Vela Pulsar Timing & Simplified XNAV Demonstration

Research-style signal analysis project using Vela pulsar photon event data

Author: Victoria Kupina
Role: Research / Data Analyst — Signal Processing & Systems Analysis

This project demonstrates how photon arrival-time data from the Vela pulsar can be analyzed to detect periodic structure, build a folded pulse profile and illustrate the basic timing logic behind X-ray pulsar navigation (XNAV).

The goal is not to claim a production-grade navigation system. The goal is to show a reproducible analytical workflow for working with noisy observational data where the measured signal is an indirect projection of a physical process.

This project is positioned at the intersection of:

• time-series analysis;
• signal processing;
• astrophysical data analysis;
• systems thinking;
• reproducible research workflows.

Pulsars are rapidly rotating neutron stars that emit highly periodic signals. Because of their stable timing behavior, pulsars are often discussed in the context of high-precision timing and X-ray pulsar navigation concepts.

In real observational data, the signal is not presented as a clean periodic curve. It must be reconstructed from photon arrival events under noise, sampling limitations and preprocessing assumptions.

This project asks:

Can a dominant periodic structure be extracted from photon event data and transformed into an interpretable folded pulse profile?

1. How can photon event data be transformed into a clean analytical format?
2. Can periodic structure be detected from arrival-time observations?
3. How does epoch folding help reconstruct a pulse profile?
4. How can phase shifts be interpreted as timing errors in a simplified XNAV-style demonstration?
5. What are the limitations of this simplified workflow compared with a real navigation-grade system?

The project follows a structured research pipeline:

1. Data loading

   • read FITS photon event data;
   • inspect available columns and event structure.

2. Exploratory analysis

   • analyze photon arrival times;
   • inspect energy distribution;
   • examine inter-arrival behavior.

3. Preprocessing

   • convert event data into a clean tabular format;
   • create relative time values;
   • apply energy-based filtering.

4. Period detection

   • search for the dominant pulsation period using an epoch-folding approach;
   • evaluate the strongest candidate period.

5. Epoch folding

   • fold photon events by phase;
   • construct a phase-aligned pulse profile.

6. Simplified XNAV demonstration

   • simulate phase shifts;
   • convert phase shift into timing error;
   • illustrate the relationship between timing error and approximate range error.

pulsar/
├── data/
│   └── README.md
├── notebooks/
│   ├── 01_data_loading.ipynb
│   ├── 02_exploratory_analysis.ipynb
│   ├── 03_preprocessing.ipynb
│   ├── 04_period_detection.ipynb
│   ├── 05_epoch_folding.ipynb
│   ├── 06_xnav_demo.ipynb
│   └── images/
├── requirements.txt
├── LICENSE
└── README.md

• FITS data loading and inspection;
• photon arrival-time analysis;
• exploratory data analysis;
• signal preprocessing;
• epoch-folding period detection;
• pulse profile reconstruction;
• phase-shift simulation;
• simplified timing-to-range interpretation.

The workflow detects a dominant pulsation period close to the expected Vela pulsar timing scale:

Dominant period ≈ 0.0893 s

The project also produces visual outputs for:

• period detection;
• folded pulse profile;
• simulated XNAV phase shift;
• approximate phase-shift-to-range-error relationship.

The project produces several visual artifacts that summarize the main analytical steps: period detection, pulse-profile reconstruction and simplified XNAV timing interpretation.

The epoch-folding search identifies the strongest candidate pulsation period in the photon arrival-time data.

Photon events are folded by phase using the detected period to reconstruct the pulsar pulse profile.

A simplified XNAV-style example showing how a phase shift can be interpreted as a timing offset.

A conceptual visualization of how timing error can be translated into approximate range error.

This project demonstrates skills that are useful for research, BI/data and systems-oriented roles in technical companies.

• ability to work with unfamiliar technical domains;
• understanding of scientific / engineering context;
• structured decomposition of a physical-data problem;
• clear documentation of assumptions and limitations.

• reproducible analytical pipeline;
• clean transformation from raw data to interpretable outputs;
• data quality awareness;
• structured notebook-based reporting.

• translation of raw observations into system-level interpretation;
• phase-shift and timing-error reasoning;
• explicit limitations and boundary conditions;
• decomposition of a complex technical idea into steps, artifacts and outputs.

This is a simplified research and demonstration project. It does not include:

• barycentric corrections;
• relativistic corrections;
• full spacecraft orbit determination;
• uncertainty estimation;
• multi-pulsar navigation;
• sensor fusion;
• production-grade validation.

The XNAV section should be interpreted as a conceptual timing demonstration, not as a real navigation system.

The value of the project is in the analytical structure: how raw observational data is transformed into a reproducible sequence of technical artifacts.

• Python
• NumPy
• pandas
• Matplotlib
• SciPy
• Astropy
• psrqpy
• Jupyter Notebook

Raw FITS data is not included in this repository because large data files are ignored by Git.

To run the notebooks, place the photon event file at:

data/raw/vela_photons.fits

Additional details are provided in:

data/README.md

Clone the repository:

git clone https://github.com/kva99kva-eng/pulsar.git

Go to the project folder:

cd pulsar

Create and activate a virtual environment:

python -m venv .venv
.venv\Scripts\activate

Install dependencies:

pip install -r requirements.txt

Place the FITS file here:

data/raw/vela_photons.fits

Run Jupyter Lab:

jupyter lab

Then run the notebooks in order from 01 to 06.

To make the project closer to a production-grade research workflow, the next improvements would be:

• add uncertainty estimation for the detected period;
• compare epoch-folding results with another period-search method;
• move reusable logic from notebooks into src/;
• add tests for preprocessing and phase calculations;
• add a project-level configuration file;
• document assumptions and parameters in a separate technical note;
• add a short architecture diagram for the analysis pipeline.

This project is licensed under the MIT License.