# Relative Postion Calculation using Accelerometer

• I_am_learning
In summary: If you constantly monitor the acceleration in all three axis, I could be able to tell the instanteneus velocity about those axixes. Then time integral should provide me the displacement?
I_am_learning
I am starting to learn Mobile Phone Application Development.
Suddenly this idea clicked in.
The app starts with the Phone in rest on your living room table.
Now, the phone is picked up from the living room and transported to the dining room.
Could the app be able to tell this?
Here is how I think it.
If I constantly monitor the acceleration in all three axis, I could be able to tell the instanteneus velocity about those axixes. Then time integral should provide me the displacement?
Is there flaw somewhere?
Can the mobile phone accelerometer be fast and accurate enough?

The acceleration vector described by the phones accelerometers will be the sum of 2 component vectors, the actual acceleration of the phone, and the force of gravity. In order to make your idea work you need a way to figure out the orientation of the phone at every instant so that you know the direction of the gravity vector (you already know the amplitude is 9.8 m/s2). Once you know the gravity component you can subtract it from the vector measured by the phone to obtain the acceleration. Then you could, in principal, integrate over time to keep track of relative displacement.

The tricky part is finding the direction of the gravity vector. I can think of no way to do it. someone more clever then I might have an idea though.

Theoretically, it's very possible.

Practically, there's a problem. Accelerometers aren't perfect, which means that the larger the displacement (especially when the discplacement occurs in all directions in the three dimensions), the larger the error. Using only an accelerometer, you have no way of knowing how large this error is.

mrspeedybob said:
The acceleration vector described by the phones accelerometers will be the sum of 2 component vectors, the actual acceleration of the phone, and the force of gravity. In order to make your idea work you need a way to figure out the orientation of the phone at every instant so that you know the direction of the gravity vector (you already know the amplitude is 9.8 m/s2). Once you know the gravity component you can subtract it from the vector measured by the phone to obtain the acceleration. Then you could, in principal, integrate over time to keep track of relative displacement.

The tricky part is finding the direction of the gravity vector. I can think of no way to do it. someone more clever then I might have an idea though.

Yeah, the rotation thing is what is bothering me too.
Lets suppose the Phone starts flat on the table, with x-acceleration = 0, y-acceleration = 0 and z-acceleration = 9.8m/s.
Now, if our kind volunteer would always transport the phone, with its plane parallel to the ground (like in the initial condition), then we could always subtract 9.8m/s from z-acceleration.
But what if he rotates the phone? What acceleration is felt during the rotation? Can I distinguish rotation from translation?, and if yes, can I find the new orientation, and thus be able to correctly subtract the gravity?

what other sensors does it have? magnetometer? gyro?

Many phones have gyroscope sensors and some have magnetic compasses but those have decreased accuracy indoors

## 1. What is an accelerometer and how does it work?

An accelerometer is a device that measures acceleration, or changes in velocity, of an object in three-dimensional space. It works by using a small mass suspended by springs or other elastic materials. When the object moves, the mass is displaced and this movement is measured by sensors, usually in the form of electrical signals.

## 2. How does an accelerometer calculate relative position?

An accelerometer uses the data it collects about acceleration to calculate relative position. By measuring the changes in acceleration in all three dimensions, the device can calculate the relative position of the object in space. This is commonly done using a process called double integration, which involves integrating the acceleration data twice to get the position data.

## 3. What are the common applications of relative position calculation using accelerometers?

Accelerometers are used in a variety of applications where measuring relative position is important. Some common examples include navigation systems, motion control systems, and virtual reality devices. They are also used in smartphones and fitness trackers to track movement and activity.

## 4. Are there any limitations to using accelerometers for relative position calculation?

Yes, accelerometers have some limitations when it comes to calculating relative position. They are affected by external factors such as vibration, shock, and temperature changes, which can introduce errors in the data. Additionally, they may not be as accurate in certain situations, such as when the object is not moving in a linear fashion.

## 5. How can the accuracy of relative position calculation using accelerometers be improved?

To improve the accuracy of relative position calculation, multiple accelerometers can be used in conjunction with each other. This allows for more accurate measurements and also helps to compensate for any external factors that may affect the data. Additionally, advanced algorithms and filtering techniques can be used to reduce errors and improve the overall accuracy of the calculations.

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