Underpasses: GNSS/INS Post-Processing That Holds Fix

1 / 4

‹ ›

Part 1 – Typical Underpasses

What happens when a car drives under a bridge?

1. Approach: Full sky, good geometry. Phase ambiguities are resolved. Position is centimetre-level.
2. Under the bridge (1–3 s): Most or all satellites are blocked. GNSS receiver may report 0 tracked SVs. The filter coasts on IMU + odometry.
3. Exit: Satellites reappear, but not all at once. The receiver needs time to re-acquire signals, re-establish tracking loops, and report measurements. Phase observations may restart with new ambiguities.

Step 3 is where things go wrong in real-time. The filter has to decide, in a single forward pass, whether the returning phase is continuous (ambiguity preserved) or has a cycle slip (ambiguity reset). If it guesses wrong, you get a jump.

Why The Exit Is Harder Than The Entry

On entry, the filter is in a good state: ambiguities are known, geometry is strong, the IMU is recently calibrated. Even if satellites vanish quickly, the filter can smoothly transition to inertial coasting.

On exit, the filter is in a degraded state: IMU has been coasting for 1–3 s (with a consumer/MEMS IMU, that’s enough for decimetres of drift), ambiguities may have changed, and the returning satellites appear one by one with possibly corrupted first measurements (multipath from the bridge structure, low C/N0 as the receiver reacquires).

A real-time filter must commit: it either accepts the returning phase and tries to keep fix, or it drops to float and re-converges. Both choices are risky when done in a single forward pass.

Part 2 – Pivot Satellite in Double Differences: Why Dynamic Wins

In double-difference (DD) processing, one satellite per constellation is chosen as the “pivot” (reference). All other satellites are differenced against it. This eliminates receiver clock and several common errors. But it also means: if the pivot satellite loses lock, every DD ambiguity in that constellation is affected.

Static Pivot (Classical Approach)

The classical approach picks the highest-elevation satellite as pivot and keeps it as long as it is tracked. Under a bridge:

• Pivot loses lock (bridge blocks it).
• After the bridge, a new pivot must be selected. All DD ambiguities must be re-initialized because the pivot changed.
• Even if other satellites maintained lock through the underpass (unlikely for short bridges, but possible for rail overpasses), their DD ambiguities are invalid because the reference satellite changed.

Result: complete ambiguity reset after every underpass. Re-convergence to fix takes 5–30 s depending on geometry and baseline length. In that window, position can jump.

Dynamic Pivot (AlgoNav Approach)

Our approach changes the pivot dynamically and algebraically propagates the DD ambiguities through the pivot change:

1. Before the bridge, we know all ambiguities relative to pivot A.
2. Pivot A loses lock under the bridge.
3. After the bridge, we pick pivot B (whichever satellite has the cleanest reacquisition).
4. Ambiguities that survived (any satellite that kept lock or can be re-connected) are algebraically transformed: N_iB = N_iA - N_BA.
5. This requires knowing N_BA – but we knew it before the bridge (both A and B were tracked, ambiguities resolved). In post-processing, we even have the future data to confirm it.

Result: ambiguities that survived the bridge are instantly valid with the new pivot. No re-convergence needed.

Post-Processing Advantage

In post-processing, we have the backward pass as well. The backward filter approaches the bridge from the other side – with full sky and resolved ambiguities. The forward and backward solutions can be combined at the bridge, choosing the better-determined state at each epoch. This effectively shrinks the “uncertain window” to the physical bridge shadow, not the re-convergence tail.

For the 20 drives in our dataset, we counted 47 underpass events total (bridges, overpasses, low structures). With dynamic pivot + forward/backward combination:

• 0 complete ambiguity resets were needed when at least 3 satellites maintained phase through the underpass.
• Re-convergence (when it happened) was < 1 s in 42 of 47 cases.
• In 5 cases (very long overpasses or stacked structures), re-convergence took 1–3 s, but the backward filter filled the gap.

Practical Takeaways

• The bridge itself is not the hard part. IMU easily coasts 1–3 s. The exit transition is where errors creep in.
• Dynamic pivot selection preserves ambiguities through the outage. Algebraic transformation is exact, not a re-estimation.
• Post-processing wins by design: forward + backward + known data quality means you pick the best solution at every epoch.
• Real-time re-convergence gaps are avoidable. If you can post-process, do. The bridge will not be in your trajectory.
• Tightly-coupled IMU is essential. Without it, even 1 s of GNSS loss becomes a position gap. With it, the gap is bridged (pun intended) and the returning GNSS is accepted with a tight prediction.

What This Means For Your Projects

If you drive urban or suburban routes, underpasses are everywhere: highway bridges, rail crossings, parking structures. Each is a potential ambiguity reset in real-time. With post-processing, dynamic pivot management, and tightly-coupled IMU, those events become transparent. Your trajectory stays on fix, and you avoid the lateral jumps that otherwise pile up in urban/suburban driving.