Skip to content

one_euro_filter

OneEuroFilter

One Euro Filter for smoothing signals, taken from https://github.com/HoBeom/OneEuroFilter-Numpy

Examples:

>>> from fast_cody import OneEuroFilter
>>> import numpy as np
>>> mu = np.ones((3, 1))
>>> x0 =  np.random.randn(3, 1) + mu
>>> f = OneEuroFilter(x0)
>>> x = np.random.randn(3, 1) + mu
>>> x_filtered = f(x)
>>> print(x_filtered)
Source code in src\fast_cody\one_euro_filter.py 
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
class OneEuroFilter:
    """
    One Euro Filter for smoothing signals, taken from https://github.com/HoBeom/OneEuroFilter-Numpy

    Examples
    --------
    ```
    >>> from fast_cody import OneEuroFilter
    >>> import numpy as np
    >>> mu = np.ones((3, 1))
    >>> x0 =  np.random.randn(3, 1) + mu
    >>> f = OneEuroFilter(x0)
    >>> x = np.random.randn(3, 1) + mu
    >>> x_filtered = f(x)
    >>> print(x_filtered)
    ```
    """
    def __init__(self, x0, dx0=0.0, min_cutoff=1.0, beta=0.0,
                 d_cutoff=1.0):
        """Initialize the one euro filter.

        Parameters
        ----------
        x0 : float
            Initial value for the filtered signal.
        dx0 : float
            Initial value for the derivative.
        min_cutoff : float
            Minimum cutoff frequency.
        beta : float
            Cutoff slope.
        d_cutoff : float
            Cutoff frequency for the derivate.

        """
        # The parameters.
        self.data_shape = x0.shape
        self.min_cutoff = np.full(x0.shape, min_cutoff)
        self.beta = np.full(x0.shape, beta)
        self.d_cutoff = np.full(x0.shape, d_cutoff)
        # Previous values.
        self.x_prev = x0.astype(float)
        self.dx_prev = np.full(x0.shape, dx0)
        self.t_prev = time()

    def __call__(self, x):
        """Compute the filtered signal."""
        assert x.shape == self.data_shape

        t = time()
        t_e = t - self.t_prev
        t_e = np.full(x.shape, t_e)

        # The filtered derivative of the signal.
        a_d = smoothing_factor(t_e, self.d_cutoff)
        dx = (x - self.x_prev) / t_e
        dx_hat = exponential_smoothing(a_d, dx, self.dx_prev)

        # The filtered signal.
        cutoff = self.min_cutoff + self.beta * np.abs(dx_hat)
        a = smoothing_factor(t_e, cutoff)
        x_hat = exponential_smoothing(a, x, self.x_prev)

        # Memorize the previous values.
        self.x_prev = x_hat
        self.dx_prev = dx_hat
        self.t_prev = t

        return x_hat

__call__(x)

Compute the filtered signal.

Source code in src\fast_cody\one_euro_filter.py 
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
def __call__(self, x):
    """Compute the filtered signal."""
    assert x.shape == self.data_shape

    t = time()
    t_e = t - self.t_prev
    t_e = np.full(x.shape, t_e)

    # The filtered derivative of the signal.
    a_d = smoothing_factor(t_e, self.d_cutoff)
    dx = (x - self.x_prev) / t_e
    dx_hat = exponential_smoothing(a_d, dx, self.dx_prev)

    # The filtered signal.
    cutoff = self.min_cutoff + self.beta * np.abs(dx_hat)
    a = smoothing_factor(t_e, cutoff)
    x_hat = exponential_smoothing(a, x, self.x_prev)

    # Memorize the previous values.
    self.x_prev = x_hat
    self.dx_prev = dx_hat
    self.t_prev = t

    return x_hat

__init__(x0, dx0=0.0, min_cutoff=1.0, beta=0.0, d_cutoff=1.0)

Initialize the one euro filter.

Parameters:

Name Type Description Default
x0 float

Initial value for the filtered signal.

 required
dx0 float

Initial value for the derivative.

 0.0
min_cutoff float

Minimum cutoff frequency.

 1.0
beta float

Cutoff slope.

 0.0
d_cutoff float

Cutoff frequency for the derivate.

 1.0
Source code in src\fast_cody\one_euro_filter.py 
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
def __init__(self, x0, dx0=0.0, min_cutoff=1.0, beta=0.0,
             d_cutoff=1.0):
    """Initialize the one euro filter.

    Parameters
    ----------
    x0 : float
        Initial value for the filtered signal.
    dx0 : float
        Initial value for the derivative.
    min_cutoff : float
        Minimum cutoff frequency.
    beta : float
        Cutoff slope.
    d_cutoff : float
        Cutoff frequency for the derivate.

    """
    # The parameters.
    self.data_shape = x0.shape
    self.min_cutoff = np.full(x0.shape, min_cutoff)
    self.beta = np.full(x0.shape, beta)
    self.d_cutoff = np.full(x0.shape, d_cutoff)
    # Previous values.
    self.x_prev = x0.astype(float)
    self.dx_prev = np.full(x0.shape, dx0)
    self.t_prev = time()