Block 5 — Multi-State Kalman Filter

Block 5 — Multi-State Kalman Filter#

Block 05~60 min2 demos

Generalizes to a vector state with cross-covariance, runs constant-velocity 4D and Gauss-Markov 6D filters on simulated 2D motion, and shows how a position measurement updates correlated velocity states automatically.

What you’ll learn#

  1. Explain why navigation problems require multi-state estimation.

  2. Generalize the scalar Kalman filter equations to vector states.

  3. Write the state transition matrix \(\mathbf{F}\) for constant-velocity 2D motion.

  4. Write the measurement matrix \(\mathbf{H}\) for a position-only sensor.

  5. Interpret the off-diagonal terms of the covariance matrix \(\mathbf{P}\) as cross-correlation between states.

  6. Run a 4-state filter that simultaneously estimates 2D position and velocity from noisy 2D position fixes.

In this block#

Reading

Reading

Vector states, F and H, and cross-covariance.

 Flashcards

Flashcards

Click-to-reveal cards for the block's key terms and equations.

 Demo

Demo · 4D Kalman Filter

Constant-velocity 4D filter on 2D motion; position fixes correct velocity through cross-covariance.

 Demo

Demo · 6D Kalman Filter

Gauss-Markov accelerations: 6D state with position, velocity, and acceleration.
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