Does UKF have smoothing?

[tugrul512bit]

I tried gps_position smoothing from one of examples by adding random noise to measurement but it does not smooth it:

#define UKF_DOUBLE_PRECISION
//#define real_t double
#include <iostream>
#include <Eigen/Core>
#include <Eigen/Geometry>
#include <cmath>
#include "UKF/Types.h"
#include "UKF/Integrator.h"
#include "UKF/StateVector.h"
#include "UKF/MeasurementVector.h"
#include "UKF/Core.h"


/* Set up state vector class. */
enum MyStateFields {
    Position,
    Velocity,
    Attitude,
    AngularVelocity
};

using MyStateVector = UKF::StateVector<
    UKF::Field<Position, UKF::Vector<3>>,
    UKF::Field<Velocity, UKF::Vector<3>>,
    UKF::Field<Attitude, UKF::Quaternion>,
    UKF::Field<AngularVelocity, UKF::Vector<3>>
>;
namespace UKF {
    namespace Parameters {
        template <> constexpr real_t AlphaSquared<MyStateVector> = 1e-6;
    }

    /*
    State vector process model. One version takes body frame kinematic
    acceleration and angular acceleration as inputs, the other doesn't (assumes
    zero accelerations).
    */
    template <> template <>
    MyStateVector MyStateVector::derivative<UKF::Vector<3>, UKF::Vector<3>>(
        const UKF::Vector<3>& acceleration, const UKF::Vector<3>& angular_acceleration) const {
        MyStateVector temp;

        /* Position derivative. */
        temp.set_field<Position>(get_field<Velocity>());

        /* Velocity derivative. */
        temp.set_field<Velocity>(get_field<Attitude>().conjugate() * acceleration);

        /* Attitude derivative. */
        UKF::Quaternion temp_q;
        temp_q.vec() = get_field<AngularVelocity>();
        temp_q.w() = 0;
        temp.set_field<Attitude>(temp_q);

        /* Angular velocity derivative. */
        temp.set_field<AngularVelocity>(angular_acceleration);

        return temp;
    }

    template <> template <>
    MyStateVector MyStateVector::derivative<>() const {
        return derivative(UKF::Vector<3>(0, 0, 0), UKF::Vector<3>(0, 0, 0));
    }

}

/* Set up measurement vector class. */
enum MyMeasurementFields {
    GPS_Position,
    GPS_Velocity,
    Accelerometer,
    Magnetometer,
    Gyroscope
};

using MyMeasurementVector = UKF::DynamicMeasurementVector<
    UKF::Field<GPS_Position, UKF::Vector<3>>,
    UKF::Field<GPS_Velocity, UKF::Vector<3>>,
    UKF::Field<Accelerometer, UKF::Vector<3>>,
    UKF::Field<Magnetometer, UKF::FieldVector>,
    UKF::Field<Gyroscope, UKF::Vector<3>>
>;

using MyCore = UKF::Core<
    MyStateVector,
    MyMeasurementVector,
    UKF::IntegratorRK4
>;

namespace UKF {
    /*
    Define measurement model to be used in tests. NOTE: These are just for
    testing, don't expect them to make any physical sense whatsoever.
    */
    template <> template <>
    UKF::Vector<3> MyMeasurementVector::expected_measurement
        <MyStateVector, GPS_Position>(const MyStateVector& state) {
        return state.get_field<Position>();
    }

    template <> template <>
    UKF::Vector<3> MyMeasurementVector::expected_measurement
        <MyStateVector, GPS_Velocity>(const MyStateVector& state) {
        return state.get_field<Velocity>();
    }

    template <> template <>
    UKF::Vector<3> MyMeasurementVector::expected_measurement
        <MyStateVector, Accelerometer>(const MyStateVector& state) {
        return state.get_field<Attitude>() * UKF::Vector<3>(0, 0, -9.8);
    }

    template <> template <>
    UKF::FieldVector MyMeasurementVector::expected_measurement
        <MyStateVector, Magnetometer>(const MyStateVector& state) {
        return state.get_field<Attitude>() * UKF::FieldVector(1, 0, 0);
    }

    template <> template <>
    UKF::Vector<3> MyMeasurementVector::expected_measurement
        <MyStateVector, Gyroscope>(const MyStateVector& state) {
        return state.get_field<AngularVelocity>();
    }

