# LeastSquaresFilter¶

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.leastsq.LeastSquaresFilter(dt, order, noise_sigma=0.0)[source]

Implements a Least Squares recursive filter. Formulation is per Zarchan [R12].

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.

References

 [R12] (1, 2) Zarchan and Musoff. “Fundamentals of Kalman Filtering: A Practical Approach.” Third Edition. AIAA, 2009.

Methods

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(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. 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.
__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.
reset()[source]

reset filter back to state at time of construction

errors()[source]

Computes and returns the error and standard deviation of the filter at this time step.

Returns: error : np.array size 1xorder+1 std : np.array size 1xorder+1