Background credits: NASA/Reid Wiseman

Digging for debris

Generalized matched filtering and discrete polynomial-phase transforms


Daniel Kastinen, Juha Vierinen, Tom Grydeland

Background credits: NASA/Reid Wiseman

EISCAT and Space Situational Awareness (SSA)

    A space object detection:

  • Monostatic: [range, doppler, doppler drift, SNR] vs time
  • Tristatic: [position, velocity, acceleration, RCS] vs time

The typical current mode: monostatic beampark

EISCAT and Space Situational Awareness (SSA)

The typical current mode: monostatic beampark

Kastinen et. al, 2023
Using radar beam-parks to characterize the Kosmos-1408 fragmentation event

EISCAT and Space Situational Awareness (SSA)

Photo: Lars-Göran Vanhainen

EISCAT and Space Situational Awareness (SSA)

    Contributions

  • Validate and calibrate the ESA MASTER model
  • Characterize fragmentation events
    • Kosmos-1408 (Russian ASAT)
    • MicrosatR (Indian ASAT)
    • Iridium-Kosmos (Active-inactive collision)
    • ...
  • Characterize the small space debris population
  • Size estimation (work in progress) and orbit refinement
  • ...

Photo: Lars-Göran Vanhainen

EISCAT and Space Situational Awareness (SSA)

Photo: EISCAT

EISCAT and Space Situational Awareness (SSA)

Photo: EISCAT

EISCAT and Space Situational Awareness (SSA)

    EISCAT 3D

  • Tristatic measurnments
  • Flexible and rapid pointing
    • Tracking
    • Scanning
    • Discovery
    • Size estimation
    • ...
  • Comparatively extreme performance
  • Suboptimal frequency
  • ...

Photo: EISCAT

NOrdic Space Tracking RAdar - NOSTRA

ESA funded Phase 0 study to start fall 2024

  • Optimized for space object measurements
  • Multi-static phased arrays
  • Each site TX and RX $ \rightarrow $ MIMO
  • Dedicated to STM & SSA
  • Still available for research

Photo: EISCAT

Hardtarget analysis

So lots of things are going on $ \rightarrow $ lets improve and clean up the software

  • Based on Juha's code
  • Digital RF inputs and NetCDF like h5 outputs
  • Will end up on PyPI and Github (v1.0 soon ready)
  • 3 different ways of analyzing data
  • 3 Variants of implementation: Python (numpy, numba, ...), C, CUDA

Hardtarget analysis

  • Coherent target $\rightarrow$ deterministic phase model
  • Dynamics change "slowly" $\rightarrow$ phase predictable across pulses

Hardtarget analysis

Generalized match function $$ \mathrm{GMF}(\boldsymbol{\theta}) = \frac{\langle x, \Phi(\boldsymbol{\theta}) \rangle}{|\Phi(\boldsymbol{\theta})|}\\ $$

  • Signal $ x \in \mathbb{C} $
  • Model signal $ \Phi \in \mathbb{C} $
  • Model parameters $ \boldsymbol{\theta} \in \mathbb{R}^k $

Target phase model: $ \phi(t) = \phi_0 + \omega t + \alpha t^2 $ $\Rightarrow (r, \dot{r}, \ddot{r})$

Hardtarget analysis

  • 3 different ways of analyzing data

Hardtarget analysis

  • 3 different ways of analyzing data
    • Full Generalized Matched Filter [GMF]

      • (slow)

    • Approximate evaluation using one FFT (Fast GMF)

      • (fast, recommended)

    • Further approximate evaluation using two FFT's
      (Fast Discrete Polynomial-phase Transform [DPT])

      • (mega fast, half as sensitive)

Thank you for your attention!