# Source code for filterpy.kalman.mmae

# -*- 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:

Supporting book at:
https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python

"""
from __future__ import absolute_import, division

from copy import deepcopy
import numpy as np
from filterpy.common import pretty_str

[docs]class MMAEFilterBank(object):
"""
Implements the fixed Multiple Model Adaptive Estimator (MMAE). This
is a bank of independent Kalman filters. This estimator computes the
likelihood that each filter is the correct one, and blends their state
estimates weighted by their likelihood to produce the state estimate.

Parameters
----------

filters : list of Kalman filters
List of Kalman filters.

p : list-like of floats
Initial probability that each filter is the correct one. In general
you'd probably set each element to 1./len(p).

dim_x : float
number of random variables in the state X

H : Measurement matrix

Attributes
----------
x : numpy.array(dim_x, 1)
Current state estimate. Any call to update() or predict() updates
this variable.

P : numpy.array(dim_x, dim_x)
Current state covariance matrix. Any call to update() or predict()

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

P_prior : numpy.array(dim_x, dim_x)
Prior (predicted) state covariance matrix. Read Only.

x_post : numpy.array(dim_x, 1)
Posterior (updated) state estimate. Read Only.

P_post : numpy.array(dim_x, dim_x)
Posterior (updated) state covariance matrix. Read Only.

z : ndarray
Last measurement used in update(). Read only.

filters : list of Kalman filters
List of Kalman filters.

Examples
--------

..code:
ca = make_ca_filter(dt, noise_factor=0.6)
cv = make_ca_filter(dt, noise_factor=0.6)
cv.F[:,2] = 0 # remove acceleration term
cv.P[2,2] = 0
cv.Q[2,2] = 0

filters = [cv, ca]
bank = MMAEFilterBank(filters, p=(0.5, 0.5), dim_x=3)

for z in zs:
bank.predict()
bank.update(z)

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

References
----------

Zarchan and Musoff. "Fundamentals of Kalman filtering: A Practical
Approach." AIAA, third edition.

"""

[docs]    def __init__(self, filters, p, dim_x, H=None):
if len(filters) != len(p):
raise ValueError('length of filters and p must be the same')

if dim_x < 1:
raise ValueError('dim_x must be >= 1')

self.filters = filters
self.p = np.asarray(p)
self.dim_x = dim_x
if H is None:
self.H = None
else:
self.H = np.copy(H)

# try to form a reasonable initial values, but good luck!
try:
self.z = np.copy(filters.z)
self.x = np.copy(filters.x)
self.P = np.copy(filters.P)

except AttributeError:
self.z = 0
self.x = None
self.P = None

# these will always be a copy of x,P after predict() is called
self.x_prior = self.x.copy()
self.P_prior = self.P.copy()

# these will always be a copy of x,P after update() is called
self.x_post = self.x.copy()
self.P_post = self.P.copy()

[docs]    def predict(self, u=0):
"""
Predict next position using the Kalman filter state propagation
equations for each filter in the bank.

Parameters
----------

u : np.array
Optional control vector. If non-zero, it is multiplied by B
to create the control input into the system.
"""

for f in self.filters:
f.predict(u)

# save prior
self.x_prior = self.x.copy()
self.P_prior = self.P.copy()

[docs]    def update(self, z, R=None, H=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.

H : np.array,  or None
Optionally provide H to override the measurement function for this
one call, otherwise  self.H will be used.
"""

if H is None:
H = self.H

# new probability is recursively defined as prior * likelihood
for i, f in enumerate(self.filters):
f.update(z, R, H)
self.p[i] *= f.likelihood

self.p /= sum(self.p) # normalize

# compute estimated state and covariance of the bank of filters.
self.P = np.zeros(self.filters.P.shape)

# state can be in form [x,y,z,...] or [[x, y, z,...]].T
is_row_vector = (self.filters.x.ndim == 1)
if is_row_vector:
self.x = np.zeros(self.dim_x)
for f, p in zip(self.filters, self.p):
self.x += np.dot(f.x, p)
else:
self.x = np.zeros((self.dim_x, 1))
for f, p in zip(self.filters, self.p):
self.x = np.zeros((self.dim_x, 1))
self.x += np.dot(f.x, p)

for x, f, p in zip(self.x, self.filters, self.p):
y = f.x - x
self.P += p*(np.outer(y, y) + f.P)

# save measurement and posterior state
self.z = deepcopy(z)
self.x_post = self.x.copy()
self.P_post = self.P.copy()

def __repr__(self):
return '\n'.join([
'MMAEFilterBank object',
pretty_str('dim_x', self.dim_x),
pretty_str('x', self.x),
pretty_str('P', self.P),
pretty_str('log-p', self.p),
])