Dead Reckoning

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Dead Reckoning
An Introduction

Prof. David Bernstein
James Madison University

Computer Science Department

bernstdh@jmu.edu

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Getting Started

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Definition:
- The process of determining the location of a point from the location of another point, a speed, a duration of time, and a heading
Notation:
- $a \in \mathbb{R}^2$ denotes the original point on the plane
- $\alpha$ denotes the heading (by convention, $0^\circ$ is to the right, $90^\circ$ is up, etc.)
- $s$ is the speed
- $t$ is the time duration

Performing the Calculations (cont.)

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The Solution:
Words of Caution:
- These illustrations are for headings in the interval $[0^\circ, 90^\circ]$ , you should think carefully about what happens in the other quadrants
- You need to be careful about units

An Example

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The Initial Point:
- $0, 0$
The Measured Data:
- $\alpha = 30^\circ$
- $s = 30\text{mph}$
- $t = 15\text{min} = 0.25\text{hr}$

An Example (cont.)

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Distance Traveled:
- $s \cdot t = 30\text{mph} \cdot 0.25\text{hr} = 7.5\text{mi}$
The Trigonometry:
- $\cos(\alpha) = \cos(30^\circ) = 0.866$
- $\sin(\alpha) = \sin(30^\circ) = 0.500$
The New Location:
- $(0.0 + 0.866 \cdot 7.5, 0.0 + 0.500 \cdot 7.5) = (6.495, 3.750)$

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