RETINAsolver

A high-precision telemetry solver for bistatic passive radar systems. RETINAsolver processes simultaneous detections from multiple sensors to determine target position and velocity using Levenberg-Marquardt least squares optimization.

Features

• 3-Detection System: Processes three simultaneous radar detections for enhanced accuracy
• 6D State Estimation: Solves for full position (x, y, z) and velocity (vx, vy, vz)
• High Precision: Sub-meter position accuracy with robust convergence
• Bistatic Radar Support: Handles sensors paired with illuminators of opportunity (IoO)
• Optional Initial Guess: Accept user-provided initial estimates for improved convergence
• JSON Interface: Simple input/output format for easy integration
• Modular Design: Clean separation of detection parsing, initial guess, and solver components

Repository Structure

RETINAsolver/
├── main_3det.py               # Main solver entry point
├── detection_triple.py        # Input data structures and parsing
├── lm_solver_3det.py          # Levenberg-Marquardt solver implementation
├── initial_guess_3det.py      # Initial guess generation algorithms
├── Geometry.py                # Coordinate system conversions
├── test_*.py                  # Unit and integration tests
├── ../adsb2dd/               # ADS-B to delay-doppler converter (sibling directory)
├── ../synthetic-adsb/        # Synthetic radar data generator (sibling directory)
├── test_3detections_final/   # Comprehensive test cases
├── analysis_tools/           # Performance analysis scripts
└── README.md                 # This file

Quick Start

Prerequisites

pip install numpy scipy

Basic Usage

1. Prepare detection data in JSON format:

{
  "detection1": {
    "sensor_lat": 40.7128,
    "sensor_lon": -74.0060,
    "ioo_lat": 40.7589,
    "ioo_lon": -73.9851,
    "freq_mhz": 1090.0,
    "timestamp": 1700000000,
    "bistatic_range_km": 25.5,
    "doppler_hz": 150.0
  },
  "detection2": {
    "sensor_lat": 40.6782,
    "sensor_lon": -73.9442,
    "ioo_lat": 40.7589,
    "ioo_lon": -73.9851,
    "freq_mhz": 1090.0,
    "timestamp": 1700000000,
    "bistatic_range_km": 28.2,
    "doppler_hz": 125.0
  },
  "detection3": {
    "sensor_lat": 40.7500,
    "sensor_lon": -73.9860,
    "ioo_lat": 40.7589,
    "ioo_lon": -73.9851,
    "freq_mhz": 1090.0,
    "timestamp": 1700000000,
    "bistatic_range_km": 22.8,
    "doppler_hz": 175.0
  }
}

2. Optional: Add initial guess for improved convergence:

{
  "detection1": { ... },
  "detection2": { ... },
  "detection3": { ... },
  "initial_guess": {
    "position_lla": {
      "lat": 40.8,
      "lon": -74.0,
      "alt": 10000.0
    },
    "velocity_enu": {
      "east": 70.0,
      "north": 300.0,
      "up": 200.0
    }
  }
}

3. Run the solver:

python main_3det.py input_detections.json

4. Get results:

{
  "timestamp": 1700000000,
  "latitude": 40.799619,
  "longitude": -73.970136,
  "altitude": 10142.0,
  "velocity_east": 69.7,
  "velocity_north": 298.6,
  "velocity_up": 200.0,
  "convergence_metric": 0.617,
  "residuals": [0.52, 21.3, -0.09, 7.5, -0.62, -124.2]
}

Key Features

Optional Initial Guess Support

You can now provide an initial guess to improve convergence for challenging scenarios:

Benefits:

• Faster convergence for distant targets
• Improved success rate in challenging geometries
• Backward compatible - works without initial guess
• Automatic validation and fallback to generated guess

Input Format: LLA position + ENU velocity in JSON Validation: Altitude 0-100km, velocity ±1000 m/s bounds checking Conversion: Automatic LLA→ENU coordinate transformation

Data Pipeline

The complete workflow from synthetic data to solved positions:

../synthetic-adsb → ../adsb2dd → RETINAsolver → analysis

1. Generate synthetic data: Create realistic aircraft trajectories and radar measurements
2. Convert to detection format: Transform ADS-B tracking data to bistatic measurements
3. Solve for position/velocity: Process detections to recover target state
4. Analyze performance: Validate accuracy and convergence characteristics

Algorithm Overview

How It Works

RETINAsolver implements a passive radar telemetry system that:

1. Takes simultaneous detections from three sensors, each measuring:

   • Bistatic range (IoO → Target → Sensor path length)
   • Doppler shift (frequency difference due to target motion)

2. Converts coordinates from geographic (lat/lon) to local ENU (East/North/Up) for calculations

3. Generates initial guess using ellipse intersection geometry or accepts user-provided estimate

4. Solves 6D optimization using Levenberg-Marquardt algorithm to minimize measurement residuals

5. Returns solution in geographic coordinates with velocity vector

Coordinate Systems

• Input/Output: Geographic WGS84 (lat/lon/alt)
• Internal Processing: Local ENU tangent plane
• Conversions: Direct LLA↔ENU transformations

