Observations, Sensors, and Multimodal Data › Key Parameters

The key parameters for the fusion example are:

• dt: Base time step (0.01 s, the 100 Hz rate at which the encoder and filter run). It appears in $F$, $B$, and $Q$, so changing it changes the dynamics, control mapping, uncertainty growth, and number of updates per physical second.
• q_accel: Continuous white-acceleration spectral density (0.09 m$^2$/s$^3$). It scales $Q$ and therefore predicted covariance growth. Larger values generally make measurement updates more influential because prediction becomes less certain.
• R_ENC: Encoder measurement noise variance (0.05$^2$ m$^2$). Smaller values make the filter trust encoder updates more heavily.
• R_CAM: Camera measurement noise variance (0.02$^2$ m$^2$). The camera is 6.25 times as precise as the encoder when a frame is available. Relative sensor variances affect their weighting, but their absolute scale relative to $Q$ and the propagated covariance also matters. Scaling only the two $R$ values changes the Kalman gain; covariance-scale invariance would require scaling $P_0$, $Q$, and all $R$ values together.
• DELAY: Camera latency in base-rate steps (6 steps, 60 ms). Replay work per delayed frame and the minimum retained buffer grow linearly with this value. This teaching implementation retains the full $T$-step state history and encoder-update array, so its actual memory use is $O(T)$; a production implementation can prune entries older than the maximum supported delay.