    /*
    These versions of the predicted measurement functions take kinematic
    acceleration and angular acceleration as inputs. Note that in reality, the
    inputs would probably be a control vector and the accelerations would be
    calculated using the state vector and a dynamics model.
    */
    template <> template <>
    UKF::Vector<3> MyMeasurementVector::expected_measurement
        <MyStateVector, GPS_Position>(const MyStateVector& state,
            const UKF::Vector<3>& acceleration, const UKF::Vector<3>& angular_acceleration) {
        return state.get_field<Position>();
    }

    template <> template <>
    UKF::Vector<3> MyMeasurementVector::expected_measurement
        <MyStateVector, GPS_Velocity>(const MyStateVector& state,
            const UKF::Vector<3>& acceleration, const UKF::Vector<3>& angular_acceleration) {
        return state.get_field<Velocity>();
    }

    template <> template <>
    UKF::Vector<3> MyMeasurementVector::expected_measurement
        <MyStateVector, Accelerometer, UKF::Vector<3>>(const MyStateVector& state,
            const UKF::Vector<3>& acceleration, const UKF::Vector<3>& angular_acceleration) {
        return state.get_field<Attitude>() * UKF::Vector<3>(0, 0, -9.8) + acceleration;
    }

    template <> template <>
    UKF::FieldVector MyMeasurementVector::expected_measurement
        <MyStateVector, Magnetometer, UKF::Vector<3>>(const MyStateVector& state,
            const UKF::Vector<3>& acceleration, const UKF::Vector<3>& angular_acceleration) {
        return state.get_field<Attitude>() * UKF::FieldVector(1, 0, 0);
    }

    template <> template <>
    UKF::Vector<3> MyMeasurementVector::expected_measurement
        <MyStateVector, Gyroscope, UKF::Vector<3>>(const MyStateVector& state,
            const UKF::Vector<3>& acceleration, const UKF::Vector<3>& angular_acceleration) {
        return state.get_field<AngularVelocity>();
    }

}

MyCore create_initialised_test_filter() {
    MyCore test_filter;
    test_filter.state.set_field<Position>(UKF::Vector<3>(0, 0, 0));
    test_filter.state.set_field<Velocity>(UKF::Vector<3>(0, 0, 0));
    test_filter.state.set_field<Attitude>(UKF::Quaternion(1, 0, 0, 0));
    test_filter.state.set_field<AngularVelocity>(UKF::Vector<3>(0, 0, 0));
    test_filter.covariance = MyStateVector::CovarianceMatrix::Zero();
    test_filter.covariance.diagonal() << 10000, 10000, 10000, 100, 100, 100, 1, 1, 5, 10, 10, 10;
    test_filter.measurement_covariance << 10, 10, 10, 1, 1, 1, 5e-1, 5e-1, 5e-1, 5e-1, 5e-1, 5e-1, 0.05, 0.05, 0.05;
    
    real_t a, b;
    real_t dt = 0.01;
    a = std::sqrt(0.1 * dt * dt);
    b = std::sqrt(0.1 * dt);
    test_filter.process_noise_covariance << 
        a, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, a, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 0, a, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 0, 0, b, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 0, 0, 0, b, 0, 0, 0, 0, 0, 0, 0,
        0, 0, 0, 0, 0, b, 0, 0, 0, 0, 0, 0,
        0, 0, 0, 0, 0, 0, a, 0, 0, 0, 0, 0,
        0, 0, 0, 0, 0, 0, 0, a, 0, 0, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 0, a, 0, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 0, 0, b, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, b, 0,
        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, b;

    return test_filter;
}

#include <random>
static std::random_device rd; // random device engine, usually based on /dev/random on UNIX-like systems
// initialize Mersennes' twister using rd to generate the seed
static std::mt19937 rng{ rd() };

double dice()
{
    static std::uniform_real_distribution<double> uid(-5, 5); // random dice
    return uid(rng); // use rng as a generator
}

int main() {
    MyCore test_filter = create_initialised_test_filter();
    MyMeasurementVector m;

    m.set_field<GPS_Position>(UKF::Vector<3>(100, 10, -50));
    m.set_field<GPS_Velocity>(UKF::Vector<3>(20, 0, 0));
    m.set_field<Accelerometer>(UKF::Vector<3>(0, 0, -14.8));
    m.set_field<Magnetometer>(UKF::FieldVector(0, -1, 0));
    m.set_field<Gyroscope>(UKF::Vector<3>(0.5, 0, 0));

    for (int i = 0; i < 100; i++)
    {
        // gps position: 100 +/- 5, 10, -50 measured
        m.set_field<GPS_Position>(UKF::Vector<3>(100+dice(), 10, -50));
        test_filter.step(0.01, m, UKF::Vector<3>(0, 0, -5), UKF::Vector<3>(1, 0, 0));
        
        // does not smooth
        std::cout << m.get_field<Position>() << std::endl;
        std::cout << "-------------" << std::endl;
    }

    return 0;

}