observations of the observable type specified by the weight_per_observable parameter.
 Parameters
constant_weight (Dict[
ObservableType
, float ]) – Constant weight factor that is to be applied to all observations. Returns
Function modifies the object inplace.
 Return type
None
 class PodOutput#
Class collecting all outputs from the estimation process.
 property correlations#
readonly
Correlation matrix of the estimation result.
 Type
numpy.ndarray[numpy.float64[m, m]]
 property covariance#
readonly
(Unnormalized) estimation covariance matrix.
 Type
numpy.ndarray[numpy.float64[m, m]]
 property design_matrix#
readonly
Matrix of unnormalized partial derivatives.
 Type
numpy.ndarray[numpy.float64[m, n]]
 property final_residuals#
readonly
Vector of postfit observation residuals.
 Type
numpy.ndarray[numpy.float64[m, 1]]
 property formal_errors#
readonly
Formal error vector of the estimation result. Correlation matrix of the estimation result.
 Type
numpy.ndarray[numpy.float64[m, 1]]
 property inverse_covariance#
readonly
(Unnormalized) inverse estimation covariance matrix.
 Type
numpy.ndarray[numpy.float64[m, m]]
 property normalization_terms#
No documentation found.
 property normalized_design_matrix#
readonly
Matrix of partial derivatives.
 Type
numpy.ndarray[numpy.float64[m, n]]
 property parameter_history#
readonly
Parameter vectors, concatenated per iteration into a matrix. Column 0 contains preestimation values.
 Type
numpy.ndarray[numpy.float64[m, n]]
 property residual_history#
readonly
Residual vectors, concatenated per iteration into a matrix.
 Type
numpy.ndarray[numpy.float64[m, n]]
 property weighted_design_matrix#
readonly
Matrix of weighted partial derivatives.
 Type
numpy.ndarray[numpy.float64[m, n]]
 property weighted_normalized_design_matrix#
readonly
Matrix of weighted, normalized partial derivatives.
 Type
numpy.ndarray[numpy.float64[m, n]]