## Introduction and Overview¶

Implements a polynomial fading memory filter. You can achieve the same results, and more, using the KalmanFilter class. However, some books use this form of the fading memory filter, so it is here for completeness. I suppose some would also find this simpler to use than the standard Kalman filter.

Copyright 2015 Roger R Labbe Jr.

FilterPy library. http://github.com/rlabbe/filterpy

Supporting book at: https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python

class filterpy.memory.FadingMemoryFilter(x0, dt, order, beta)[source]

Creates a fading memory filter of order 0, 1, or 2.

The KalmanFilter class also implements a more general fading memory filter and should be preferred in most cases. This is probably faster for low order systems.

This algorithm is based on the fading filter algorithm developed in Zarcan’s “Fundamentals of Kalman Filtering” [1].

Parameters: x0 : 1D np.array or scalar Initial value for the filter state. Each value can be a scalar or a np.array. You can use a scalar for x0. If order > 0, then 0.0 is assumed for the higher order terms. x[0] is the value being tracked x[1] is the first derivative (for order 1 and 2 filters) x[2] is the second derivative (for order 2 filters) dt : scalar timestep order : int order of the filter. Defines the order of the system 0 - assumes system of form x = a_0 + a_1*t 1 - assumes system of form x = a_0 +a_1*t + a_2*t^2 2 - assumes system of form x = a_0 +a_1*t + a_2*t^2 + a_3*t^3 beta : float filter gain parameter.

References

Paul Zarchan and Howard Musoff. “Fundamentals of Kalman Filtering: A Practical Approach” American Institute of Aeronautics and Astronautics, Inc. Fourth Edition. p. 521-536. (2015)

Attributes: x : np.array State of the filter. x[0] is the value being tracked x[1] is the derivative of x[0] (order 1 and 2 only) x[2] is the 2nd derivative of x[0] (order 2 only) This is always an np.array, even for order 0 where you can initialize x0 with a scalar. P : np.array The diagonal of the covariance matrix. Assumes that variance is one; multiply by sigma^2 to get the actual variances. This is a constant and will not vary as the filter runs. e : np.array The truncation error of the filter. Each term must be multiplied by the a_1, a_2, or a_3 of the polynomial for the system. For example, if the filter is order 2, then multiply all terms of self.e by a_3 to get the actual error. Multipy by a_2 for order 1, and a_1 for order 0.
__init__(x0, dt, order, beta)[source]

x.__init__(…) initializes x; see help(type(x)) for signature

update(z)[source]

update the filter with measurement z. z must be the same type (or treatable as the same type) as self.x[0].