Building aegis-filter: Why Standard Kalman Filters Fail in Adversarial Environments (and How We Replaced Them in Pure Rust)

When building telemetry filters for autonomous drones or robotics, the textbook recommendation is always the same: “Just slap a Kalman Filter on it.”

In theory, the linear Kalman filter is mathematically optimal under Gaussian white noise. In the real world, however, physical sensors do not live in textbook conditions:

1. Adversarial GPS/Baro Spoofing: A rogue transmitter or RF jammer injects sudden, massive delta jumps (e.g., +150 meters in a single millisecond).
2. Numerical Covariance Degeneracy: Floating-point round-off errors over millions of iterations cause the error covariance matrix $P$ to lose its positive-definiteness ($P \not\succ 0$), producing negative variances and exploding state estimates.
3. Severe Non-Linearities: Radar range calculations ($r = \sqrt{x^2 + y^2}$) and orientation quaternions break linear assumptions; Extended Kalman Filters (EKF) require calculating brittle analytical Jacobian matrices that drift rapidly.

To solve these mission-critical vulnerabilities, we built and open-sourced aegis-filter under Exploidus—a cyber-resilient, #![no_std], hard real-time estimation engine written from scratch in pure Rust.

Here is the engineering breakdown of how it works and what the simulation numbers prove.

1. The Core Architecture

aegis-filter is engineered with three core defenses:

A. Joseph-Stabilized Covariance Update

Standard Kalman filters update covariance using $P_k = (I - K_k H_k) P_{k|k-1}$. In finite-precision IEEE 754 floating-point arithmetic, subtraction can yield asymmetric, non-positive-definite matrices.

aegis-filter enforces the Joseph Stabilized Form:
$$P_k = (I - K_k H_k) P_{k|k-1} (I - K_k H_k)^T + K_k R_k K_k^T$$

Because both terms are quadratic forms ($A P A^T + B R B^T$), positive-definiteness is mathematically guaranteed across infinite operational lifetimes.

B. Chi-Square / 3-Sigma Outlier Rejection Gating

Before any raw measurement is allowed to alter the state vector, the innovation $\tilde{y}k = z_k - H_k \hat{x}{k|k-1}$ is evaluated against the innovation covariance $S_k = H_k P_{k|k-1} H_k^T + R_k$:
$$\text{Reject if } |\tilde{y}_k| > \gamma \sqrt{S_k}$$

If an adversary transmits a spoofed altitude or an IMU glitches, the reading is gated at line-rate. The filter falls back safely to its physical state propagation without corrupting the state.

C. Unscented Kalman Filtering (UKF) & $H_\infty$ Robust Minimax

• UKF (Merwe Scaled Sigma Points): Replaces brittle Jacobian derivations by propagating $2n + 1$ deterministic sigma points through non-linear observation closures.
• $H_\infty$ Minimax: Optimizes state estimation against the worst-case disturbance rather than assuming well-behaved Gaussian noise.

2. Flight Telemetry & Spoofing Resilience Simulation

To prove real-world resilience, we simulated a quadcopter ascending at $1.5\text{ m/s}$ subjected to atmospheric turbulence, normal sensor noise, and deliberate adversarial spoofing:

• Step 12: Instantaneous $+150\text{m}$ GPS spoofing attack.
• Step 22: Severe $-80\text{m}$ sensor hardware dropout glitch.

Here is the telemetry log produced by running cargo run --example flight_telemetry:

