Kalman Filter (1-D)

This interactive simulator explores Kalman Filter (1-D) in Визуализация математики. Recursive optimal estimation: noisy measurements, hidden truth, predict + update with Q and R; random-walk or constant-velocity model with ±2σ band and innovations. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Для кого: Best once you already know the basic definitions and want to build intuition. Typical context: Визуализация математики.

Ключевые понятия

  • kalman
  • filter
  • kalman 1d
  • math

Как это работает

**1-D Kalman filter**: optimally combines a noisy measurement **z** of a hidden true signal with a **dynamic model**. Each step does **predict** (propagate state and covariance through the model **F**, growing **P** by process noise **Q**) and **update** (shrink toward the new measurement by Kalman gain **K = P_p H^T / (H P_p H^T + R)**). Crank up **R** and the filter trusts the model; crank up **Q** and it tracks the measurements aggressively. The 2-state **constant-velocity** mode lets the filter estimate velocity from position-only measurements — try the **ramp** preset to see velocity locking onto the true slope.

Основные формулы

predict: x̂⁻ = F x̂, P⁻ = F P Fᵀ + Q
update: K = P⁻ Hᵀ (H P⁻ Hᵀ + R)⁻¹
x̂ = x̂⁻ + K (z − H x̂⁻), P = (I − K H) P⁻