rlabbe
LinAlgError: 1-th leading minor of the array is not positive definite
Dear Friends,
I am a beginner in using the Unscented Kalman Filter (UKF) and would greatly appreciate your assistance with an issue I'm encountering. Despite my efforts, I consistently receive the error: LinAlgError: 1-th leading minor of the array is not positive definite.
I've tried to mitigate this issue by adding a regularization term to relax the condition when the state covariance matrix P becomes non-positive definite after the prediction step. However, despite numerous adjustments to the parameters, the error persists.
Currently, I'm working with a simple degradation model that incorporates a Wiener process. My goal is to understand and resolve this issue before further refining the model.
Any guidance or suggestions would be immensely helpful.
from filterpy.kalman import UnscentedKalmanFilter as UKF from filterpy.kalman import MerweScaledSigmaPoints import numpy as np import matplotlib.pyplot as plt degradation_rate = 0.1 # Set this to your desired degradation rate
Define the state transition function
def f(x, dt): degradation_rate = 0.1 # Set this to your desired degradation rate w = np.random.normal(0, 1) # Wiener process return np.abs(x - dt * degradation_rate + w) # Use absolute value to ensure the state is non-negative
def h(x): return x
dt = 0.1 # time step
points = MerweScaledSigmaPoints(1, alpha=0.001, beta=2., kappa=0)
ukf = UKF(dim_x=1, dim_z=1, dt=dt, fx=f, hx=h, points=points)
ukf.x = np.array([1.]) # initial RUL
ukf.P = np.eye(1) * 10.0 # Set P to be a diagonal matrix
regularization_value = 1e-3
ukf.Q = np.eye(1) * 10.0 + regularization_value # Set Q to be a diagonal matrix and add regularization
ukf.R = np.array([[0.1]])+ regularization_value
Generate ground truth and observations
t = np.arange(0, 10, dt) ground_truth = 100 - t * degradation_rate observations = ground_truth + np.random.normal(0, np.sqrt(ukf.R[0, 0]), size=t.shape)
Apply the UKF and collect predictions
predictions = [] for z in observations: ukf.predict() ukf.update(np.array([z])) predictions.append(ukf.x[0])
Plot ground truth, UKF predictions, and observations
plt.figure(figsize=(10, 6)) plt.plot(t, ground_truth, 'g-', label='Ground Truth') plt.plot(t, predictions, 'r-', label='UKF Predictions') plt.scatter(t, observations, c='b', label='Observations') plt.legend() plt.xlabel('Time') plt.ylabel('RUL') plt.title('UKF for RUL Estimation') plt.grid(True) plt.show()
Hello,
I have the same problem as you when using the UKF. Did you make any progress onsolving the issue?
