Filtering Logic & Design¶

Numerical Stability¶

kalbee prioritizes numerical stability.

Joseph Form¶

For covariance updates in Kalman Filters, we use the Joseph Form: $$P = (I - KH)P(I - KH)^T + KRK^T$$

This ensures that the covariance matrix $P$: 1. Remains symmetric. 2. Remains positive semi-definite.

Standard implementations often use $P = (I - KH)P$, which is computationally cheaper but can lead to numerical instability (negative variances) due to floating-point errors.

Extensibility¶

The BaseFilter class allows you to implement custom filters by simply defining predict and update.

class MyCustomFilter(BaseFilter):
    def predict(self, dt, **kwargs):
        # ... logic
        return self.state

    def update(self, measurement, **kwargs):
        # ... logic
        return self.state