LeastSquaresFilter¶
Copyright 2015 Roger R Labbe Jr.
FilterPy library. http://github.com/rlabbe/filterpy
Documentation at: https://filterpy.readthedocs.org
Supporting book at: https://github.com/rlabbe/KalmanandBayesianFiltersinPython
This is licensed under an MIT license. See the readme.MD file for more information.

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.
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.
References
[1] (1, 2) Zarchan and Musoff. “Fundamentals of Kalman Filtering: A Practical Approach.” Third Edition. AIAA, 2009. Examples
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.update(z) # get the filtered estimate. print('error: {}, velocity error: {}'.format( lsq.error, lsq.derror))
Attributes:  n : int
step in the recursion. 0 prior to first call, 1 after the first call, etc.
 K : np.array
Gains for the filter. K[0] for all orders, K[1] for orders 0 and 1, and K[2] for order 2
 x: np.array (order + 1, 1)
estimate(s) of the output. It is a vector containing the estimate x and the derivatives of x: [x x’ x’‘].T. It contains as many derivatives as the order allows. That is, a zero order filter has no derivatives, a first order has one derivative, and a second order has two.
 y : float
residual (difference between measurement projection of previous estimate to current time).

__init__
(dt, order, noise_sigma=0.0)[source]¶ x.__init__(…) initializes x; see help(type(x)) for signature