doc/en/ref_algorithm_UnscentedKalmanFilter.rst

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   2    Copyright (C) 2008-2023 EDF R&D
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  20    See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
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  22    Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
  23
  24 .. index:: single: UnscentedKalmanFilter
  25 .. _section_ref_algorithm_UnscentedKalmanFilter:
  26
  27 Calculation algorithm "*UnscentedKalmanFilter*"
  28 -----------------------------------------------
  29
  30 .. ------------------------------------ ..
  31 .. include:: snippets/Header2Algo01.rst
  32
  33 This algorithm realizes an estimation of the state of a dynamic system by a
  34 "unscented" Kalman Filter, avoiding to have to perform the tangent and adjoint
  35 operators for the observation and evolution operators, as in the simple or
  36 extended Kalman filter.
  37
  38 It applies to non-linear observation and incremental evolution (process)
  39 operators with excellent robustness and performance qualities. It can be
  40 compared to the :ref:`section_ref_algorithm_EnsembleKalmanFilter`, whose
  41 qualities are similar for non-linear systems.
  42
  43 We notice that there is no analysis performed at the initial time step
  44 (numbered 0 in the time indexing) because there is no forecast at this time
  45 (the background is stored as a pseudo analysis at the initial time step). If
  46 the observations are provided in series by the user, the first one is therefore
  47 not used.
  48
  49 In case of linear of "slightly" non-linear operators, one can easily use the
  50 :ref:`section_ref_algorithm_ExtendedKalmanFilter` or even the
  51 :ref:`section_ref_algorithm_KalmanFilter`, which are often far less expensive
  52 to evaluate on small systems. One can verify the linearity of the operators
  53 with the help of the :ref:`section_ref_algorithm_LinearityTest`.
  54
  55 .. index::
  56     pair: Variant ; UKF
  57     pair: Variant ; 2UKF
  58
  59 A difference is made between the "unscented" Kalman filter taking into account
  60 bounds on the states (the variant named "2UKF", which is recommended and used
  61 by default), and the canonical "unscented" Kalman filter conducted without any
  62 constraint (the variant named "UKF", which is not recommended).
  63
  64 .. ------------------------------------ ..
  65 .. include:: snippets/Header2Algo02.rst
  66
  67 .. include:: snippets/Background.rst
  68
  69 .. include:: snippets/BackgroundError.rst
  70
  71 .. include:: snippets/EvolutionError.rst
  72
  73 .. include:: snippets/EvolutionModel.rst
  74
  75 .. include:: snippets/Observation.rst
  76
  77 .. include:: snippets/ObservationError.rst
  78
  79 .. include:: snippets/ObservationOperator.rst
  80
  81 .. ------------------------------------ ..
  82 .. include:: snippets/Header2Algo03AdOp.rst
  83
  84 .. include:: snippets/BoundsWithNone.rst
  85
  86 .. include:: snippets/ConstrainedBy.rst
  87
  88 .. include:: snippets/EstimationOf_State.rst
  89
  90 .. include:: snippets/AlphaBeta.rst
  91
  92 StoreSupplementaryCalculations
  93   .. index:: single: StoreSupplementaryCalculations
  94
  95   *List of names*. This list indicates the names of the supplementary
  96   variables, that can be available during or at the end of the algorithm, if
  97   they are initially required by the user. Their avalability involves,
  98   potentially, costly calculations or memory consumptions. The default is then
  99   a void list, none of these variables being calculated and stored by default
 100   (excepted the unconditionnal variables). The possible names are in the
 101   following list (the detailed description of each named variable is given in
 102   the following part of this specific algorithmic documentation, in the
 103   sub-section "*Information and variables available at the end of the
 104   algorithm*"): [
 105   "Analysis",
 106   "APosterioriCorrelations",
 107   "APosterioriCovariance",
 108   "APosterioriStandardDeviations",
 109   "APosterioriVariances",
 110   "BMA",
 111   "CostFunctionJ",
 112   "CostFunctionJAtCurrentOptimum",
 113   "CostFunctionJb",
 114   "CostFunctionJbAtCurrentOptimum",
 115   "CostFunctionJo",
 116   "CostFunctionJoAtCurrentOptimum",
 117   "CurrentOptimum",
 118   "CurrentState",
 119   "ForecastCovariance",
 120   "ForecastState",
 121   "IndexOfOptimum",
 122   "InnovationAtCurrentAnalysis",
 123   "InnovationAtCurrentState",
 124   "SimulatedObservationAtCurrentAnalysis",
 125   "SimulatedObservationAtCurrentOptimum",
 126   "SimulatedObservationAtCurrentState",
 127   ].
 128
 129   Example :
 130   ``{"StoreSupplementaryCalculations":["CurrentState", "Residu"]}``
 131
 132 .. include:: snippets/Variant_UKF.rst
 133
 134 .. ------------------------------------ ..
 135 .. include:: snippets/Header2Algo04.rst
 136
 137 .. include:: snippets/Analysis.rst
 138
 139 .. ------------------------------------ ..
 140 .. include:: snippets/Header2Algo05.rst
 141
 142 .. include:: snippets/Analysis.rst
 143
 144 .. include:: snippets/APosterioriCorrelations.rst
 145
 146 .. include:: snippets/APosterioriCovariance.rst
 147
 148 .. include:: snippets/APosterioriStandardDeviations.rst
 149
 150 .. include:: snippets/APosterioriVariances.rst
 151
 152 .. include:: snippets/BMA.rst
 153
 154 .. include:: snippets/CostFunctionJ.rst
 155
 156 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 157
 158 .. include:: snippets/CostFunctionJb.rst
 159
 160 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 161
 162 .. include:: snippets/CostFunctionJo.rst
 163
 164 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 165
 166 .. include:: snippets/CurrentOptimum.rst
 167
 168 .. include:: snippets/CurrentState.rst
 169
 170 .. include:: snippets/ForecastCovariance.rst
 171
 172 .. include:: snippets/ForecastState.rst
 173
 174 .. include:: snippets/IndexOfOptimum.rst
 175
 176 .. include:: snippets/InnovationAtCurrentAnalysis.rst
 177
 178 .. include:: snippets/InnovationAtCurrentState.rst
 179
 180 .. include:: snippets/SimulatedObservationAtCurrentAnalysis.rst
 181
 182 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 183
 184 .. include:: snippets/SimulatedObservationAtCurrentState.rst
 185
 186 .. ------------------------------------ ..
 187 .. _section_ref_algorithm_UnscentedKalmanFilter_examples:
 188 .. include:: snippets/Header2Algo06.rst
 189
 190 - :ref:`section_ref_algorithm_KalmanFilter`
 191 - :ref:`section_ref_algorithm_ExtendedKalmanFilter`
 192 - :ref:`section_ref_algorithm_EnsembleKalmanFilter`
 193
 194 .. ------------------------------------ ..
 195 .. include:: snippets/Header2Algo07.rst
 196
 197 - [WikipediaUKF]_