Merge pull request #60 from xEnVrE/impl/gaussian_pdf

Implement utility for evaluating multivariate Gaussian density.

Author: claudiofantacci

CHANGELOG.md

@@ -12,6 +12,8 @@
 - Implemented method GaussianMixture::resize().
 - Implemented method Gaussian::resize().
 - Implemented method ParticleSet::resize().
+- Implemented evaluation of a multivariate Gaussian probability density function in method utils::multivariate_gaussian_density.
+- Implemented evaluation of the logarithm of a multivariate Gaussian probability density function in method utils::multivariate_gaussian_log_density.
 - Methods EstimatesExtraction::extract() return a std::pair containing a boolean indicating if the estimate is valid and the estracted estimate.
 - Methods EstimatesExtraction::extract() assume that particle weights are in the log space.
 - Constructor HistoryBuffer::HistoryBuffer() takes the state size.
@@ -23,9 +25,14 @@
 ##### `Filtering functions`
 - Added pure public virtual method GaussianPrediction::getStateModel() (required to properly implement GPFPrediction::getStateModel()).
 - Implemented method KFPrediction::getStateModel().
+- Implemented method KFCorrection::getLikelihood().
 - Implemented method UKFPrediction::getStateModel().
+- Implemented method UKFCorrection::getLikelihood().
+- Changed implementation of GaussianLikelihood::likelihood().
 - Changed implementation of GPFPrediction::getStateModel().
 - Changed implementation of GPFCorrection::getLikelihood().
+- Changed implementation of GPFCorrection::evaluateProposal().
+- Changed implementation of WhiteNoiseAcceleration::getTransitionProbability().
 - Fixed missing const(s) keywords in signature of method StateModel::getTransitionProbability().
 - Fixed missing const(s) keywords in signature of method WhiteNoiseAcceleration::getTransitionProbability().
 - SUKFCorrection::getNoiseCovarianceMatrix() is now virtual.

src/BayesFilters/include/BayesFilters/KFCorrection.h

@@ -30,11 +30,16 @@ class bfl::KFCorrection : public GaussianCorrection
 
     MeasurementModel& getMeasurementModel() override;
 
+    std::pair<bool, Eigen::VectorXd> getLikelihood() override;
+
 protected:
     void correctStep(const GaussianMixture& pred_state, GaussianMixture& corr_state) override;
 
-private:
     std::unique_ptr<LinearMeasurementModel> measurement_model_;
+
+    Eigen::MatrixXd innovations_;
+
+    GaussianMixture meas_covariances_;
 };
 
 #endif /* KFCORRECTION_H */

src/BayesFilters/include/BayesFilters/UKFCorrection.h

@@ -34,6 +34,8 @@ class bfl::UKFCorrection : public GaussianCorrection
 
     MeasurementModel& getMeasurementModel() override;
 
+    std::pair<bool, Eigen::VectorXd> getLikelihood() override;
+
 protected:
     void correctStep(const GaussianMixture& pred_state, GaussianMixture& corr_state) override;
 
@@ -53,6 +55,10 @@ class bfl::UKFCorrection : public GaussianCorrection
      * Unscented transform weight.
      */
     sigma_point::UTWeight ut_weight_;
+
+    Eigen::MatrixXd innovations_;
+
+    GaussianMixture predicted_meas_;
 };
 
 #endif /* UKFCORRECTION_H */

src/BayesFilters/include/BayesFilters/utils.h

@@ -61,6 +61,44 @@ std::unique_ptr<T> make_unique(Args&& ...args)
 double log_sum_exp(const Eigen::Ref<const Eigen::VectorXd>& arguments);
 
