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Background:

I am a newbie in DSP. I am implementing a simple Kalman Filter that estimates the heading direction of a robot. The robot is equipped with a compass and a gyroscope.

My Understanding:

I am thinking about representing my state as a 2D vector $$(x, \dot{x})$$, where $$x$$ is the current heading direction and $$\dot{x}$$ is the rotation rate reported by the gyroscope.

Questions:

1. If my understanding is correct, there will be no control term, $$u$$ in my filter. Is it true? What if I take the state as a 1D vector $$(x)$$? Then does my $$\dot{x}$$becomes the control term $$u$$? Will these two methods yield different results?
2. As we know, the main noise source comes from the compass when the compass is in a distorted magnetic field. Here, I suppose the Gaussian noise is less significant. But the magnetic distortion is totally unpredictable. How do we model it in the Kalman Filter?
3. In Kalman Filter, is the assumption that "all the noises are white" necessary? Say, if my noise distribution is actually a Laplacian distribution, can I still use a Kalman Filter? Or I have to switch to another filter, like Extended Kalman Filter?

Background:

I am a newbie in DSP. I am implementing a simple Kalman Filter that estimates the heading direction of a robot. The robot is equipped with a compass and a gyroscope.

My Understanding:

I am thinking about representing my state as a 2D vector $$(x, \dot{x})$$, where $$x$$ is the current heading direction and $$\dot{x}$$ is the rotation rate reported by the gyroscope.

Questions:

1. If my understanding is correct, there will be no control term, $$u$$ in my filter. Is it true? What if I take the state as a 1D vector $$(x)$$? Then does my $$\dot{x}$$becomes the control term $$u$$? Will these two methods yield different results?
2. As we know, the main noise source comes from the compass when the compass is in a distorted magnetic field. Here, I suppose the Gaussian noise is less significant. But the magnetic distortion is totally unpredictable. How do we model it in the Kalman Filter?
3. In Kalman Filter, is the assumption that "all the noises are white" necessary? Say, if my noise distribution is actually a Laplacian distribution, can I still use a Kalman Filter? Or I have to switch to another filter, like Extended Kalman Filter?

Background:

I am implementing a simple Kalman Filter that estimates the heading direction of a robot. The robot is equipped with a compass and a gyroscope.

My Understanding:

I am thinking about representing my state as a 2D vector $$(x, \dot{x})$$, where $$x$$ is the current heading direction and $$\dot{x}$$ is the rotation rate reported by the gyroscope.

Questions:

1. If my understanding is correct, there will be no control term, $$u$$ in my filter. Is it true? What if I take the state as a 1D vector $$(x)$$? Then does my $$\dot{x}$$becomes the control term $$u$$? Will these two methods yield different results?
2. As we know, the main noise source comes from the compass when the compass is in a distorted magnetic field. Here, I suppose the Gaussian noise is less significant. But the magnetic distortion is totally unpredictable. How do we model it in the Kalman Filter?
3. In Kalman Filter, is the assumption that "all the noises are white" necessary? Say, if my noise distribution is actually a Laplacian distribution, can I still use a Kalman Filter? Or I have to switch to another filter, like Extended Kalman Filter?
1

# How to model unpredictable noise in Kalman Filter?

Background:

I am a newbie in DSP. I am implementing a simple Kalman Filter that estimates the heading direction of a robot. The robot is equipped with a compass and a gyroscope.

My Understanding:

I am thinking about representing my state as a 2D vector $$(x, \dot{x})$$, where $$x$$ is the current heading direction and $$\dot{x}$$ is the rotation rate reported by the gyroscope.

Questions:

1. If my understanding is correct, there will be no control term, $$u$$ in my filter. Is it true? What if I take the state as a 1D vector $$(x)$$? Then does my $$\dot{x}$$becomes the control term $$u$$? Will these two methods yield different results?
2. As we know, the main noise source comes from the compass when the compass is in a distorted magnetic field. Here, I suppose the Gaussian noise is less significant. But the magnetic distortion is totally unpredictable. How do we model it in the Kalman Filter?
3. In Kalman Filter, is the assumption that "all the noises are white" necessary? Say, if my noise distribution is actually a Laplacian distribution, can I still use a Kalman Filter? Or I have to switch to another filter, like Extended Kalman Filter?