Dead reckoning is a navigational method used to estimate the current position of a moving object based on its previously known position, speed, direction and time elapsed. This technique does not require external references (like GPS or landmarks) and relies on continuous monitoring of movement data. This method is especially useful in applications such as maritime and aviation navigation, automotive systems, pedestrian tracking and robotics, where consistent positional data is crucial.

## How Dead reckoning method works

Following steps summarize working of Dead reckoning method.
Step-2 : Perform velocity measurement by determining the speed and direction of travel.
Step-3 : Estimate time elapsed i.e. Keep track of the time over which the object has been moving.
Step-4 : Use the speed and time to calculate the distance traveled.
Step-5 : Update the position based on the direction and distance moved from the initial position.

### Mathematical formula

If the initial position is (Xo,Yo) , speed is 'v', the direction (bearing) is θ and time elapsed from beginning is 't'; then the new position (X1, Y1) can be estimated as per following formula.
➨ X1 = Xo + v * t * cost( θ)
➨ Y1 = Yo + v * t * sin( θ)

Let us understand Dead reckoning with example.
• Imagine a hiker starting at a known position with a compass and a pedometer. By tracking the number of steps taken (distance) and the direction of travel (bearing), the hiker can estimate their current position through dead reckoning.
• However, over long distances, errors in step count or direction can lead to significant inaccuracies, so the hiker periodically checks their position using a map or GPS to correct for drift.
Also refer Dead Reckoning basics >> to know more on its working principle.

Following are dead reckoning sensors used in positioning calculation and correction.
1. Accelerometers: Measure acceleration to estimate changes in velocity and direction.
2. Gyroscopes: Measure angular velocity to track changes in orientation.
3. Magnetometers: Provide heading information by detecting the Earth's magnetic field.
4. Odometers: Measure the distance traveled (commonly used in vehicles).

Following are popular Dead reckoning applications commonly found in various navigational domains.
• Maritime Navigation: Used by ships and submarines when GPS signals are unavailable.
• Aviation: Assists in navigation, particularly in cases of GPS failure or in conjunction with other navigation systems.
• Automotive Navigation: Enhances GPS data in tunnels, urban canyons or areas with poor satellite reception.
• Pedestrian Navigation: Used in fitness trackers and smartphones to track movement indoors where GPS is unreliable.
• Robotics: Helps robots and drones navigate in environments where external references are not available.

1. Independence from External Signals : Works without relying on external signals, making it useful in environments where GPS or other signals are weak or unavailable.
2. Continuity : Provides continuous position updates, which is particularly useful for applications requiring real time tracking.

1. Accumulation of Errors: Small errors in speed, direction and time measurements accumulate over time, leading to increasing inaccuracies in the estimated position.
2. Drift or Error : Without external corrections, the position estimate will drift away from the true position, necessitating periodic recalibration or corrections from reliable external references.

### Conclusion :

Dead reckoning is popular due to its ability to provide continuous, real-time position updates without reliance on external signals, making it invaluable in environments where GPS or other navigation systems are unavailable or unreliable. Despite its susceptibility to cumulative errors, dead reckoning's independence from external references and its integration with other sensors for enhanced accuracy ensure its continued relevance and utility across various fields.