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Projectile Motion: Equations01:26

Projectile Motion: Equations

10.4K
Projectile motion is commonly observed in our day-to-day life. For example, a basketball thrown by a player, an arrow shot from a bow, and kids jumping into the pool, all undergo projectile motion.
Any projectile motion problem can be solved by using the following strategy:
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Projectile Motion01:20

Projectile Motion

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An object thrown in the air follows a parabolic path under the influence of Earth's gravitational force. The motion of such an object is called projectile motion, and the object itself a projectile. The parabolic path followed by the projectile is called the trajectory. Some common examples of projectile motion are the launching of fireworks, a golf ball in the air, meteors entering the Earth's atmosphere, and the firing of bullets.
When an object falls under gravity and has no...
15.5K
Projectile Motion: Example01:18

Projectile Motion: Example

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The theory of projectile motion is very useful for players of several sports to improve their performance. For example, a javelin thrower needs to throw their javelin in such a way that it travels as far as possible. The javelin thrower takes a short run-up to increase the initial speed of the javelin. The range of a projectile is at its maximum at a 45° angle so javelin throwers try to angle their throw as close to 45° as possible.
When we speak of the range (R) of a projectile on...
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Field Application of Global Positioning System01:28

Field Application of Global Positioning System

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The Global Positioning System (GPS) has become an indispensable tool in fieldwork, offering unparalleled precision and efficiency for surveying, navigation, and infrastructure development. By harnessing signals from a constellation of satellites, GPS receivers determine the location of objects with remarkable speed and accuracy, often completing calculations within a second.Advantages of Modern GPS TechnologyContemporary GPS receivers are designed to meet the practical demands of field...
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Impact: Problem Solving01:26

Impact: Problem Solving

249
In an experiment conducted during a Mars mission, a rover propels a projectile with an initial velocity, and the projectile rebounds after colliding with the Martian surface. To ascertain the maximum height attained by the projectile after this collision, the known restitution coefficient and acceleration due to gravity are employed.
By designating the launch point as the origin and utilizing kinematic equations, the vertical component of the projectile's velocity at the point of impact is...
249
Errors in Global Positioning System01:26

Errors in Global Positioning System

79
Global Positioning System (GPS) technology has revolutionized navigation and positioning, but its accuracy is often compromised by various errors. These errors, stemming from environmental, satellite, and receiver-related factors, require careful mitigation to ensure reliable performance across applications.Atmospheric ErrorsGPS signals travel through the Earth’s ionosphere and troposphere, introducing delays which affect accuracy. The ionosphere is strongly influenced by charged particles,...
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Updated: Aug 5, 2025

Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

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LSTM-Based Projectile Trajectory Estimation in a GNSS-Denied Environment.

Alicia Roux1,2, Sébastien Changey1, Jonathan Weber2

  • 1French-German Research Institute of Saint-Louis, 5 Rue du Général Casssagnou, 68300 Saint-Louis, France.

Sensors (Basel, Switzerland)
|March 30, 2023
PubMed
Summary
This summary is machine-generated.

This study uses Artificial Intelligence (AI) with Long-Short-Term-Memories (LSTMs) to accurately estimate projectile trajectories without Global Navigation Satellite System (GNSS) signals. The AI approach significantly improves position and velocity estimations compared to traditional methods.

Keywords:
long-short-term-memorynavigationprojectile trajectory

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Area of Science:

  • Aerospace Engineering
  • Artificial Intelligence
  • Navigation Systems

Background:

  • Accurate projectile trajectory estimation is critical in Global Navigation Satellite System (GNSS)-denied environments.
  • Traditional Dead-Reckoning algorithms struggle with accumulating errors over time.
  • Deep learning offers a potential solution for enhanced navigation accuracy.

Purpose of the Study:

  • To develop and evaluate a deep learning approach using Long-Short-Term-Memories (LSTMs) for projectile trajectory estimation.
  • To investigate the impact of data pre-processing techniques on estimation accuracy.
  • To analyze the influence of sensor error models on the performance of the LSTM network.

Main Methods:

  • Trained Long-Short-Term-Memories (LSTMs) on simulated projectile flight data.
  • Utilized embedded Inertial Measurement Unit (IMU) data, magnetic field reference, flight parameters, and time as network inputs.
  • Implemented and analyzed data pre-processing steps including normalization and navigation frame rotation.
  • Compared LSTM estimations against a classical Dead-Reckoning algorithm.

Main Results:

  • The LSTM-based approach demonstrated superior accuracy in estimating projectile position and velocity compared to Dead-Reckoning.
  • Data pre-processing significantly influenced the estimation accuracy by rescaling 3D projectile data.
  • The Artificial Intelligence (AI) contribution was evident, outperforming even GNSS-guided projectiles in certain aspects.

Conclusions:

  • Deep learning, specifically LSTMs, provides a robust and accurate method for projectile trajectory estimation in GNSS-denied scenarios.
  • Optimized data pre-processing is crucial for maximizing the performance of AI-driven navigation systems.
  • The proposed AI method offers a significant advancement over conventional navigation algorithms for unguided projectiles.