Source code for filterpy.kalman.information_filter
# -*- coding: utf-8 -*-
# pylint: disable=invalid-name, too-many-instance-attributes
"""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.
"""
from __future__ import (absolute_import, division)
from copy import deepcopy
import math
import sys
import numpy as np
from numpy import dot, zeros, eye
from filterpy.stats import logpdf
from filterpy.common import pretty_str, reshape_z
[docs]class InformationFilter(object):
"""
Create a linear Information filter. Information filters
compute the
inverse of the Kalman filter, allowing you to easily denote having
no information at initialization.
You are responsible for setting the various state variables to reasonable
values; the defaults below will not give you a functional filter.
Parameters
----------
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.
self.compute_log_likelihood = compute_log_likelihood
self.log_likelihood = math.log(sys.float_info.min)
Attributes
----------
x : numpy.array(dim_x, 1)
State estimate vector
P_inv : numpy.array(dim_x, dim_x)
inverse state covariance matrix
x_prior : numpy.array(dim_x, 1)
Prior (predicted) state estimate. The *_prior and *_post attributes
are for convienence; they store the prior and posterior of the
current epoch. Read Only.
P_inv_prior : numpy.array(dim_x, dim_x)
Inverse prior (predicted) state covariance matrix. Read Only.
x_post : numpy.array(dim_x, 1)
Posterior (updated) state estimate. Read Only.
P_inv_post : numpy.array(dim_x, dim_x)
Inverse posterior (updated) state covariance matrix. Read Only.
z : ndarray
Last measurement used in update(). Read only.
R_inv : numpy.array(dim_z, dim_z)
inverse of measurement noise matrix
Q : numpy.array(dim_x, dim_x)
Process noise matrix
H : numpy.array(dim_z, dim_x)
Measurement function
y : numpy.array
Residual of the update step. Read only.
K : numpy.array(dim_x, dim_z)
Kalman gain of the update step. Read only.
S : numpy.array
Systen uncertaintly projected to measurement space. Read only.
log_likelihood : float
log-likelihood of the last measurement. Read only.
likelihood : float
likelihood of last measurment. Read only.
Computed from the log-likelihood. The log-likelihood can be very
small, meaning a large negative value such as -28000. Taking the
exp() of that results in 0.0, which can break typical algorithms
which multiply by this value, so by default we always return a
number >= sys.float_info.min.
inv : function, default numpy.linalg.inv
If you prefer another inverse function, such as the Moore-Penrose
pseudo inverse, set it to that instead: kf.inv = np.linalg.pinv
Examples
--------
See my book Kalman and Bayesian Filters in Python
https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
"""
[docs] def __init__(self, dim_x, dim_z, dim_u=0, compute_log_likelihood=True):
if dim_x < 1:
raise ValueError('dim_x must be 1 or greater')
if dim_z < 1:
raise ValueError('dim_z must be 1 or greater')
if dim_u < 0:
raise ValueError('dim_u must be 0 or greater')
self.dim_x = dim_x
self.dim_z = dim_z
self.dim_u = dim_u
self.x = zeros((dim_x, 1)) # state
self.P_inv = eye(dim_x) # uncertainty covariance
self.Q = eye(dim_x) # process uncertainty
self.B = 0. # control transition matrix
self._F = 0. # state transition matrix
self._F_inv = 0. # state transition matrix
self.H = np.zeros((dim_z, dim_x)) # Measurement function
self.R_inv = eye(dim_z) # state uncertainty
self.z = np.array([[None]*self.dim_z]).T
# gain and residual are computed during the innovation step. We
# save them so that in case you want to inspect them for various
# purposes
self.K = 0. # kalman gain
self.y = zeros((dim_z, 1))
self.z = zeros((dim_z, 1))
self.S = 0. # system uncertainty in measurement space
# identity matrix. Do not alter this.
self._I = np.eye(dim_x)
self._no_information = False
self.compute_log_likelihood = compute_log_likelihood
self.log_likelihood = math.log(sys.float_info.min)
self.likelihood = sys.float_info.min
self.inv = np.linalg.inv
# save priors and posteriors
self.x_prior = np.copy(self.x)
self.P_inv_prior = np.copy(self.P_inv)
self.x_post = np.copy(self.x)
self.P_inv_post = np.copy(self.P_inv)
[docs] def update(self, z, R_inv=None):
"""
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.
