# Unit of Velocity from a Random Walk measured by an accelerometer

• hoddy
In summary: It seems to me that the measurement equation should describe the relationship between the observed measurement and the current state, but the random walk process contributes to the evolution of the state from its previous value to its current value, rather than to the mapping of the current state to the observed measurement.Don't forget that the Gaussian random walk process is continuous, whereas the state vector is discrete. If you propagate the state vector from one time step to the next by adding a Gaussian random variable, you are assuming that it takes on a different value at each of the infinitely many intermediate times. But in reality, you only observe the state vector at discrete times, and you only know that it falls within a certain range of values at each time. So if you want to
hoddy
TL;DR Summary
Hi, I am working on a kalman filter where my measurement equation involves "-g + v" , where g is in m/s^2 and v is velocity random walk given in m/s/sqrt(hr). Feels like a stupid question, but how can I transform the unit of velocity random walk so I can do the calculation correctly?
Hi, I am working on a kalman filter where my measurement equation involves "-g + v" , where g is in m/s^2 and v is velocity random walk given in m/s/sqrt(hr). Feels like a stupid question, but how can I transform the unit of velocity random walk so I can do the calculation correctly?

hoddy said:
Summary: Hi, I am working on a kalman filter where my measurement equation involves "-g + v" , where g is in m/s^2 and v is velocity random walk given in m/s/sqrt(hr). Feels like a stupid question, but how can I transform the unit of velocity random walk so I can do the calculation correctly?

Hi, I am working on a kalman filter where my measurement equation involves "-g + v" , where g is in m/s^2 and v is velocity random walk given in m/s/sqrt(hr). Feels like a stupid question, but how can I transform the unit of velocity random walk so I can do the calculation correctly?
It looks to me as though you are trying to add quantities with incommensurate units. ##g## has units of acceleration, and ##v## has units that are neither velocity or acceleration. That suggests that there is an error somewhere in the derivation of the ##-g+v## term. Maybe you have assumed that some variable has a value of ##1##, and forgotten to carry along its units.

scottdave
Also, I wonder why you are including your random walk process in the measurement equation rather than in the state propagation equation?

## 1. What is a random walk?

A random walk is a mathematical concept that describes the movement of a particle or object in a random or unpredictable manner. It is often used to model the behavior of a wide range of systems, including the movement of molecules, stock prices, and even the behavior of animals.

## 2. What is an accelerometer?

An accelerometer is a device that measures acceleration, which is the rate of change of velocity over time. It typically consists of a small mass attached to a spring, which moves when subjected to acceleration, and a sensor that measures the movement of the mass.

## 3. How does an accelerometer measure velocity from a random walk?

An accelerometer measures acceleration, which can then be integrated to calculate velocity. In the case of a random walk, the accelerometer records the acceleration caused by the random movements of the object, and this data can be used to calculate the overall velocity of the object.

## 4. What is the unit of velocity in a random walk measured by an accelerometer?

The unit of velocity in a random walk measured by an accelerometer is meters per second (m/s). This is the standard unit for velocity and represents the distance traveled by an object in one second.

## 5. How accurate is the velocity measurement from a random walk using an accelerometer?

The accuracy of the velocity measurement from a random walk using an accelerometer depends on several factors, including the sensitivity and precision of the accelerometer, the duration of the random walk, and the complexity of the movement. In general, accelerometers can provide accurate velocity measurements, but the margin of error may increase with longer or more complex random walks.

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