Camera-Radar Fusion for Single-Image 3D Projectile Tracking

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Solution Overview

Problem

Existing camera calibration methods require decomposition into explicit extrinsic and intrinsic parameters, leading to reprojection errors and assumptions that may not be true, and they lack the ability to determine 3D position of a projectile with a single 2D image and radar measurements.

Innovation Solution

A method using a calibrated camera and continuous wave radar to determine the position and speed of a projectile in 3D world coordinates without decomposing camera parameters, utilizing a homographic transformation and time-synchronized radar with a higher sampling rate to calculate the 3D position from a single image and radar measurements.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of manufacture

If camera calibration decomposes parameters into explicit extrinsic and intrinsic parameters, then calibration can be performed using standard pinhole camera model, but reprojection errors occur and assumptions about lens distortion and tilt may not be true

Engineering Contradiction:

Improvecalibration processVSAvoidreprojection accuracy

Core Design Contradiction:

Ease of manufactureVSMeasurement precision

Solution Approach 1:

The patent extracts only the essential geometric transformation information needed for 3D position determination, avoiding the traditional decomposition into extrinsic and intrinsic parameters. By using a homographic transformation matrix that directly maps 3D world coordinates to 2D image coordinates, the method eliminates reprojection errors associated with assuming standard pinhole camera models and makes no assumptions about lens distortion or tilt.

Inventive Principle:

Principle #2Taking out (Extraction)

2Measurement precision

If traditional calibration methods are used, then camera parameters can be estimated, but the ability to determine 3D position of projectile with single 2D image and radar measurements is lost

Engineering Contradiction:

Improvecamera parameter estimationVSAvoid3D position determination capability

Core Design Contradiction:

Measurement precisionVSAdaptability or versatility

Solution Approach 1:

The patent merges camera imaging data with radar range and velocity measurements to determine 3D projectile position. The homographic transformation matrix combines geometric projection information from the camera with depth information from radar, enabling accurate 3D position reconstruction from a single 2D image point and corresponding radar measurements.

Inventive Principle:

Principle #5Merging (Combining)

3Ease of manufacture

If decomposition into intrinsic and extrinsic parameters is performed, then camera model can be established, but several assumptions and constraints must be made which might not be true

Engineering Contradiction:

Improvecamera model setupVSAvoidparameter assumptions

Core Design Contradiction:

Ease of manufactureVSReliability

Solution Approach 1:

Instead of decomposing the projection matrix into extrinsic and intrinsic parameters as in traditional methods, the patent inverts the approach by directly using the homographic transformation matrix without decomposition. This reversal eliminates the need for assumptions about lens distortion, tilt, and other camera model constraints, providing more reliable results when those assumptions don't hold.

Inventive Principle:

Principle #13The other way round (Inversion)

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

Enables accurate determination of the 3D position and speed of a projectile without making assumptions about intrinsic or extrinsic camera parameters, improving calibration accuracy and efficiency.

Implementation Method 1

determining a radial speed of the projectile at a particular time based on the radar measurements

Methodology Applied

Scientific EffectDoppler effect: Doppler Effect

Data Source

PatentUS12586248B2Camera and radar fusion for determining position of projectile in motion

Publication Date: 2026.03.24 RAPSODO

AI summary

Disclosed are embodiments for determining the position and speed of a projectile in three-dimensional world coordinates using a single camera and radar. In some embodiments, a method comprises: determining a zero radial speed time of the projectile based on radar measurements of the projectile; determining a radial speed of the projectile at a particular time based on the radar measurements; determining a radial speed slope at the particular time based on the radial speed measurements; determining a two-dimensional image point of the projectile at the particular time; determining a depth scale coefficient at the particular time based on the zero radial speed time, the radial speed, the radial speed slope, the image point, and a homographic transformation; and determining a position of the projectile in space at the particular time based on a three-dimensional position of the camera, the depth scale coefficient, the image point and the homographic transformation.