LEO-PNT GNSS Convergence Simulator

Constellation

MEO satellites (GPS/Galileo-class) 24

LEO augmentation satellites 18

Elevation mask 10°

Time acceleration 600×

Live Readouts

GDOP

—

Visible (M/L)

0 / 0

Position σ

300.0 m

Elapsed (sim)

0 s

How it works

Every satellite orbits on a real Keplerian circle. Its orbital period 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, so their sky geometry barely changes minute to minute. LEO augmentation satellites (a ≈ 6,971 km, ~600 km altitude) complete one in ~97 min — over 7× faster angular motion.

At each instant, only satellites above the elevation mask contribute. Their unit line-of-sight vectors u_i = (x,y,z) plus a clock-bias term build the geometry matrix H (rows [x,y,z,1]). Position accuracy depends on:

G = (Hᵀ H)⁻¹
GDOP = sqrt(G₁₁ + G₂₂ + G₃₃ + G₄₄)

Lower GDOP means the visible satellites are spread across more of the sky, so ranging noise maps to less position error. This sim integrates a simplified information-accumulation model each frame:

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

Because LEO satellites sweep through completely new geometry every few minutes (instead of every few hours like MEO), they inject fresh, decorrelated ranging geometry far faster — which is exactly why proposed LEO-PNT augmentation layers are studied as a way to cut GNSS/PPP convergence time from tens of minutes down to under a minute. Try LEO count = 0 vs. 30+ at the same time acceleration and watch σ converge at very different rates.

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

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.