trilateration-coordfinder 1.0.1

High-precision geospatial trilateration solver using multiple optimization methods

Trilateration Coordinate Finder

High-precision geospatial trilateration solver using multiple optimization methods to determine unknown coordinates from known reference points and distances.

Features

• Multiple Optimization Methods: Uses differential evolution, L-BFGS-B, Nelder-Mead, Powell, CG, and BFGS algorithms
• Two-Phase Refinement: Initial optimization followed by iterative precision refinement
• High Precision: Sub-meter accuracy in optimal conditions
• Vincenty Distance Calculations: Uses WGS-84 ellipsoid for accurate geodesic distances
• Professional CLI: Clean, apt-style progress indicators and status updates
• TTY-Aware: Adapts output based on terminal capabilities

Installation

From PyPI

pip install trilateration-coordfinder

Usage

Command Line Interface

Run the interactive CLI:

trilateration

You'll be prompted to enter:

1. Three reference points (latitude, longitude)
2. Distance from each reference point to the unknown location (in meters)

As a Python Library

from trilateration import (
    multi_stage_optimization,
    refine_position,
    verify_solution
)

# Define reference points and distances
reference_points = {
    "lat": [50.8561306, 49.8109078, 48.5883175],
    "lon": [14.7763778, 18.6925036, 12.4846475]
}
measured_distances = [91070, 304700, 218100]  # in meters

# Phase 1: Initial optimization
solution = multi_stage_optimization(reference_points, measured_distances)

# Phase 2: Precision refinement
final_point, errors, iterations, total_checked, total_error = refine_position(
    solution,
    reference_points,
    measured_distances
)

print(f"Final position: {final_point[0]:.8f}, {final_point[1]:.8f}")

How It Works

Phase 1: Global Optimization

The solver tries three different optimization approaches:

1. Multi-stage optimization: Combines differential evolution (global search) with L-BFGS-B (local refinement)
2. Alternative optimization: Tests multiple methods from different starting points, including antipodal positions
3. Geometric approach: Uses grid search to find candidates, then refines with local optimization

The best solution from these methods is selected and further refined.

Phase 2: Iterative Refinement

Starting from the Phase 1 solution, the solver:

• Generates surrounding points at multiple radii (from nanometers to kilometers)
• Tests 8 directions (N, NE, E, SE, S, SW, W, NW) at each radius
• Iteratively moves toward the point with minimum total distance error
• Converges when no improvement is found or tolerance is met

Output Interpretation

The solver provides residuals (distance errors) for each reference point:

• < 1m: Optimal - High precision result
• 100-5000m: Sub-optimal - Good approximation
• 5000-10000m: Non-optimal - Rough estimate
• > 10000m: Failed - Poor solution quality

Requirements

• Python >= 3.7
• numpy >= 1.21.0
• scipy >= 1.7.0
• geopy >= 2.2.0

Author

LOKAI77

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

Acknowledgments

• Uses Vincenty's formula via geopy for accurate geodesic calculations
• Optimization algorithms provided by scipy
• Inspired by real-world GPS trilateration challenges