FadingKalmanFilter¶
Implements a fading memory Kalman filter.
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.
Fading Memory Kalman filter

class
filterpy.kalman.
FadingKalmanFilter
(alpha, dim_x, dim_z, dim_u=0)[source]¶ 
__init__
(alpha, dim_x, dim_z, dim_u=0)[source]¶ Create a Kalman filter. You are responsible for setting the various state variables to reasonable values; the defaults below will not give you a functional filter.
Parameters: alpha : float, >= 1
alpha controls how much you want the filter to forget past measurements. alpha==1 yields identical performance to the Kalman filter. A typical application might use 1.01
dim_x : int
Number of state variables for the Kalman filter. For example, if you are tracking the position and velocity of an object in two dimensions, dim_x would be 4.
This is used to set the default size of P, Q, and u
dim_z : int
Number of of measurement inputs. For example, if the sensor provides you with position in (x,y), dim_z would be 2.
dim_u : int (optional)
size of the control input, if it is being used. Default value of 0 indicates it is not used.
**Attributes**
You will have to assign reasonable values to all of these before
running the filter. All must have dtype of float
x : ndarray (dim_x, 1), default = [0,0,0...0]
state of the filter
P : ndarray (dim_x, dim_x), default identity matrix
covariance matrix
Q : ndarray (dim_x, dim_x), default identity matrix
Process uncertainty matrix
R : ndarray (dim_z, dim_z), default identity matrix
measurement uncertainty
H : ndarray (dim_z, dim_x)
measurement function
F : ndarray (dim_x, dim_x)
state transistion matrix
B : ndarray (dim_x, dim_u), default 0
control transition matrix

update
(z, R=None)[source]¶ Add a new measurement (z) to the kalman filter. If z is None, nothing is changed.
Parameters: z : np.array
measurement for this update.
R : np.array, scalar, or None
Optionally provide R to override the measurement noise for this one call, otherwise self.R will be used.

predict
(u=0)[source]¶ Predict next position.
Parameters: u : np.array
Optional control vector. If nonzero, it is multiplied by B to create the control input into the system.

batch_filter
(zs, Rs=None, update_first=False)[source]¶ Batch processes a sequences of measurements.
Parameters: zs : listlike
list of measurements at each time step self.dt Missing measurements must be represented by ‘None’.
Rs : listlike, optional
optional list of values to use for the measurement error covariance; a value of None in any position will cause the filter to use self.R for that time step.
update_first : bool, optional,
controls whether the order of operations is update followed by predict, or predict followed by update. Default is predict>update.
Returns: means: np.array((n,dim_x,1))
array of the state for each time step after the update. Each entry is an np.array. In other words means[k,:] is the state at step k.
covariance: np.array((n,dim_x,dim_x))
array of the covariances for each time step after the update. In other words covariance[k,:,:] is the covariance at step k.
means_predictions: np.array((n,dim_x,1))
array of the state for each time step after the predictions. Each entry is an np.array. In other words means[k,:] is the state at step k.
covariance_predictions: np.array((n,dim_x,dim_x))
array of the covariances for each time step after the prediction. In other words covariance[k,:,:] is the covariance at step k.

get_prediction
(u=0)[source]¶ Predicts the next state of the filter and returns it. Does not alter the state of the filter.
Parameters: u : np.array
optional control input
Returns: (x, P)
State vector and covariance array of the prediction.

residual_of
(z)[source]¶ returns the residual for the given measurement (z). Does not alter the state of the filter.

measurement_of_state
(x)[source]¶ Helper function that converts a state into a measurement.
Parameters: x : np.array
kalman state vector
Returns: z : np.array
measurement corresponding to the given state

Q
¶ Process uncertainty

P
¶ covariance matrix

R
¶ measurement uncertainty

H
¶ Measurement function

F
¶ state transition matrix

B
¶ control transition matrix

x
¶ state vector.

K
¶ Kalman gain

y
¶ measurement residual (innovation)

S
¶ system uncertainy in measurement space
