kalman.cpp

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/*
 * Copyright 2010,
 * Nicolas Mansard,
 * François Bleibel,
 * Olivier Stasse,
 * Florent Lamiraux
 *
 * CNRS/AIST
 *
 */
 
/* --- SOT --- */
#include <dynamic-graph/command-setter.h>
#include <dynamic-graph/factory.h>
 
#include <sot/core/debug.hh>
#include <sot/core/exception-tools.hh>
#include <sot/core/factory.hh>
#include <sot/core/kalman.hh> /* Header of the class implemented here.   */
 
namespace dynamicgraph {
using command::Setter;
namespace sot {
 
DYNAMICGRAPH_FACTORY_ENTITY_PLUGIN(Kalman, "Kalman");
 
Kalman::Kalman(const std::string &name)
    : Entity(name),
      measureSIN(NULL, "Kalman(" + name + ")::input(vector)::y"),
      modelTransitionSIN(NULL, "Kalman(" + name + ")::input(matrix)::F"),
      modelMeasureSIN(NULL, "Kalman(" + name + ")::input(matrix)::H"),
      noiseTransitionSIN(NULL, "Kalman(" + name + ")::input(matrix)::Q"),
      noiseMeasureSIN(NULL, "Kalman(" + name + ")::input(matrix)::R")
 
      ,
      statePredictedSIN(0, "Kalman(" + name + ")::input(vector)::x_pred"),
      observationPredictedSIN(0, "Kalman(" + name + ")::input(vector)::y_pred"),
      varianceUpdateSOUT("Kalman(" + name + ")::output(vector)::P"),
      stateUpdateSOUT("Kalman(" + name + ")::output(vector)::x_est"),
      stateEstimation_(),
      stateVariance_() {
  sotDEBUGIN(15);
  varianceUpdateSOUT.setFunction(
      boost::bind(&Kalman::computeVarianceUpdate, this, _1, _2));
  stateUpdateSOUT.setFunction(
      boost::bind(&Kalman::computeStateUpdate, this, _1, _2));
 
  signalRegistration(measureSIN << observationPredictedSIN << modelTransitionSIN
                                << modelMeasureSIN << noiseTransitionSIN
                                << noiseMeasureSIN << statePredictedSIN
                                << stateUpdateSOUT << varianceUpdateSOUT);
 
  std::string docstring =
      "  Set initial state estimation\n"
      "\n"
      "  input:\n"
      "    - a vector: initial state\n";
  addCommand("setInitialState",
             new Setter<Kalman, Vector>(*this, &Kalman::setStateEstimation,
                                        docstring));
 
  docstring =
      "  Set variance of initial state estimation\n"
      "\n"
      "  input:\n"
      "    - a matrix: variance covariance matrix\n";
  addCommand(
      "setInitialVariance",
      new Setter<Kalman, Matrix>(*this, &Kalman::setStateVariance, docstring));
  sotDEBUGOUT(15);
}
 
Matrix &Kalman::computeVarianceUpdate(Matrix &Pk_k, const sigtime_t &time) {
  sotDEBUGIN(15);
  if (time == 0) {
    // First time return variance initial state
    Pk_k = stateVariance_;
    // Set dependency to input signals for latter computations
    varianceUpdateSOUT.addDependency(noiseTransitionSIN);
    varianceUpdateSOUT.addDependency(modelTransitionSIN);
  } else {
    const Matrix &Q = noiseTransitionSIN(time);
    const Matrix &R = noiseMeasureSIN(time);
    const Matrix &F = modelTransitionSIN(time);
    const Matrix &H = modelMeasureSIN(time);
    const Matrix &Pk_1_k_1 = stateVariance_;
 
    sotDEBUG(15) << "Q=" << Q << std::endl;
    sotDEBUG(15) << "R=" << R << std::endl;
    sotDEBUG(15) << "F=" << F << std::endl;
    sotDEBUG(15) << "H=" << H << std::endl;
    sotDEBUG(15) << "Pk_1_k_1=" << Pk_1_k_1 << std::endl;
 
    FP_ = F * Pk_1_k_1;
    Pk_k_1_ = FP_ * F.transpose();
    Pk_k_1_ += Q;
 
    sotDEBUG(15) << "F " << std::endl << F << std::endl;
    sotDEBUG(15) << "P_{k-1|k-1} " << std::endl << Pk_1_k_1 << std::endl;
    sotDEBUG(15) << "F^T " << std::endl << F.transpose() << std::endl;
    sotDEBUG(15) << "P_{k|k-1} " << std::endl << Pk_k_1_ << std::endl;
 
    S_ = H * Pk_k_1_ * H.transpose() + R;
    K_ = Pk_k_1_ * H.transpose() * S_.inverse();
    Pk_k = Pk_k_1_ - K_ * H * Pk_k_1_;
 
    sotDEBUG(15) << "S_{k} " << std::endl << S_ << std::endl;
    sotDEBUG(15) << "K_{k} " << std::endl << K_ << std::endl;
    sotDEBUG(15) << "P_{k|k} " << std::endl << Pk_k << std::endl;
 
    sotDEBUGOUT(15);
 
    stateVariance_ = Pk_k;
  }
  return Pk_k;
}
 
//               ^
//   z = y  - h (x     )
//    k   k       k|k-1
//
//   ^     ^
//   x   = x      + K  z
//    k|k   k|k-1    k  k
//
//                  T
//   S = H  P      H  + R
//    k   k  k|k-1  k
//
//               T  -1
//   K = P      H  S
//    k   k|k-1  k  k
//
//   P   = (I - K  H ) P
//    k|k        k  k   k|k-1
 
Vector &Kalman::computeStateUpdate(Vector &x_est, const sigtime_t &time) {
  sotDEBUGIN(15);
  if (time == 0) {
    // First time return variance initial state
    x_est = stateEstimation_;
    // Set dependency to input signals for latter computations
    stateUpdateSOUT.addDependency(measureSIN);
    stateUpdateSOUT.addDependency(observationPredictedSIN);
    stateUpdateSOUT.addDependency(modelMeasureSIN);
    stateUpdateSOUT.addDependency(noiseTransitionSIN);
    stateUpdateSOUT.addDependency(noiseMeasureSIN);
    stateUpdateSOUT.addDependency(statePredictedSIN);
    stateUpdateSOUT.addDependency(varianceUpdateSOUT);
  } else {
    varianceUpdateSOUT.recompute(time);
    const Vector &x_pred = statePredictedSIN(time);
    const Vector &y_pred = observationPredictedSIN(time);
    const Vector &y = measureSIN(time);
 
    sotDEBUG(25) << "K_{k} = " << std::endl << K_ << std::endl;
    sotDEBUG(25) << "y = " << y << std::endl;
    sotDEBUG(25) << "h (\\hat{x}_{k|k-1}) = " << y_pred << std::endl;
    sotDEBUG(25) << "y = " << y << std::endl;
 
    // Innovation: z_ = y - Hx
    z_ = y - y_pred;
    // x_est = x_pred + (K*(y-(H*x_pred)));
    x_est = x_pred + K_ * z_;
 
    sotDEBUG(25) << "z_{k} = " << z_ << std::endl;
    sotDEBUG(25) << "x_{k|k} = " << x_est << std::endl;
 
    stateEstimation_ = x_est;
  }
  sotDEBUGOUT(15);
  return x_est;
}
 
/* -------------------------------------------------------------------------- */
/* --- MODELE --------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
 
void Kalman::display(std::ostream &) const {}
 
}  // namespace sot
}  // namespace dynamicgraph