```// Copyright (C) 2012  Davis E. King (davis@dlib.net)
#undef DLIB_KALMAN_FiLTER_ABSTRACT_Hh_
#ifdef DLIB_KALMAN_FiLTER_ABSTRACT_Hh_

#include "../serialize.h"
#include "../matrix.h"

namespace dlib
{

// ----------------------------------------------------------------------------------------

template <
long states,
long measurements
>
class kalman_filter
{
/*!
REQUIREMENTS ON states
states > 0

REQUIREMENTS ON measurements
measurements > 0

WHAT THIS OBJECT REPRESENTS
This object implements the Kalman filter, which is a tool for
recursively estimating the state of a process given measurements
related to that process.  To use this tool you will have to
be familiar with the workings of the Kalman filter.  An excellent
introduction can be found in the paper:
An Introduction to the Kalman Filter
by Greg Welch and Gary Bishop

!*/

public:

kalman_filter(
);
/*!
- #get_observation_model()    == 0
- #get_transition_model()     == 0
- #get_process_noise()        == 0
- #get_measurement_noise()    == 0
- #get_current_state()        == 0
- #get_predicted_next_state() == 0
- #get_current_estimation_error_covariance() == the identity matrix
!*/

void set_observation_model (
const matrix<double,measurements,states>& H
);
/*!
ensures
- #get_observation_model() == H
!*/

void set_transition_model  (
const matrix<double,states,states>& A
);
/*!
ensures
- #get_transition_model() == A
!*/

void set_process_noise     (
const matrix<double,states,states>& Q
);
/*!
ensures
- #get_process_noise() == Q
!*/

void set_measurement_noise (
const matrix<double,measurements,measurements>& R
);
/*!
ensures
- #get_measurement_noise() == R
!*/

void set_estimation_error_covariance (
const matrix<double,states,states>& P
);
/*!
ensures
- #get_current_estimation_error_covariance() == P
(Note that you should only set this before you start filtering
since the Kalman filter will maintain the value of P on its own.
So only set this during initialization unless you are sure you
understand what you are doing.)
!*/

void set_state (
const matrix<double,states,1>& xb
);
/*!
ensures
- This function can be used when the initial state is known, or if the
state needs to be corrected before the next update().
- #get_predicted_next_state() == xb
- If (update() hasn't been called yet) then
- #get_current_state() == xb
!*/

const matrix<double,measurements,states>& get_observation_model (
) const;
/*!
ensures
- Returns the matrix "H" which relates process states x to measurements z.
The relation is linear, therefore, z = H*x.  That is, multiplying a
state by H gives the measurement you expect to observe for that state.
!*/

const matrix<double,states,states>& get_transition_model (
) const;
/*!
ensures
- Returns the matrix "A" which determines how process states change over time.
The relation is linear, therefore, given a state vector x, the value you
expect it to have at the next time step is A*x.
!*/

const matrix<double,states,states>& get_process_noise (
) const;
/*!
ensures
- returns the process noise covariance matrix.  You can think of this
covariance matrix as a measure of how wrong the assumption of
linear state transitions is.
!*/

const matrix<double,measurements,measurements>& get_measurement_noise (
) const;
/*!
ensures
- returns the measurement noise covariance matrix.  That is, when we
measure a state x we only obtain H*x corrupted by Gaussian noise.
The measurement noise is the covariance matrix of this Gaussian
noise which corrupts our measurements.
!*/

void update (
);
/*!
ensures
- propagates the current state estimate forward in time one
time step.  In particular:
- #get_current_state() == get_predicted_next_state()
- #get_predicted_next_state() == get_transition_model()*get_current_state()
- #get_current_estimation_error_covariance() == the propagated value of this covariance matrix
!*/

void update (
const matrix<double,measurements,1>& z
);
/*!
ensures
- propagates the current state estimate forward in time one time step.
Also applies a correction based on the given measurement z.  In particular:
- #get_current_state(), #get_predicted_next_state(), and
#get_current_estimation_error_covariance() are updated using the
Kalman filter method based on the new measurement in z.