 
+/**
+ * Evaluate the logarithm of a multivariate Gaussian probability density function.
+ *
+ * @param input Input representing the argument of the function as a vector or matrix.
+ * @param mean The mean of the associated Gaussian distribution as a vector.
+ * @param covariance The covariance matrix of the associated Gaussian distribution as a matrix.
+ *
+ * @return The value of the logarithm of the density function evaluated on the input data as a vector.
+ */
+template<typename Derived>
+Eigen::VectorXd multivariate_gaussian_log_density(const Eigen::MatrixBase<Derived>& input, const Eigen::Ref<const Eigen::VectorXd>& mean, const Eigen::Ref<const Eigen::MatrixXd>& covariance)
+{
+    const auto diff = input.colwise() - mean;
+
+    Eigen::VectorXd values(diff.cols());
+    for (std::size_t i = 0; i < diff.cols(); i++)
+        values(i) = - 0.5 * (static_cast<double>(diff.rows()) * std::log(2.0 * M_PI) + std::log(covariance.determinant()) + (diff.col(i).transpose() * covariance.inverse() * diff.col(i)));
+
+    return values;
+}
+
+
+/**
+ * Evaluate a multivariate Gaussian probability density function.
+ *
+ * @param input Input representing the argument of the function as a vector or matrix.
+ * @param mean The mean of the associated Gaussian distribution as a vector.
+ * @param covariance The covariance matrix of the associated Gaussian distribution as a matrix.
+ *
+ * @return The value of the density function evaluated on the input data as a vector.
+ */
+template<typename Derived>
+Eigen::VectorXd multivariate_gaussian_density(const Eigen::MatrixBase<Derived>& input, const Eigen::Ref<const Eigen::VectorXd>& mean, const Eigen::Ref<const Eigen::MatrixXd>& covariance)
+{
+    return multivariate_gaussian_log_density(input, mean, covariance).array().exp();
+}
+
+
 /**
  * This template class provides methods to keep track of time. The default time unit is milliseconds,
  * but can be changed during object creation using a different std::chrono::duration type.

src/BayesFilters/src/GPFCorrection.cpp

@@ -6,6 +6,7 @@
  */
 
 #include <BayesFilters/GPFCorrection.h>
+#include <BayesFilters/utils.h>
 
 #include <Eigen/Cholesky>
 
@@ -144,7 +145,5 @@ double GPFCorrection::evaluateProposal
 {
     /* Evaluate the proposal distribution, a Gaussian centered in 'mean' and having
        covariance 'covariance', in the state 'state'. */
-    VectorXd difference = state - mean;
-
-    return (-0.5 * static_cast<double>(difference.size()) * log(2.0 * M_PI) -0.5 * log(covariance.determinant()) -0.5 * (difference.transpose() * covariance.inverse() * difference).array()).exp().coeff(0);
+    return utils::multivariate_gaussian_density(state, mean, covariance).coeff(0);
 }

src/BayesFilters/src/GaussianLikelihood.cpp

@@ -6,6 +6,7 @@
  */
 
 #include <BayesFilters/GaussianLikelihood.h>
+#include <BayesFilters/utils.h>
 
 using namespace bfl;
 using namespace Eigen;
@@ -68,9 +69,7 @@ std::pair<bool, VectorXd> GaussianLikelihood::likelihood
     if (!valid_covariance_matrix)
         return std::make_pair(false, VectorXd::Zero(1));
 
-
-    for (unsigned int i = 0; i < innovations.cols(); ++i)
-        likelihood(i) = scale_factor_ * (-0.5 * static_cast<double>(innovations.rows()) * log(2.0*M_PI) - 0.5 * log(covariance_matrix.determinant()) - 0.5 * (innovations.col(i).transpose() * covariance_matrix.inverse() * innovations.col(i)).array()).exp().coeff(0);
+    likelihood = scale_factor_ * utils::multivariate_gaussian_density(innovations, VectorXd::Zero(innovations.rows()), covariance_matrix);
 
     return std::make_pair(true, likelihood);
 }

src/BayesFilters/src/KFCorrection.cpp

@@ -6,6 +6,7 @@
  */
 
 #include <BayesFilters/KFCorrection.h>
+#include <BayesFilters/utils.h>
 
 using namespace bfl;
 using namespace Eigen;
@@ -31,6 +32,21 @@ MeasurementModel& KFCorrection::getMeasurementModel()
 }
 
 
+std::pair<bool, VectorXd> KFCorrection::getLikelihood()
+{
+    if ((innovations_.rows() == 0) || (innovations_.cols() == 0))
+        return std::make_pair(false, VectorXd());
+
+    VectorXd likelihood(innovations_.cols());
+    for (std::size_t i = 0; i < likelihood.size(); i++)
+    {
+        likelihood(i) = utils::multivariate_gaussian_density(innovations_.col(i), VectorXd::Zero(innovations_.rows()), meas_covariances_.covariance(i)).coeff(0);
+    }
+
+    return std::make_pair(true, likelihood);
+}
+
+
 void KFCorrection::correctStep(const GaussianMixture& pred_state, GaussianMixture& corr_state)
 {
     /* Get the current measurement if available. */
@@ -79,25 +95,29 @@ void KFCorrection::correctStep(const GaussianMixture& pred_state, GaussianMixtur
     MatrixXd H = measurement_model_->getMeasurementMatrix();
 