"""
if z is None:
self.z = None
self.x_post = self.x.copy()
self.P_inv_post = self.P_inv.copy()
return
if R_inv is None:
R_inv = self.R_inv
elif np.isscalar(R_inv):
R_inv = eye(self.dim_z) * R_inv
# rename for readability and a tiny extra bit of speed
H = self.H
H_T = H.T
P_inv = self.P_inv
x = self.x
if self._no_information:
self.x = dot(P_inv, x) + dot(H_T, R_inv).dot(z)
self.P_inv = P_inv + dot(H_T, R_inv).dot(H)
self.log_likelihood = math.log(sys.float_info.min)
self.likelihood = sys.float_info.min
else:
# y = z - Hx
# error (residual) between measurement and prediction
self.y = z - dot(H, x)
# S = HPH' + R
# project system uncertainty into measurement space
self.S = P_inv + dot(H_T, R_inv).dot(H)
self.K = dot(self.inv(self.S), H_T).dot(R_inv)
# x = x + Ky
# predict new x with residual scaled by the kalman gain
self.x = x + dot(self.K, self.y)
self.P_inv = P_inv + dot(H_T, R_inv).dot(H)
self.z = np.copy(reshape_z(z, self.dim_z, np.ndim(self.x)))
if self.compute_log_likelihood:
self.log_likelihood = logpdf(x=self.y, cov=self.S)
self.likelihood = math.exp(self.log_likelihood)
if self.likelihood == 0:
self.likelihood = sys.float_info.min
# save measurement and posterior state
self.z = deepcopy(z)
self.x_post = self.x.copy()
self.P_inv_post = self.P_inv.copy()
[docs] def predict(self, u=0):
""" Predict next position.
Parameters
----------
u : ndarray
Optional control vector. If non-zero, it is multiplied by B
to create the control input into the system.
"""
# x = Fx + Bu
A = dot(self._F_inv.T, self.P_inv).dot(self._F_inv)
#pylint: disable=bare-except
try:
AI = self.inv(A)
invertable = True
if self._no_information:
try:
self.x = dot(self.inv(self.P_inv), self.x)
except:
self.x = dot(0, self.x)
self._no_information = False
except:
invertable = False
self._no_information = True
if invertable:
self.x = dot(self._F, self.x) + dot(self.B, u)
self.P_inv = self.inv(AI + self.Q)
# save priors
self.P_inv_prior = np.copy(self.P_inv)
self.x_prior = np.copy(self.x)
else:
I_PF = self._I - dot(self.P_inv, self._F_inv)
FTI = self.inv(self._F.T)
FTIX = dot(FTI, self.x)
AQI = self.inv(A + self.Q)
self.x = dot(FTI, dot(I_PF, AQI).dot(FTIX))
# save priors
self.x_prior = np.copy(self.x)
self.P_inv_prior = np.copy(AQI)
[docs] def batch_filter(self, zs, Rs=None, update_first=False, saver=None):
""" 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.
saver : filterpy.common.Saver, optional
filterpy.common.Saver object. If provided, saver.save() will be
called after every epoch
Returns
-------
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`.
"""
raise NotImplementedError("this is not implemented yet")
#pylint: disable=unreachable, no-member
# this is a copy of the code from kalman_filter, it has not been
# turned into the information filter yet. DO NOT USE.
n = np.size(zs, 0)
if Rs is None:
Rs = [None] * n
# mean estimates from Kalman Filter
means = zeros((n, self.dim_x, 1))
# state covariances from Kalman Filter
covariances = zeros((n, self.dim_x, self.dim_x))
if update_first:
for i, (z, r) in enumerate(zip(zs, Rs)):
self.update(z, r)
means[i, :] = self.x
covariances[i, :, :] = self._P
self.predict()
if saver is not None:
saver.save()
else:
for i, (z, r) in enumerate(zip(zs, Rs)):
self.predict()
self.update(z, r)
means[i, :] = self.x
covariances[i, :, :] = self._P
if saver is not None:
saver.save()
return (means, covariances)
@property
def F(self):
"""State Transition matrix"""
return self._F
@F.setter
def F(self, value):
"""State Transition matrix"""
self._F = value
self._F_inv = self.inv(self._F)
@property
def P(self):
"""State covariance matrix"""
return self.inv(self.P_inv)
def __repr__(self):
return '\n'.join([
'InformationFilter object',
pretty_str('dim_x', self.dim_x),
pretty_str('dim_z', self.dim_z),
pretty_str('dim_u', self.dim_u),
pretty_str('x', self.x),
pretty_str('P_inv', self.P_inv),
pretty_str('x_prior', self.x_prior),
pretty_str('P_inv_prior', self.P_inv_prior),
pretty_str('F', self.F),
pretty_str('_F_inv', self._F_inv),
pretty_str('Q', self.Q),
pretty_str('R_inv', self.R_inv),
pretty_str('H', self.H),
pretty_str('K', self.K),
pretty_str('y', self.y),
pretty_str('z', self.z),
pretty_str('S', self.S),
pretty_str('B', self.B),
pretty_str('log-likelihood', self.log_likelihood),
pretty_str('likelihood', self.likelihood),
pretty_str('inv', self.inv)
])