.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/tracking/plotSimulatedTrajectoryDWPA.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_tracking_plotSimulatedTrajectoryDWPA.py>`
        to download the full example code. or to run this example in your browser via Binder

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_tracking_plotSimulatedTrajectoryDWPA.py:


Sampling from a Discrete Wiener Process Acceleration Model
==========================================================

The code below samples from a Discrete Wiener Process Acceleration (DWPA)
model.

.. GENERATED FROM PYTHON SOURCE LINES 12-14

Import packages
~~~~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 14-22

.. code-block:: Python


    import numpy as np
    import plotly.graph_objs as go

    import lds.tracking.utils
    import lds.simulation









.. GENERATED FROM PYTHON SOURCE LINES 23-25

Set initial conditions and parameters
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 25-39

.. code-block:: Python


    pos_x0 = 0.0
    pos_y0 = 0.0
    vel_x0 = 0.0
    vel_y0 = 0.0
    ace_x0 = 0.0
    ace_y0 = 0.0
    dt = 1e-3
    num_pos = 1000
    sigma_a = 1.0
    sigma_x = 1.0
    sigma_y = 1.0
    sqrt_diag_V0_value = 1e-03








.. GENERATED FROM PYTHON SOURCE LINES 40-42

Set LDS parameters
~~~~~~~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 42-50

.. code-block:: Python


    B, Q, Z, R, Qe = lds.tracking.utils.getLDSmatricesForTracking(
        dt=dt, sigma_a=sigma_a, sigma_x=sigma_x, sigma_y=sigma_y)
    R = np.diag([sigma_x**2, sigma_y**2])
    m0 = np.array([pos_x0, vel_x0, ace_x0, pos_y0, vel_y0, ace_y0],
                  dtype=np.double)
    V0 = np.diag(np.ones(len(m0))*sqrt_diag_V0_value**2)








.. GENERATED FROM PYTHON SOURCE LINES 51-55

Sample from the LDS
~~~~~~~~~~~~~~~~~~~
View source code of `lds.simulation.simulateLDS
<https://joacorapela.github.io/lds_python/_modules/lds/simulation.html#simulateLDS>`_

.. GENERATED FROM PYTHON SOURCE LINES 55-59

.. code-block:: Python


    x0, x, y = lds.simulation.simulateLDS(N=num_pos, B=B, Q=Q, Z=Z, R=R,
                                                 m0=m0, V0=V0)








.. GENERATED FROM PYTHON SOURCE LINES 60-62

Plot state positions and measurements
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 62-77

.. code-block:: Python

    fig = go.Figure()
    trace_x = go.Scatter(x=x[0, :], y=x[3, :], mode="markers",
                         showlegend=True, name="state position")
    trace_y = go.Scatter(x=y[0, :], y=y[1, :], mode="markers",
                         showlegend=True, name="measured position", opacity=0.3)
    trace_start = go.Scatter(x=[x0[0]], y=[x0[3]], mode="markers",
                             text="initial state position", marker={"size": 7},
                             showlegend=False)
    fig.add_trace(trace_x)
    fig.add_trace(trace_y)
    fig.add_trace(trace_start)
    # fig_filename_pattern = "../../figures/simulated_pos.{:s}"
    # fig.write_image(fig_filename_pattern.format("png"))
    # fig.write_html(fig_filename_pattern.format("html"))
    fig





.. raw:: html

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.. _sphx_glr_download_auto_examples_tracking_plotSimulatedTrajectoryDWPA.py:

.. only:: html

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    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/joacorapela/lds_python/gh-pages?filepath=notebooks/auto_examples/tracking/plotSimulatedTrajectoryDWPA.ipynb
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    .. container:: sphx-glr-download sphx-glr-download-zip

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