unsFlt.hpp

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#ifndef _BAYES_FILTER_UNSCENTED
#define _BAYES_FILTER_UNSCENTED

/*
 * Bayes++ the Bayesian Filtering Library
 * Copyright (c) 2002 Michael Stevens
 * See accompanying Bayes++.htm for terms and conditions of use.
 *
 * $Id: unsFlt.hpp 562 2006-04-05 20:46:23 +0200 (Wed, 05 Apr 2006) mistevens $
 */

/*
 * Unscented Filter Scheme.
 *  A Julier-Uhlmann Unscented non-linear Kalman filter
 *  Uses the classic implementation of Duplex Unscented transform.
 * The Unscented transform is used for non-linear state and observation predictions
 *
 * Observations are fused using innovation gain equations from a Covariance filter
 *
 * Predictions of state and state covariance (and observation) use
 * unscented transformations to interpolate the non-linear predict and observe
 * models. unscented transforms can be further optimised by vary the Kappa
 * parameter from its usual value of 1.
 * Discontinous observe models require that a normailisation function.
 *
 * The predict model is represtented by the state prediction function and a 
 * seperate prediction noise matrix.
 * The observe model is represtented by the observation prediction function and
 * a function to normalise observeations.
 *
 * The filter is operated by performing a
 *  predict, observe
 * cycle defined by the base class
 */
#include "bayesFlt.hpp"

/* Filter namespace */
namespace Bayesian_filter
{

class Unscented_predict_model : public Predict_model_base
/* Specific Unscented prediction model for Addative noise
 *  x(k|k-1) = f(x(k-1|k-1)) + w(x(k))
 *
 * Unscented filter requires
 *  f the function part of the non-linear model
 *  Q the covariance of the addative w(x(k)), w is specificly allow to be a function of state
 */
{
public:
    Unscented_predict_model (std::size_t q_size)
    {
        q_unscented = q_size;
    }

    virtual const FM::Vec& f(const FM::Vec& x) const = 0;
    // Functional part of addative model
    // Note: Reference return value as a speed optimisation, MUST be copied by caller.

    virtual const FM::SymMatrix& Q(const FM::Vec& x) const = 0;
    // Covariance of addative noise
    // Note: Reference return value as a speed optimisation, MUST be copied by caller.
private:
    friend class Unscented_filter;  // Filter implementation need to know noise size
    std::size_t q_unscented;
};


class Unscented_scheme : public Linrz_kalman_filter, public Functional_filter
{
private:
    std::size_t q_max;          // Maxiumum size allocated for noise model, constructed before XX
public:
    FM::ColMatrix XX;       // Unscented form of state, with associated kappa
    Float kappa;

    Unscented_scheme (std::size_t x_size, std::size_t z_initialsize = 0);
    Unscented_scheme& operator= (const Unscented_scheme&);
    // Optimise copy assignment to only copy filter state

    void init ();
    void init_XX ();
    void update ();
    void update_XX (Float kappa);

    void predict (Unscented_predict_model& f);
    // Efficient Unscented prediction 
    void predict (Functional_predict_model& f);
    void predict (Addative_predict_model& f);
    Float predict (Linrz_predict_model& f)
    {   // Adapt to use the more general addative model
        predict(static_cast<Addative_predict_model&>(f));
        return 1.;      // Always well condition for addative predict
    }
    
    Float observe (Uncorrelated_addative_observe_model& h, const FM::Vec& z);
    Float observe (Correlated_addative_observe_model& h, const FM::Vec& z);
    // Unscented filter implements general addative observe models 
    
    Float observe (Linrz_uncorrelated_observe_model& h, const FM::Vec& z)
    {   // Adapt to use the more general addative model
        return observe (static_cast<Uncorrelated_addative_observe_model&>(h),z);
    }
    Float observe (Linrz_correlated_observe_model& h, const FM::Vec& z)
    {   // Adapt to use the more general addative model
        return observe (static_cast<Correlated_addative_observe_model&>(h),z);
    }

public:                     // Exposed Numerical Results
    FM::Vec s;                  // Innovation
    FM::SymMatrix S, SI;        // Innovation Covariance and Inverse

protected:
    virtual Float predict_Kappa (std::size_t size) const;
    virtual Float observe_Kappa (std::size_t size) const;
    /* unscented Kappa values
       default uses the rule which minimise mean squared error of 4th order term
    */

protected:                  // allow fast operation if z_size remains constant
    std::size_t last_z_size;
    void observe_size (std::size_t z_size);

private:
    void unscented (FM::ColMatrix& XX, const FM::Vec& x, const FM::SymMatrix& X, Float scale);
    /* Determine Unscented points for a distribution */
    std::size_t x_size;
    std::size_t XX_size;    // 2*x_size+1

protected:                  // Permenantly allocated temps
    FM::ColMatrix fXX;
};


}//namespace
#endif

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