# 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 [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

reset()[source]

reset filter back to state at time of construction

update(z)[source]

Update filter with new measurement z

Returns: x : np.array estimate for this time step (same as self.x)
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