LEO-PNT GNSS Convergence Simulator (2D)

Constellation

MEO satellites (GPS/Galileo-class) 24

Enable LEO augmentation

LEO augmentation satellites 18

Elevation mask 10°

Time acceleration 600×

Live Readouts

GDOP (2D)

—

Visible (M/L)

0 / 0

Position σ

300.0 m

Elapsed (sim)

0 s

Time to 1 m fix

—

How it works

This is a 2D single-plane analog of the 3D LEO-PNT convergence model. Every satellite still orbits on a real Keplerian circle — its angular speed comes straight from Kepler's third law:

T = 2π · sqrt(a³ / μ),  μ_Earth = 398,600.44 km³/s²

MEO satellites (a ≈ 26,571 km, like GPS Block III / Galileo FOC / GLONASS-K2 / BeiDou-3) complete an orbit in ~12 h. LEO augmentation satellites (a ≈ 6,971 km, ~600 km altitude) complete one in ~97 min — over 7× faster angular motion, which is why the LEO ring visibly sweeps past the receiver while the MEO ring barely moves.

Because this view is a flat 2D plane instead of full 3D, the receiver only has 2 position unknowns (not 3) plus a clock bias, so the geometry matrix uses 2D line-of-sight direction u_i = (cos θ, sin θ) plus a clock term (rows [cos θ, sin θ, 1]):

G = (Hᵀ H)⁻¹  (3×3)
GDOP = sqrt(G₁₁ + G₂₂ + G₃₃)

Only satellites above the elevation mask (measured from the receiver's local "up" direction, radially outward from Earth's center) contribute a row. This sim then integrates the same simplified information-accumulation model as the 3D version:

dI/dt = k · N_visible / GDOP²
σ(t) = σ₀ / sqrt(1 + I(t))

Toggle LEO augmentation off and σ crawls down slowly, driven only by the slow-moving MEO ring. Turn it on and add more LEO satellites and the fast-sweeping ring injects fresh, decorrelated geometry every few minutes instead of every few hours — cutting the time to a 1 m fix dramatically. That's the real argument for proposed LEO-PNT augmentation layers: not more satellites, but faster-changing geometry.

MEO (GPS-class) LEO augmentation Line of sight (visible) Receiver