     /* Cast innovations once for all. */
-    MatrixXd innovations = any::any_cast<MatrixXd&&>(std::move(innovation));
+    innovations_ = any::any_cast<MatrixXd&&>(std::move(innovation));
+
+    /* Initialize measurement covariances.
+       GaussianMixture will effectively resize only if it needs to. */
+    meas_covariances_.resize(pred_state.components, H.rows());
 
     /* Process all the components in the mixture. */
-    for (size_t i=0; i < pred_state.components; i++)
+    for (size_t i = 0; i < pred_state.components; i++)
     {
         /* Evaluate the measurement covariance matrix
            Py = H * Px * H' + R */
-        MatrixXd Py = H * pred_state.covariance(i) * H.transpose() + R;
+        meas_covariances_.covariance(i) = H * pred_state.covariance(i) * H.transpose() + R;
 
         /* Evaluate the Kalman Gain
            K = Px * H' * (Py)^{-1} */
-        MatrixXd K = pred_state.covariance(i) * H.transpose() * Py.inverse();
+        MatrixXd K = pred_state.covariance(i) * H.transpose() * meas_covariances_.covariance(i).inverse();
 
         /* Evaluate the filtered mean
            x_{k}+ = x{k}- + K * (y - y_predicted) */
-        corr_state.mean(i) = pred_state.mean(i) + K * innovations.col(i);
+        corr_state.mean(i) = pred_state.mean(i) + K * innovations_.col(i);
 
         /* Evaluate the filtered covariance
            P_{k}+ = P_{k}- - K * Py * K' */
-        corr_state.covariance(i).noalias() = pred_state.covariance(i) - K * Py * K.transpose();
+        corr_state.covariance(i).noalias() = pred_state.covariance(i) - K * meas_covariances_.covariance(i) * K.transpose();
     }
 }

src/BayesFilters/src/UKFCorrection.cpp

@@ -6,6 +6,7 @@
  */
 
 #include <BayesFilters/UKFCorrection.h>
+#include <BayesFilters/utils.h>
 
 using namespace bfl;
 using namespace bfl::sigma_point;
@@ -61,6 +62,21 @@ MeasurementModel& UKFCorrection::getMeasurementModel()
 }
 
 
+std::pair<bool, VectorXd> UKFCorrection::getLikelihood()
+{
+    if ((innovations_.rows() == 0) || (innovations_.cols() == 0))
+        return std::make_pair(false, VectorXd());
+
+    VectorXd likelihood(innovations_.cols());
+    for (std::size_t i = 0; i < innovations_.cols(); i++)
+    {
+        likelihood(i) = utils::multivariate_gaussian_density(innovations_.col(i), VectorXd::Zero(innovations_.rows()), predicted_meas_.covariance(i)).coeff(0);
+    }
+
+    return std::make_pair(true, likelihood);
+}
+
+
 void UKFCorrection::correctStep(const GaussianMixture& pred_state, GaussianMixture& corr_state)
 {
     /* Pick the correct measurement model. */
@@ -80,7 +96,8 @@ void UKFCorrection::correctStep(const GaussianMixture& pred_state, GaussianMixtu
     /* Initialize predicted measurement GaussianMixture. */
     std::pair<std::size_t, std::size_t> meas_sizes = model.getOutputSize();
     std::size_t meas_size = meas_sizes.first + meas_sizes.second;
-    GaussianMixture pred_meas(pred_state.components, meas_size);
+    /* GaussianMixture will effectively resize only if it needs to. */
+    predicted_meas_.resize(pred_state.components, meas_size);
 
     /* Evaluate the joint state-measurement statistics, if possible. */
     bool valid = false;
@@ -94,11 +111,11 @@ void UKFCorrection::correctStep(const GaussianMixture& pred_state, GaussianMixtu
         std::tie(std::ignore, noise_covariance_matrix) = model.getNoiseCovarianceMatrix();
         pred_state_augmented.augmentWithNoise(noise_covariance_matrix);
 
