Added AxialKalmanFilter

Author: FlorianPfaff

pyrecest/filters/axial_kalman_filter.py

@@ -0,0 +1,54 @@
+import numpy as np
+from pyrecest.distributions import GaussianDistribution
+from beartype import beartype
+from pyrecest.filters.abstract_axial_filter import AbstractAxialFilter
+
+class AxialKalmanFilter(AbstractAxialFilter):
+    def __init__(self, initial_state=None):
+        if initial_state is None:
+            initial_state = GaussianDistribution(np.array([1, 0, 0, 0]), np.eye(4, 4))
+        self.filter_state = initial_state
+
+    @property
+    def filter_state(self):
+        return self._filter_state
+        
+    @filter_state.setter
+    @beartype
+    def filter_state(self, new_state: GaussianDistribution):
+        assert new_state.mu.shape == (2,) or new_state.mu.shape == (4,), "mu must be a 2d or 4d vector"
+        assert abs(np.linalg.norm(new_state.mu) - 1) < 1e-5, "mean must be a unit vector"
+        self._filter_state = new_state
+        # TODO: define composition operator
+
+    @beartype
+    def predict_identity(self, gauss_w: GaussianDistribution):
+        assert abs(np.linalg.norm(gauss_w.mu) - 1) < 1e-5, "mean must be a unit vector"
+        mu_ = self.composition_operator(self.gauss.mu, gauss_w.mu)
+        C_ = self.gauss.C + gauss_w.C
+        self.filter_state = GaussianDistribution(mu_, C_)
+
+    @beartype
+    def update_identity(self, gauss_v: GaussianDistribution, z: np.ndarray):
+        assert abs(np.linalg.norm(gauss_v.mu) - 1) < 1e-5, "mean must be a unit vector"
+        assert gauss_v.mu.shape[0] == self.gauss.mu.shape[0]
+        assert np.shape(z) == np.shape(self.gauss.mu)
+        assert abs(np.linalg.norm(z) - 1) < 1e-5, "measurement must be a unit vector"
+
+        mu_v_conj = np.concatenate(([gauss_v.mu[0]], -gauss_v.mu[1:]))
+        z = self.composition_operator(mu_v_conj, z)
+
+        if np.dot(z, self.gauss.mu) < 0:
+            z = -z
+
+        d = self.dim
+        H = np.eye(d, d)
+        IS = H @ self.filter_state.C @ H.T + gauss_v.C
+        K = self.filter_state.C @ H.T @ np.linalg.inv(IS)
+        IM = z - H @ self.filter_state.mu
+        mu = self.filter_state.mu + K @ IM
+        C = (np.eye(d, d) - K @ H) @ self.filter_state.C
+
+        mu = mu / np.linalg.norm(mu)
+        self.filter_state = GaussianDistribution(mu, C)
+