=============================================================================== AEGIS-FILTER :: FLIGHT TELEMETRY & ADVERSARIAL RESILIENCE SIMULATION Developed under Exploidus (https://github.com/Exploidus) =============================================================================== Step | True Alt (m) | Sensor Raw (m) | Aegis Est (m) | Abs Error | Status -------+--------------+----------------+----------------+--------------+----------- 1 | 1.50 | 1.79 | 1.75 | 0.254 | VALID 2 | 3.00 | 3.22 | 3.24 | 0.238 | VALID 3 | 4.50 | 3.46 | 4.31 | 0.187 | VALID 4 | 6.00 | 6.74 | 6.06 | 0.057 | VALID 5 | 7.50 | 7.67 | 7.58 | 0.081 | VALID 6 | 9.00 | 8.90 | 9.04 | 0.045 | VALID 7 | 10.50 | 9.68 | 10.39 | 0.113 | VALID 8 | 12.00 | 12.98 | 12.08 | 0.075 | VALID 9 | 13.50 | 13.41 | 13.55 | 0.047 | VALID 10 | 15.00 | 14.69 | 14.99 | 0.009 | VALID 11 | 16.50 | 16.04 | 16.42 | 0.080 | VALID 12 | 18.00 | 168.00 | 17.92 | 0.080 | SPOOF REJECT 13 | 19.50 | 19.08 | 19.36 | 0.138 | VALID 14 | 21.00 | 20.65 | 20.83 | 0.172 | VALID 15 | 22.50 | 22.43 | 22.34 | 0.156 | VALID 16 | 24.00 | 24.93 | 24.01 | 0.012 | VALID 17 | 25.50 | 24.79 | 25.40 | 0.099 | VALID 18 | 27.00 | 26.78 | 26.88 | 0.116 | VALID 19 | 28.50 | 28.76 | 28.44 | 0.060 | VALID 20 | 30.00 | 30.64 | 30.04 | 0.044 | VALID 21 | 31.50 | 30.61 | 31.41 | 0.095 | VALID 22 | 33.00 | -47.00 | 32.91 | 0.095 | SPOOF REJECT 23 | 34.50 | 34.96 | 34.50 | 0.003 | VALID 24 | 36.00 | 36.25 | 36.04 | 0.036 | VALID 25 | 37.50 | 36.60 | 37.39 | 0.110 | VALID 26 | 39.00 | 39.34 | 38.96 | 0.041 | VALID 27 | 40.50 | 40.99 | 40.54 | 0.039 | VALID 28 | 42.00 | 41.84 | 42.01 | 0.009 | VALID 29 | 43.50 | 42.78 | 43.40 | 0.100 | VALID 30 | 45.00 | 45.60 | 45.00 | 0.003 | VALID ------------------------------------------------------------------------------- SIMULATION SUMMARY: - Total Steps Processed : 30 - Valid Readings Fused : 28 - Adversarial Spikes Blocked : 2 (100% Gated) - Final Variance Confidence : 0.1185 =============================================================================== 

Key Takeaways from the Data:

• Millimeter Tracking Precision: Under normal noisy conditions (Step 10, Step 30), estimation error dropped to 0.003–0.009 meters (3–9 mm).
• Flawless Spoof Rejection: When the raw altitude leaped to $168\text{m}$ at Step 12, the filter isolated the anomaly, kept the aircraft altitude at $17.92\text{m}$ (error: $0.080\text{m}$), and prevented a fatal motor cut.

3. Quick Start (Rust)

Add aegis-filter to your Cargo.toml:

[dependencies] aegis-filter = "0.1.0" 

For bare-metal Cortex-M/RISC-V embedded targets:

[dependencies] aegis-filter = { version = "0.1.0", default-features = false } 

1D Outlier-Gated Fusion Example:

use aegis_filter::{ScalarKalmanFilter, FilterError}; fn main() -> Result<(), FilterError> { // Initial state: 0.0m, Initial variance: 5.0, Process noise: 0.02, Measurement noise: 0.8 let mut filter = ScalarKalmanFilter::new(0.0, 5.0, 0.02, 0.8)?; let sensor_stream = [1.5, 3.1, 4.4, 168.0 /* Spoofed spike */, 6.0]; for &raw_reading in &sensor_stream { filter.predict(1.5)?; // Predict forward by 1.5m climb match filter.update(raw_reading, Some(3.0)) { // 3-sigma gate Ok(estimated_alt) => println!("Estimated Altitude: {:.2}m", estimated_alt), Err(FilterError::MeasurementGated) => { println!("Spoofed sensor reading ({:.1}m) rejected! Holding state.", raw_reading); } Err(e) => return Err(e), } } Ok(()) } 

4. Open Source Links

The engine is open-source under dual MIT/Apache-2.0 licenses:

• Crates.io: crates.io/crates/aegis-filter
• GitHub Repository: Exploidus/aegis-filter
• Documentation: docs.rs/aegis-filter

Feedback, issues, and PRs from control engineers and systems developers are warmly welcome!