types.estimation.EKFResult

types.estimation.EKFResult()

Extended Kalman Filter (EKF) state and result.

EKF extends the Kalman filter to nonlinear systems by linearizing the dynamics and measurement functions at each time step via Jacobians.

Fields

state_estimate : StateVector Current state estimate x̂[k] (nx,) covariance : CovarianceMatrix Current error covariance P[k] (nx, nx) innovation : OutputVector Measurement innovation y[k] - h(x̂⁻[k]) (ny,) innovation_covariance : CovarianceMatrix Innovation covariance S[k] = H P⁻ H’ + R (ny, ny) kalman_gain : GainMatrix Kalman gain K[k] = P⁻ H’ S⁻¹ (nx, ny) likelihood : float Log-likelihood of measurement log p(y[k]|y[1:k-1])

Examples

>>> # Nonlinear pendulum system
>>> def dynamics(x, u):
...     theta, omega = x
...     return np.array([omega, -np.sin(theta) + u[0]])
>>>
>>> def measurement(x):
...     return np.array([x[0]])  # Measure angle only
>>>
>>> # Create EKF
>>> ekf = ExtendedKalmanFilter(
...     dynamics_fn=dynamics,
...     measurement_fn=measurement,
...     Q=0.01 * np.eye(2),
...     R=0.1 * np.eye(1)
... )
>>>
>>> # Initialize
>>> ekf.initialize(x0=np.array([0.1, 0.0]), P0=np.eye(2))
>>>
>>> # Update loop
>>> for k in range(N):
...     # Predict
...     ekf.predict(u[k])
...
...     # Update with measurement
...     result: EKFResult = ekf.update(y[k])
...
...     # Extract estimate
...     x_hat = result['state_estimate']
...     P = result['covariance']
...
...     # Check innovation
...     innovation = result['innovation']
...     if np.linalg.norm(innovation) > 3.0:
...         print(f"Large innovation at k={k}")
>>>
>>> # Examine likelihood for outlier detection
>>> log_likelihood = result['likelihood']
>>> if log_likelihood < -10:
...     print("Possible outlier measurement")