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 blockVector states, F and H, and cross-covariance.
FlashcardsClick-to-reveal cards for the block's key terms and equations.
DemoConstant-velocity 4D filter on 2D motion; position fixes correct velocity through cross-covariance.
DemoGauss-Markov accelerations: 6D state with position, velocity, and acceleration.