!*/

const matrix<double,states,1>& get_current_state(
) const;
/*!
ensures
- returns the current estimate of the state of the process.  This
estimate is based on all the measurements supplied to the update()
method.
!*/

const matrix<double,states,1>& get_predicted_next_state(
) const;
/*!
ensures
- returns the next expected value of the process state.
- Specifically, returns get_transition_model()*get_current_state()

!*/

const matrix<double,states,states>& get_current_estimation_error_covariance(
) const;
/*!
ensures
- returns the current state error estimation covariance matrix.
This matrix captures our uncertainty about the value of get_current_state().
!*/

};

// ----------------------------------------------------------------------------------------

void serialize (
const kalman_filter& item,
std::ostream& out
);
/*!
provides serialization support
!*/

void deserialize (
kalman_filter& item,
std::istream& in
);
/*!
provides deserialization support
!*/

// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------

class momentum_filter
{
/*!
WHAT THIS OBJECT REPRESENTS
This object is a simple tool for filtering a single scalar value that
measures the location of a moving object that has some non-trivial
momentum.  Importantly, the measurements are noisy and the object can
experience sudden unpredictable accelerations.  To accomplish this
filtering we use a simple Kalman filter with a state transition model of:

position_{i+1} = position_{i} + velocity_{i}
velocity_{i+1} = velocity_{i} + some_unpredictable_acceleration

and a measurement model of:

measured_position_{i} = position_{i} + measurement_noise

Where some_unpredictable_acceleration and measurement_noise are 0 mean Gaussian
noise sources with standard deviations of get_typical_acceleration() and
get_measurement_noise() respectively.

To allow for really sudden and large but infrequent accelerations, at each
step we check if the current measured position deviates from the predicted
filtered position by more than get_max_measurement_deviation()*get_measurement_noise()
and if so we adjust the filter's state to keep it within these bounds.
This allows the moving object to undergo large unmodeled accelerations, far
in excess of what would be suggested by get_typical_acceleration(), without
then experiencing a long lag time where the Kalman filter has to "catch
up" to the new position.
!*/

public:

momentum_filter(
) = default;
/*!
ensures
- #get_measurement_noise() == 2
- #get_typical_acceleration() == 0.1
- #get_max_measurement_deviation() == 3
!*/

momentum_filter(
double meas_noise,
double acc,
double max_meas_dev
);
/*!
requires
- meas_noise >= 0
- acc >= 0
- max_meas_dev >= 0
ensures
- #get_measurement_noise() == meas_noise
- #get_typical_acceleration() == acc
- #get_max_measurement_deviation() == max_meas_dev
!*/

double get_measurement_noise (
) const;
/*!
ensures
- Returns the standard deviation of the 0 mean Gaussian noise that corrupts
measurements of the moving object.
!*/

double get_typical_acceleration (
) const;
/*!
ensures
- We assume that the moving object experiences random accelerations that
are distributed by 0 mean Gaussian noise with get_typical_acceleration()
standard deviation.
!*/

double get_max_measurement_deviation (
) const;
/*!
ensures
- This object will never let the filtered location of the object deviate
from the measured location by much more than
get_max_measurement_deviation()*get_measurement_noise().
!*/

void reset(
);
/*!
ensures
- Returns this object to the state immediately after construction. To be precise, we do:
*this = momentum_filter(get_measurement_noise(), get_typical_acceleration(), get_max_measurement_deviation());
!*/

double operator()(
const double measured_position
);
/*!
ensures
- Updates the Kalman filter with the new measured position of the object
and returns the new filtered estimate of the object's position, now that
we have seen the latest measured position.
- #get_predicted_next_position() == the prediction for the *next* place we
will see the object. That is, where we think it will be in the future
rather than where it is now.
!*/

double get_predicted_next_position (
) const;
/*!
ensures
- Returns the Kalman filter's estimate of the next position we will see the object.
!*/
};

std::ostream& operator << (std::ostream& out, const momentum_filter& item);
void serialize(const momentum_filter& item, std::ostream& out);
void deserialize(momentum_filter& item, std::istream& in);
/*!
Provide printing and serialization support.
