Kalman Filter State Estimation Calculator

Optimal Estimation & GNC: Calculate state time propagation, measurement correction, Kalman Gain ($K$), and a posteriori error covariance ($P$).

Prior State Estimate $\hat{x}_{k-1}$:

Prior Covariance $P_{k-1}$:

State Transition Matrix $F$ (or $A$):

Process Noise Covariance $Q$:

Measurement Observation $z_k$:

Measurement Noise $R$ ($\sigma_v^2$):

Measurement Matrix $H$:

Updated State ($\hat{x}_k$)

Innovation: y_k = --

Kalman Gain ($K_k$)

Sensor Weight: -- %

Posterior Covariance ($P_k$)

Prior P_k^- = --

Uncertainty Reduction

-- %

Post 1-sigma: --

Discrete Kalman Filter Steps:

• Time predict: $\hat{x}_k^- = F \hat{x}_{k-1}$, $P_k^- = F P_{k-1} F^T + Q$.

• Measurement update: $K = \frac{P_k^- H^T}{H P_k^- H^T + R}$, $\hat{x}_k = \hat{x}_k^- + K(z_k - H \hat{x}_k^-)$, $P_k = (I - K H) P_k^-$.

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