Kepler Nav Research - Lie Group Manifold Observability Proof & Whitepapers

IEEE Transactions Publication // Fundamental Observability
Peer-Reviewed Dossier

Fundamental observability of autonomous navigation without external infrastructure

Authored by Sanjay S (Researcher at Kepler Nav), this publication establishes the mathematical framework of non-linear state observability on the SE(3) x R³ Lie Group manifold.

Observability Matrix
rank(O) = 6

Full state recoverability under gravity

Lie Derivative Evaluation
1000 Hz Realtime

Sub-millisecond matrix updates

Doppler Residual Precision
< 0.38 mm

Zero drift divergence

PDF Document: Fundamental Observability ProofDownload Full IEEE Preprint (PDF)
Classified research dossier // Technical proof

Technical credibility before marketing.

Ground-truth evidence, rigorous mathematical theorems, and custom FPGA silicon architecture - built on decades of institutional pulsar research and space-grade verification.

Celestial Pulsar Star XNAV Research
Research foundation // NASA SEXTANT & XNAV

Inspired by decades of celestial & pulsar timing research

Building upon foundational orbital mechanics and pulsar navigation studies pioneered through NASA's SEXTANT mission on the ISS. We transformed photon-counting timing principles into a real-time 100 Hz Lie Group manifold architecture.

Research areaOrbital PNT Systems
FoundationNASA SEXTANT / XNAV
Deep Space Radio Telescope Observatory
Publication // IEEE TransactionsPeer-Reviewed Proof

Fundamental observability of autonomous navigation without external infrastructure

Establishes the rigorous mathematical proof of 6D non-linear state observability on the SE(3) x R³ manifold. Proves continuous Lie derivative time evolution recovers full 6D observability.

Theorem 1.2 (Dynamic Lie Density)

Under central gravity fields, continuous Lie derivative time evolution recovers full 6D state observability rank(O) = 6.

Author: Sanjay S, Kepler Nav200+ Peer References
Kalam Silicon Semiconductor Core
Hardware architecture // Kalam Silicon

Custom FPGA silicon matrix acceleration

Proprietary hardware netlist performing parallel sparse Cholesky elimination on AMD/Xilinx Zynq UltraScale+ MPSoC. Accelerates Factor Graph Optimization by 50x under 1.5W power.

Cholesky matrix solver50x Speedup
Target chip: AMD Zynq XCZU3EG MPSoC
Hardware schematic: Kalam-Zero< 1.42 Watts
Development roadmap & milestones

From theoretical proof to orbital deployment.

Phase 01 // 2023Completed

Theoretical research & Lie algebra proofs

Published IEEE observability research proving non-linear 6D state observability on SE(3) x R³ manifold without external GNSS signals.

Phase 02 // 2024Completed

Software engine & iSAM2 optimization

Developed C++ UNIF-PNT software core executing invariant filtering and real-time Lie derivative rank calculation.

Phase 03 // 2025Completed

Kalam silicon netlist & hardware-in-the-loop

Synthesized custom FPGA hardware sparse Cholesky elimination solver, achieving 50x acceleration under 1.5W.

Phase 04 // 2025Active pilot

Kalam-Zero 1U payload bench testing

Assembled Kalam-Zero 1U CubeSat / UAV payload pod with SA.45s CSAC clock, ADIS16497 IMU, and AD9361 SDR.

Phase 05 // 2026Upcoming

Cislunar demonstration mission

Scheduled satellite flight mission verifying autonomous orbit determination and XNAV pulsar timing.

Phase 06 // 2026+Upcoming

Deep space mission deployment

Deployment of Kalam ASIC silicon and XNAV payloads for Cislunar orbiters, Lunar Gateway, and interplanetary probes.

Enterprise & research inquiries

Build with Kepler Nav.

Partner with our engineering team to integrate the UNIF-PNT navigation engine or deploy Kalam-Zero payloads for satellite and defense platforms.

Direct research email: sanjay@keplernav.com
Location: Kepler Nav Research Labs