LeastSquaresFilter¶
Copyright 2014 Roger R Labbe Jr.
filterpy library. http://github.com/rlabbe/filterpy
Documentation at: https://filterpy.readthedocs.org
Supporting book at: https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
This is licensed under an MIT license. See the readme.MD file for more information.
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class
filterpy.leastsq.
LeastSquaresFilter
(dt, order, noise_sigma=0.0)[source]¶ Implements a Least Squares recursive filter. Formulation is per Zarchan [1].
Filter may be of order 0 to 2. Order 0 assumes the value being tracked is a constant, order 1 assumes that it moves in a line, and order 2 assumes that it is tracking a second order polynomial.
It is implemented to be directly callable like a function. See examples.
Example:
from filterpy.leastsq import LeastSquaresFilter lsq = LeastSquaresFilter(dt=0.1, order=1, noise_sigma=2.3) while True: z = sensor_reading() # get a measurement x = lsq(z) # get the filtered estimate. print('error: {}, velocity error: {}'.format(lsq.error, lsq.derror))
Member Variables
- n : int
- step in the recursion. 0 prior to first call, 1 after the first call, etc.
- K1,K2,K3 : float
- Gains for the filter. K1 for all orders, K2 for orders 0 and 1, and K3 for order 2
- x, dx, ddx: type(z)
- estimate(s) of the output. ‘d’ denotes derivative, so ‘dx’ is the first derivative of x, ‘ddx’ is the second derivative.
References
[1] Zarchan and Musoff. “Fundamentals of Kalman Filtering: A Practical Approach.” Third Edition. AIAA, 2009. Methods
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__init__
(dt, order, noise_sigma=0.0)[source]¶ Least Squares filter of order 0 to 2.
Parameters
- dt : float
- time step per update
- order : int
- order of filter 0..2
- noise_sigma : float
- sigma (std dev) in x. This allows us to calculate the error of the filter, it does not influence the filter output.