Kalman Filtering in Cybersecurity:

Enhancing Bayesian AI with Kalman Filtering for Weighted Anomaly Detection

To further improve accuracy and reduce noise, we can integrate Kalman Filtering into the Bayesian AI anomaly detection system. This helps:

• Refine probability estimates dynamically
• Reduce false positives by weighting historical evidence
• Adapt faster to changing network conditions

Why Kalman Filtering?

Kalman Filters (KF) are used in signal processing, robotics, and tracking systems to estimate variables more accurately by accounting for measurement noise and uncertainty.

In Cybersecurity, KF can:

1. Improve anomaly score accuracy by dynamically weighting previous threat probabilities.
2. Reduce false alarms by smoothing fluctuating network behavior.
3. Enhance real-time Bayesian inference by adapting faster to evolving threats.

Reference:

• Using Kalman Filtering in Intrusion Detection Systems (IEEE Xplore)

Integrating Kalman Filtering with Bayesian AI

In the previous Bayesian AI model, the anomaly score is computed independently for each event.

Now, we introduce a Kalman Filter (KF) update step to dynamically adjust the anomaly probability based on historical network traffic.

The Kalman Filter Update Equation

A Kalman Filter recursively updates a state x (the true anomaly probability) using: x_k = x_{k-1} + K (z_k - x_{k-1}) Where:

• x_k = Updated estimate of anomaly probability at time k
• z_k = Measured anomaly probability from Bayesian AI
• K = Kalman Gain (weight for trust in new measurement)

The Kalman Gain K is computed as: K = \frac{P_{k-1}}{P_{k-1} + R} Where:

• P_{k-1} = Estimated uncertainty (previous anomaly variance)
• R = Measurement noise variance

Why Kalman Filtering Improves Cybersecurity AI

• Refines Bayesian anomaly scores dynamically
• Reduces false positives by smoothing data fluctuations
• Adapts faster to evolving network conditions