-        std::tie(valid, pred_meas, Pxy) = sigma_point::unscented_transform(pred_state_augmented, ut_weight_, *measurement_model_);
+        std::tie(valid, predicted_meas_, Pxy) = sigma_point::unscented_transform(pred_state_augmented, ut_weight_, *measurement_model_);
     }
     else if (type_ == UKFCorrectionType::Additive)
     {
-        std::tie(valid, pred_meas, Pxy) = sigma_point::unscented_transform(pred_state, ut_weight_, *additive_measurement_model_);
+        std::tie(valid, predicted_meas_, Pxy) = sigma_point::unscented_transform(pred_state, ut_weight_, *additive_measurement_model_);
     }
 
     if (!valid)
@@ -113,8 +130,8 @@ void UKFCorrection::correctStep(const GaussianMixture& pred_state, GaussianMixtu
     /* This temporary is required since some MeasurementModel::innovation methods may try to cast from
        const Ref<const MatrixXd> to MatrixXd resulting in a bfl::any::bad_any_cast.
 
-       Hopefully, using std::move, it is possible to steal the memory from pred_meas.mean(). */
-    MatrixXd y_p = std::move(pred_meas.mean());
+       Hopefully, using std::move, it is possible to steal the memory from predicted_meas_.mean(). */
+    MatrixXd y_p = std::move(predicted_meas_.mean());
     std::tie(valid_innovation, innovation) = model.innovation(y_p, measurement);
 
     if (!valid_innovation)
@@ -124,21 +141,21 @@ void UKFCorrection::correctStep(const GaussianMixture& pred_state, GaussianMixtu
     }
 
     /* Cast innovations once for all. */
-    MatrixXd innovations = any::any_cast<MatrixXd&&>(std::move(innovation));
+    innovations_ = any::any_cast<MatrixXd&&>(std::move(innovation));
 
     /* Process all the components in the mixture. */
     for (size_t i=0; i < pred_state.components; i++)
     {
         /* Evaluate the Kalman Gain
            K = Pxy * (Py)^{-1} */
-        MatrixXd K = Pxy.middleCols(meas_size * i, meas_size) * pred_meas.covariance(i).inverse();
+        MatrixXd K = Pxy.middleCols(meas_size * i, meas_size) * predicted_meas_.covariance(i).inverse();
 
         /* Evaluate the filtered mean.
            x_{k}+ = x{k}- + K * innovation */
-        corr_state.mean(i) = pred_state.mean(i) + K * innovations.col(i);
+        corr_state.mean(i) = pred_state.mean(i) + K * innovations_.col(i);
 
         /* Evaluate the filtered covariance
            P_{k}+ = P_{k}- - K * Py * K' */
-        corr_state.covariance(i) = pred_state.covariance(i) - K * pred_meas.covariance(i) * K.transpose();
+        corr_state.covariance(i) = pred_state.covariance(i) - K * predicted_meas_.covariance(i) * K.transpose();
     }
 }

src/BayesFilters/src/WhiteNoiseAcceleration.cpp

@@ -6,6 +6,7 @@
  */
 
 #include <BayesFilters/WhiteNoiseAcceleration.h>
+#include <BayesFilters/utils.h>
 
 #include <cmath>
 #include <utility>
@@ -139,16 +140,7 @@ MatrixXd WhiteNoiseAcceleration::getStateTransitionMatrix()
 
 VectorXd WhiteNoiseAcceleration::getTransitionProbability(const Ref<const MatrixXd>& prev_states, const Ref<const MatrixXd>& cur_states)
 {
-    VectorXd probabilities(prev_states.cols());
-    MatrixXd differences = cur_states - prev_states;
-
-    std::size_t size = differences.rows();
-    for (std::size_t i = 0; i < prev_states.cols(); i++)
-    {
-        probabilities(i) = (-0.5 * static_cast<double>(size) * log(2.0 * M_PI) + -0.5 * log(Q_.determinant()) -0.5 * (differences.col(i).transpose() * Q_.inverse() * differences.col(i)).array()).exp().coeff(0);
-    }
-
-    return probabilities;
+    return utils::multivariate_gaussian_density(prev_states, prev_states.col(0), Q_);
 }