kalman_filter.h

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// Copyright (c) 2014 libmv authors.
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// furnished to do so, subject to the following conditions:
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// The above copyright notice and this permission notice shall be included in
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// IN THE SOFTWARE.
 
#ifndef LIBMV_TRACKING_KALMAN_FILTER_H_
#define LIBMV_TRACKING_KALMAN_FILTER_H_
 
#include "libmv/numeric/numeric.h"
 
namespace mv {
 
// A Kalman filter with order N and observation size K.
template <typename T, int N, int K>
class KalmanFilter {
 public:
  struct State {
    Eigen::Matrix<T, N, 1> mean;
    Eigen::Matrix<T, N, N> covariance;
  };
 
  // Initialize from row-major data; convenient for constant initializers.
  KalmanFilter(const T* state_transition_data,
               const T* observation_data,
               const T* process_covariance_data,
               const T* default_measurement_covariance_data)
      : state_transition_matrix_(
            Eigen::Matrix<T, N, N, Eigen::RowMajor>(state_transition_data)),
        observation_matrix_(
            Eigen::Matrix<T, K, N, Eigen::RowMajor>(observation_data)),
        process_covariance_(
            Eigen::Matrix<T, N, N, Eigen::RowMajor>(process_covariance_data)),
        default_measurement_covariance_(Eigen::Matrix<T, K, K, Eigen::RowMajor>(
            default_measurement_covariance_data)) {}
 
  KalmanFilter(const Eigen::Matrix<T, N, N>& state_transition_matrix,
               const Eigen::Matrix<T, K, N>& observation_matrix,
               const Eigen::Matrix<T, N, N>& process_covariance,
               const Eigen::Matrix<T, K, K>& default_measurement_covariance)
      : state_transition_matrix_(state_transition_matrix),
        observation_matrix_(observation_matrix),
        process_covariance_(process_covariance),
        default_measurement_covariance_(default_measurement_covariance) {}
 
  // Advances the system according to the current state estimate.
  void Step(State* state) const {
    state->mean = state_transition_matrix_ * state->mean;
    state->covariance = state_transition_matrix_ * state->covariance *
                            state_transition_matrix_.transpose() +
                        process_covariance_;
  }
 
  // Updates a state with a new measurement.
  void Update(const Eigen::Matrix<T, K, 1>& measurement_mean,
              const Eigen::Matrix<T, K, K>& measurement_covariance,
              State* state) const {
    // Calculate the innovation, which is a distribution over prediction error.
    Eigen::Matrix<T, K, 1> innovation_mean =
        measurement_mean - observation_matrix_ * state->mean;
    Eigen::Matrix<T, K, K> innovation_covariance =
        observation_matrix_ * state->covariance *
            observation_matrix_.transpose() +
        measurement_covariance;
 
    // Calculate the Kalman gain.
    Eigen::Matrix<T, 6, 2> kalman_gain = state->covariance *
                                         observation_matrix_.transpose() *
                                         innovation_covariance.inverse();
 
    // Update the state mean and covariance.
    state->mean += kalman_gain * innovation_mean;
    state->covariance = (Eigen::Matrix<T, N, N>::Identity() -
                         kalman_gain * observation_matrix_) *
                        state->covariance;
  }
 
  void Update(State* state,
              const Eigen::Matrix<T, K, 1>& measurement_mean) const {
    Update(state, measurement_mean, default_measurement_covariance_);
  }
 
 private:
  const Eigen::Matrix<T, N, N> state_transition_matrix_;
  const Eigen::Matrix<T, K, N> observation_matrix_;
  const Eigen::Matrix<T, N, N> process_covariance_;
  const Eigen::Matrix<T, K, K> default_measurement_covariance_;
};
 
}  // namespace mv
 
#endif  // LIBMV_TRACKING_KALMAN_FILTER_H_