!*/

// ----------------------------------------------------------------------------------------

momentum_filter find_optimal_momentum_filter (
const std::vector<std::vector<double>>& sequences,
const double smoothness = 1
);
/*!
requires
- sequences.size() != 0
- for all valid i: sequences[i].size() > 4
- smoothness >= 0
ensures
- This function finds the "optimal" settings of a momentum_filter based on
recorded measurement data stored in sequences.  Here we assume that each
vector in sequences is a complete track history of some object's measured
positions.  What we do is find the momentum_filter that minimizes the
following objective function:
sum of abs(predicted_location[i] - measured_location[i]) + smoothness*abs(filtered_location[i]-filtered_location[i-1])
Where i is a time index.
The sum runs over all the data in sequences.  So what we do is find the
filter settings that produce smooth filtered trajectories but also produce
filtered outputs that are as close to the measured positions as possible.
The larger the value of smoothness the less jittery the filter outputs will
be, but they might become biased or laggy if smoothness is set really high.
!*/

// ----------------------------------------------------------------------------------------

momentum_filter find_optimal_momentum_filter (
const std::vector<double>& sequence,
const double smoothness = 1
);
/*!
requires
- sequence.size() > 4
- smoothness >= 0
ensures
- performs: find_optimal_momentum_filter({1,sequence}, smoothness);
!*/

// ----------------------------------------------------------------------------------------

class rect_filter
{
/*!
WHAT THIS OBJECT REPRESENTS
This object simply contains four momentum_filters and applies them to the
4 components of a dlib::rectangle's position.  It therefore allows you to
easily filter a sequence of rectangles.  For instance, it can be used to
smooth the output of an object detector running on a video.
!*/

public:
rect_filter(
) = default;
/*!
ensures
- The four momentum_filters in this object are default initialized.
!*/

rect_filter(
const momentum_filter& filt
);
/*!
ensures
- #get_left() == filt
- #get_top() == filt
- #get_right() == filt
- #get_bottom() == filt
!*/

rect_filter(
double meas_noise,
double acc,
double max_meas_dev
) : rect_filter(momentum_filter(meas_noise, acc, max_meas_dev)) {}
/*!
requires
- meas_noise >= 0
- acc >= 0
- max_meas_dev >= 0
ensures
- Initializes this object with momentum_filter(meas_noise, acc, max_meas_dev)
!*/

drectangle operator()(
const drectangle& r
);
/*!
ensures
- Runs the given rectangle through the momentum_filters and returns the
filtered rectangle location.  That is, performs:
return drectangle(get_left()(r.left()),
get_top()(r.top()),
get_right()(r.right()),
get_bottom()(r.bottom()));
!*/

drectangle operator()(
const rectangle& r
);
/*!
ensures
- Runs the given rectangle through the momentum_filters and returns the
filtered rectangle location.  That is, performs:
return drectangle(get_left()(r.left()),
get_top()(r.top()),
get_right()(r.right()),
get_bottom()(r.bottom()));
!*/

const momentum_filter& get_left() const;
momentum_filter&       get_left();
const momentum_filter& get_top() const;
momentum_filter&       get_top();
const momentum_filter& get_right() const;
momentum_filter&       get_right();
const momentum_filter& get_bottom() const;
momentum_filter&       get_bottom();
/*!
Provides access to the 4 momentum_filters used to filter the 4 coordinates that define a rectangle.
!*/
};

void serialize(const rect_filter& item, std::ostream& out);
void deserialize(rect_filter& item, std::istream& in);
/*!
Provide serialization support.
!*/

// ----------------------------------------------------------------------------------------

rect_filter find_optimal_rect_filter (
const std::vector<rectangle>& rects,
const double smoothness = 1
);
/*!
requires
- rects.size() > 4
- smoothness >= 0
ensures
- This routine simply invokes find_optimal_momentum_filter() to find the
momentum_filter that works best on the provided sequence of rectangles.  It
then constructs a rect_filter using that momentum_filter and returns it.
Therefore, this routine finds the rect_filter that is "optimal" for filtering
the given sequence of rectangles.
!*/

// ----------------------------------------------------------------------------------------

}

#endif // DLIB_KALMAN_FiLTER_ABSTRACT_Hh_

```