Kalman

Apply a Kalman Filter to the value on its input.

Kalman FIltering, also known as linear quadratic estimation (LQE) is an algorithm that produces estimates using a series of measurements over time effectively filtering noise or smoothing a jittery signal input.

Because this algorithm produces estimates it relies on iterations of prediction-measurement cycles.

*In Modulo Kinetic this filter can be used to attenuate noise or smooth a signal but it can also be used as a mean to compensate for projector input lag especially when tracking an object with projection on it. This is done with the Delay and Interpolation properties.

Properties

• Process noise : Affects the weight of predictions in the algorithm. Lower values (<0.1) will give smoother signals but less accurate predictions. Prefer values between 0 and 0.1.
  Default : 0.01

• Measurement noise : Affects the weight of measures in the algorithm. Higher values (>10) will give smoother signals but less accurate values.
  Default : 5.0

• Error cov. post : Affects uncertainty in the initialisation of the algorithm. If your starting position is accurate, prefer lower values. If not, prefer higher values.
  Default : 0.1

• Delay : Useful when compensating for projector input lag. Leave at 0 otherwise. Unit : seconds
  Default : 0.0

• Force Evaluate : When toggled ON, will evaluate a prediction even if the input does not change.
  Default : OFF

• Interpolation : (Only visible when Force Evaluate is OFF) Adds an interpolation to the values based on the algorithm. Unit : milliseconds
  Default : 0

Predictions / Measures noise

Process noise and Measurement noise are complimentary properties. One should be rather low while the other is rather high :

• If Process noise is low : we trust the predictions to be accurate, Measurement noise can be higher to reduce noise in our measures.
  In this case the output will be smoother but may have a higher latency (delay).

• If Measurement noise is low : we trust our measures to be accurate, Process noise can be higher to reduce noise in the predictions.
  In this case the output will have a lower latency but may be noisier (jerk).

Inputs

Outputs

Example

The filter is using default values on all its properties.

Flattening noise

Smoothing a signal