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/Kalman-and-Bayesian-Filters-in-Python

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

Examples

See my book Kalman and Bayesian Filters in Python https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python

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 non-zero, 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 : list-like list of measurements at each time step self.dt Missing measurements must be represented by ‘None’. Rs : list-like, 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. 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 (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 z : np.array measurement corresponding to the given state