Filter Adjustment
Numerical errors in state estimation algorithms arise when arithmetic operations are performed on finite precision processors. Implementing state covariance scaling prevents these errors by multiplying the filter uncertainty matrix by a factor that keeps it from becoming artificially small. This modification prevents the estimator from disregarding new sensor measurements during long run cycles.
Scaling Factor
Dynamic scaling algorithms calculate a multiplier based on the ratio between the expected residual variance and the actual innovation variance. If the processor calculates that the filter is becoming too confident in its internal model while the true tracking error remains high, it increases the covariance values. This adjustment forces the gain matrix to remain responsive to real time sensor inputs.
The scale factor must be constrained to prevent the filter from oscillating or overreacting to single measurement anomalies.
Numerical Precision
Double precision floating point representations reduce the risk of numerical underflow but do not eliminate the need for scaling in complex non linear systems. Applying this scaling method ensures that the diagonal elements of the uncertainty matrix do not collapse to zero. Engineers test this stability by running simulations with highly mismatched initial state estimates.
Divergence Prevention
Preventative measures are evaluated by monitoring the filter performance during extended periods of low excitation. When no new motion occurs, a non adaptive filter would allow its uncertainty matrices to shrink to zero, making it blind to subsequent changes. Scaling maintains a baseline level of uncertainty so the filter reacts immediately when movement resumes.
