EkfdPredict and GmekfPredict classes and tests

pyest/filters/Gmkf.py

@@ -1,7 +1,7 @@
 import numpy as np
 import pyest.gm as pygm
 from pyest.filters import GaussianMixturePredict, GaussianMixtureUpdate
-from pyest.filters import KfdPredict, KfdUpdate, EkfdPredict
+from pyest.filters import KfdPredict, KfdUpdate, EkfdPredict, EkfdUpdate
 from pyest.utils import make_tuple
 
 
@@ -250,3 +250,148 @@ def lin_gauss_likelihood_agreement(z, m, P, H, R, L=None, h_args=()):
     h_args = make_tuple(h_args)
     Hk = H(*h_args)
     return pygm.eval_mvnpdf(z, Hk@m, Hk@[email protected] + LRLt)
+
+class GmekfUpdate(EkfdUpdate, GaussianMixtureUpdate):
+    """ Discrete Gaussian Mixture Extended Kalman Filter Update
+
+    Parameters
+    ----------
+    h  : callable
+        measurement function of the form :math:`h(x, ...)`
+    H  : ndarray or callable
+        (nz,nx) measurement Jacobian matrix
+        z_k = H(tk, xk, *args) @ x. If provided an ndarray instead, H will
+        automatically be recast as a callable.
+    R  : ndarray
+        (ny,ny) measurement noise covariance matrix
+    L  : (optional) ndarray
+        (nz,ny) mapping matrix mapping measurement noise into
+        measurement space
+    cov_method : (optional) string
+        method to use for covariance update. Valid options include 'general'
+        (default), 'Joseph', 'standard', and 'KWK'.
+
+    Written by Keith LeGrand, March 2019
+    """
+
+    def __init__(self, *args, **kwargs):
+        super().__init__(*args, **kwargs)
+
+    def __lin_gauss_likelihood_agreement(self, z, zhat, W):
+        return pygm.eval_mvnpdf(z, zhat, W)
+
+    def lin_gauss_cond_likelihood_prod(self, m, P, z, h_args=(), interm_vals=False):
+        """ compute the product of the linear Gaussian likelihood function and
+        another Gaussian pdf
+
+        Parameters
+        ----------
+        m : ndarray
+            (nx,) prior mean
+        P : ndarray
+            (nx,nx) prior covariance matrix
+        z  : ndarray
+            (nz,) measurement
+        h_args : (optional) tuple
+            deterministic parameters to be passed to measurement function
+        interm_vals : (optional) Boolean
+            if True, returns intermediate values from computation. False by default
+
+        Returns
+        -------
+        mp : ndarray
+            (nx,) posterior mean
+        Pp : ndarray
+            (nx,nx) posterior state error covariance
+        q : float
+            likelihood agreement, :math:`q = N(z; Hm, HPH' + R)`
+
+        If interm_vals is true, additionally returns a dictionary containing:
+        W : ndarray
+            (nz,nz) innovatations covariance
+        C : (ndarray)
+            (nx,nz) cross-covariance
+        K : (ndarray)
+            gain matrix
+        zhat : (ndarray)
+            predicted measurement
+
+        """
+        mp, Pp, interm = super().update(m, P, z, interm_vals=True, h_args=h_args)
+        q = self.__lin_gauss_likelihood_agreement(z, interm['zhat'], interm['W'])
+
+        if not interm_vals:
+            return mp, Pp, q
+        else:
+            return mp, Pp, q, interm
+
+    def cond_likelihood_prod(self, m, P, z, h_args=(), interm_vals=False):
+        """ compute the product of the linear Gaussian likelihood function and
+        another Gaussian pdf
+
+        Parameters
+        ----------
+        m : ndarray
+            (nx,) prior mean
+        P : ndarray
+            (nx,nx) prior covariance matrix
+        z  : ndarray
+            (nz,) measurement
+        h_args : (optional) tuple
+            deterministic parameters to be passed to measurement function
+        interm_vals : (optional) Boolean
+            if True, returns intermediate values from computation. False by default
+
+        Returns
+        -------
+        mp : ndarray
+            (nx,) posterior mean
+        Pp : ndarray
+            (nx,nx) posterior state error covariance
+        q : float
+            likelihood agreement, :math:`q = N(z; Hm, HPH' + R)`
+
+        If interm_vals is true, additionally returns a dictionary containing:
+        W : ndarray
+            (nz,nz) innovatations covariance
+        C : ndarray
+            (nx,nz) cross-covariance
+        K : ndarray
+            gain matrix
+        zhat : (ndarray)
+            predicted measurement
+
+        """
+        return self.lin_gauss_cond_likelihood_prod(m, P, z, h_args=h_args, interm_vals=interm_vals)
+
+    def update(self, pkm, zk, unnormalized=False, h_args=(), *args, **kwargs):
+        """ measurement-update of gm
+
+        Parameters
+        ----------
+        pkm : GaussianMixture
+            prior density at time tk
+        zk : ndarray
+            (nz,) measurement at time k
+        unnormalized : optional
+            if True, returns unnormalized distribution. False by default
+        h_args : (optional) tuple
+            deterministic parameters to be passed to measurement function
+        """
+        wkp = np.empty_like(pkm.w, dtype=float)
+        mkp = np.empty_like(pkm.m, dtype=float)
+        Pkp = np.empty_like(pkm.P, dtype=float)
+        for i, (wm,mm,Pm) in enumerate(pkm):
+            print(f"updating mixand {i+1} out of {len(pkm)}")
+            mkp[i], Pkp[i], q, interm_vals = self.lin_gauss_cond_likelihood_prod(mm, Pm, zk, h_args=h_args, interm_vals=True)
+            print(f"Q values: {q}")
+            print(f"true z: {zk}")
+            print(f"z_hat:  {interm_vals['zhat']}")
+            # print(f"W: {interm_vals["W"]}")
+            # TODO: test (z-zhat).T @ inv(W) @ (z-zhat)
+            wkp[i] = wm*q
+
+        if not unnormalized:
+            wkp /= np.sum(wkp)
+
+        return pygm.GaussianMixture(wkp, mkp, Pkp)