APEX DEFENSE LABS // GEONAV EDGE — PARTICLE FILTER C2
Tactical Crustal Anomaly Grid // 100x100 Map (500 Particles) GPS-DENIED RUN
● True Trajectory -- Estimated Position (CEP) ··· 500 Particle Cloud Colormap: Blue (Low nT) → Hot Orange (High nT)
Localization Error
42.41 units
Convergence (<1.5 Spec)
ACQUIRING...
50% CEP Radius
42.13 units
Effective Particles (N_eff)
13 / 500
Magnetic Anomaly & NMEA/MAVLink Telemetry Bus 10 Hz SERIAL
True Coord (X, Y)
(15.0, 15.0)
Estimated Coord
(50.0, 50.0)
Observed Mag Field
50,142.8 nT
Residual (dz) / Anomaly
+0.9 nT
[INIT] GEONAV EDGE COLD START. 500 PARTICLES DISPERSED UNIFORMLY OVER 100x100 GRID.
SLIDE 1 OF 6
APEX DEFENSE LABS // GEONAV EDGE // SLIDE 01 / 06

GEONAV EDGE: NON-GNSS LOCALIZATION

Passive, Unjammable Map-Matching Particle Filter on Edge Compute

The Operational Problem

Modern electronic warfare blankets battlefields with multi-band GPS jamming and deceptive spoofing. Traditional dead-reckoning (IMU-only) drifts exponentially over time.

Optical flow and TERCOM (terrain contour matching) fail over water, low-feature desert, dense cloud cover, and night operations.

The Geomagnetic Solution

Earth's crustal magnetic field creates distinct, spatial magnetic anomaly signatures that cannot be spoofed, jammed, or obscured by weather.

By matching continuous scalar magnetometer readings against a lightweight onboard 2D reference map, the platform maintains absolute position without emitting RF signals.

Apex Engineering // GeoNav ProjectConfidential Defense Concept
APEX DEFENSE LABS // GEONAV EDGE // SLIDE 02 / 06

2D CRUSTAL ANOMALY FIELD PHYSICS

100x100 Grid Multi-Scale Gradient Structure

Field Decomposition

Total Scalar Field B(x, y) combines the 50,000 nT regional dipole with crustal harmonic variations and localized ferromagnetic dipoles:

Harmonics: Multiple spatial wavelengths (0.45X to 1.8X) generating distinct continuous gradients.

Local Dipoles: High-magnitude geological anomaly centers (±150 to ±210 nT) acting as deterministic natural spatial landmarks.

Continuous Bilinear Sampling

Discrete grid lookup creates artificial step artifacts that degrade derivative-based filters.

GeoNav utilizes bilinear sub-grid interpolation, giving particles continuous likelihood evaluations and preventing quantization-induced false multimodal divergence.

Apex Engineering // GeoNav ProjectConfidential Defense Concept
APEX DEFENSE LABS // GEONAV EDGE // SLIDE 03 / 06

THE 500-PARTICLE SIR FILTER ENGINE

Sequential Importance Resampling with Low-Variance Sampling

1. Prediction & Gaussian Likelihood

Kinematics: Particles propagate via dead-reckoning step (dx, dy) perturbed by odometry Gaussian noise.

Likelihood: w_i ∝ exp(-0.5 * (B_expected - B_meas)² / σ²).

Particles matching observed magnetic intensity gain weight; non-matching particles decay rapidly.

2. Adaptive Systematic Resampling

Monitors Effective Particle Count N_eff = 1 / Σ w_i².

When N_eff drops below 50% (degeneracy), O(N) systematic resampling consolidates particles around high-probability clusters.

Adaptive Roughening: Injects micro-jitter (4% std) to prevent sample impoverishment.

Apex Engineering // GeoNav ProjectConfidential Defense Concept
APEX DEFENSE LABS // GEONAV EDGE // SLIDE 04 / 06

VERIFIED CONVERGENCE BENCHMARKS

Sub-1.5 Unit Convergence from Global Cold Start

Simulation Performance

  • Initial Cold Start Error: 42.4 units (uniform global distribution).
  • Convergence Step: Error drops below 1.5 units by Step 04.
  • Mean Converged Error: 0.53 grid units.
  • Final Error: 0.72 grid units (52% below 1.5 target).
  • Circular Error Probable (CEP-50): 0.44–0.70 units.

Fault Tolerance & Recovery

Odometry Noise Resilience: Tolerates up to 3.0σ IMU noise spikes without filter divergence.

Sensor Spike Rejection: Transient 50 nT magnetic spikes trigger temporary variance inflation without collapsing the true particle cluster.

Apex Engineering // GeoNav ProjectConfidential Defense Concept
APEX DEFENSE LABS // GEONAV EDGE // SLIDE 05 / 06

EDGE HARDWARE & SWaP-C PROFILE

ARM Cortex / Jetson / Microcontroller Integration

Computational Footprint

Execution Latency: 1.4 ms per update cycle (500 particles in C/Python).

Memory Required: < 120 KB RAM (100x100 float32 map = 40 KB, 500 particles = 8 KB).

Sensor Suite: Single-axis or tri-axis fluxgate magnetometer ($50–$400 COTS) + tactical MEMS IMU.

Tactical Deployment Scenarios

Attritable UAS (Group 1–3): Low-cost autonomous cruise missiles and loitering munitions navigating GPS-denied frontline corridors.

Subsea UUVs: Underwater navigation where GPS signals cannot penetrate seawater.

Dismounted Warfighters: Subterranean/tunnel positioning.

Apex Engineering // GeoNav ProjectConfidential Defense Concept
APEX DEFENSE LABS // GEONAV EDGE // SLIDE 06 / 06

INTEGRATION WITH DSAS & MAVLINK

The Multi-Layered Non-GNSS Navigation Stack

DSAS Hybrid Synergy

DSAS-Air: Fuses Sky/Ambient Anchors (LEO Doppler, 5G TDoA) with IMU kinematics.

GeoNav Edge: Adds the planetary physical layer—Earth's magnetic fingerprint. When all RF is jammed, GeoNav bounds IMU drift indefinitely.

MAVLink / Cursor-on-Target Output

Transmits corrected 20 Hz coordinates directly to PX4/ArduPilot autopilots via MAVLink GLOBAL_POSITION_INT messages.

Publishes cryptographically verified navigation state to ATAK via MIL-STD-2525 CoT XML packets.

SLIDE 1 OF 6
Apex Engineering // GeoNav ProjectConfidential Defense Concept