import numpy as np
[docs]
def get_kalman_gain(dt, A, C, Q, R, iterations=100):
P = np.zeros_like(Q)
for _ in range(iterations):
P = A.dot(P).dot(A.T) + dt * Q
S = C.dot(P).dot(C.T) + R
K = P.dot(C.T).dot(np.linalg.inv(S))
P = (np.eye(len(P)) - K.dot(C)).dot(P)
return K
[docs]
class KF1D:
# this EKF assumes constant covariance matrix, so calculations are much simpler
# the Kalman gain also needs to be precomputed using the control module
def __init__(self, x0, A, C, K):
self.x0_0 = x0[0][0]
self.x1_0 = x0[1][0]
self.A0_0 = A[0][0]
self.A0_1 = A[0][1]
self.A1_0 = A[1][0]
self.A1_1 = A[1][1]
self.C0_0 = C[0]
self.C0_1 = C[1]
self.K0_0 = K[0][0]
self.K1_0 = K[1][0]
self.A_K_0 = self.A0_0 - self.K0_0 * self.C0_0
self.A_K_1 = self.A0_1 - self.K0_0 * self.C0_1
self.A_K_2 = self.A1_0 - self.K1_0 * self.C0_0
self.A_K_3 = self.A1_1 - self.K1_0 * self.C0_1
# K matrix needs to be pre-computed as follow:
# import control
# (x, l, K) = control.dare(np.transpose(self.A), np.transpose(self.C), Q, R)
# self.K = np.transpose(K)
[docs]
def update(self, meas):
#self.x = np.dot(self.A_K, self.x) + np.dot(self.K, meas)
x0_0 = self.A_K_0 * self.x0_0 + self.A_K_1 * self.x1_0 + self.K0_0 * meas
x1_0 = self.A_K_2 * self.x0_0 + self.A_K_3 * self.x1_0 + self.K1_0 * meas
self.x0_0 = x0_0
self.x1_0 = x1_0
return [self.x0_0, self.x1_0]
@property
def x(self):
return [[self.x0_0], [self.x1_0]]
[docs]
def set_x(self, x):
self.x0_0 = x[0][0]
self.x1_0 = x[1][0]