Optimization Method

• Algorithm: Levenberg-Marquardt least squares
• State Vector: 6D position and velocity [x, y, z, vx, vy, vz]
• Measurements: 6 equations (3 bistatic range + 3 Doppler)
• Constraints: Altitude bounds, velocity limits, convergence criteria

Initial Guess Strategies

1. Automatic: Ellipse intersection geometry (default)
2. User-Provided: LLA position + ENU velocity (optional)
3. Validation: Bounds checking with automatic fallback

Testing & Validation

Test Suites

• Unit Tests: Individual component validation
• Integration Tests: End-to-end solver testing
• Performance Tests: Convergence rate and accuracy analysis
• Synthetic Data Tests: 20+ challenging geometric scenarios

Run Tests

# Core solver tests
python -m pytest test_*.py -v

# Integration tests with sample data
python main_3det.py test_3detections_final/3det_case_1_input.json

# Performance analysis
python analyze_initial_guess.py
python verify_3det_solution.py

Expected Performance

• Convergence Rate: >95% for well-conditioned problems
• Position Accuracy: Sub-meter typical, <10m worst-case
• Velocity Accuracy: ~1 m/s typical, <5 m/s worst-case
• Processing Time: <1 second per solve

Input/Output Specification

Detection Input

Each detection requires:

Field	Type	Description
sensor_lat	float	Sensor latitude (degrees)
sensor_lon	float	Sensor longitude (degrees)
ioo_lat	float	Illuminator of Opportunity latitude (degrees)
ioo_lon	float	Illuminator of Opportunity longitude (degrees)
freq_mhz	float	Transmission frequency (MHz)
timestamp	int	Unix timestamp (milliseconds)
bistatic_range_km	float	Total path IoO→Target→Sensor (km)
doppler_hz	float	Doppler frequency shift (Hz)

Optional Initial Guess

Field	Type	Description
initial_guess.position_lla.lat	float	Initial latitude estimate (degrees)
initial_guess.position_lla.lon	float	Initial longitude estimate (degrees)
initial_guess.position_lla.alt	float	Initial altitude estimate (meters, 0-100km)
initial_guess.velocity_enu.east	float	Initial eastward velocity (m/s, ±1000)
initial_guess.velocity_enu.north	float	Initial northward velocity (m/s, ±1000)
initial_guess.velocity_enu.up	float	Initial upward velocity (m/s, ±1000)

Solution Output

Field	Type	Description
timestamp	int	Input timestamp
latitude	float	Target latitude (degrees)
longitude	float	Target longitude (degrees)
altitude	float	Target altitude (meters)
velocity_east	float	Eastward velocity (m/s)
velocity_north	float	Northward velocity (m/s)
velocity_up	float	Upward velocity (m/s)
convergence_metric	float	Final optimization residual
residuals	array	Individual measurement residuals

Supporting Tools

This repository includes supporting tools as sibling directories:

# Use tools for data generation and processing
cd ../synthetic-adsb      # Generate synthetic radar data
cd ../adsb2dd            # Convert ADS-B to detection format

Synthetic Data Generation

cd ../synthetic-adsb
python server.py  # Start synthetic radar API

Generates realistic aircraft movement patterns and bistatic radar measurements for testing.

ADS-B Conversion

cd ../adsb2dd
npm start  # Start web-based converter

Browser-based tool to convert ADS-B aircraft tracking data to detection format.

Error Handling

The solver returns {"error": "No Solution"} when:

• Input validation fails (invalid coordinates, frequencies, etc.)
• Initial guess validation fails (if provided)
• Levenberg-Marquardt fails to converge
• Altitude constraints violated during optimization

Error types:

• {"error": "Detection X validation failed"} - Invalid detection data
• {"error": "Initial guess validation failed"} - Invalid initial guess bounds
• {"error": "No Solution"} - Optimization failed to converge

Performance Characteristics

Metric	Value
Convergence Rate	>95%
Position Accuracy	<1m typical
Velocity Accuracy	~1 m/s typical
Processing Time	<1s per solve
Memory Usage	<10MB
Dependencies	numpy, scipy only

Contributing

1. Code Standards: Follow existing modularity and style
2. Testing: Add tests for new features
3. Documentation: Update relevant README sections
4. Backward Compatibility: Maintain JSON interface compatibility
5. Performance: Validate solver accuracy before merging

Architecture Notes

• Modular Design: Core solver separated from data generation/conversion
• Sibling Directories: Tools maintained in separate repositories as sibling directories
• JSON Interface: Simple, language-agnostic input/output format
• Coordinate Flexibility: Handles global geographic coordinate systems
• Robust Validation: Comprehensive error checking and bounds validation

License

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Citation

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