Introduction and Overview

This is a basic implementation of the information filter.

Copyright 2015 Roger R Labbe Jr.

FilterPy library.

Documentation at:

Supporting book at:

This is licensed under an MIT license. See the readme.MD file for more information.

class filterpy.kalman.InformationFilter(dim_x, dim_z, dim_u=0)[source]
__init__(dim_x, dim_z, dim_u=0)[source]

Create a Information filter. You are responsible for setting the various state variables to reasonable values; the defaults below will not give you a functional filter.


dim_x : int

Number of state variables for the 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.


See my book Kalman and Bayesian Filters in Python

update(z, R_inv=None)[source]

Add a new measurement (z) to the kalman filter. If z is None, nothing is changed.


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 next position.


u : ndarray

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.


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. 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. In other words covariance[k,:,:] is the covariance at step k.


Predicts the next state of the filter and returns it. Does not alter the state of the filter.


u : np.array

optional control input


(x, P)

State vector and covariance array of the prediction.


returns the residual for the given measurement (z). Does not alter the state of the filter.


Helper function that converts a state into a measurement.


x : np.array

kalman state vector


z : np.array

measurement corresponding to the given state


State Transition matrix