- posted
18 years ago

Forgive me, but I am new to Kalman filters. I am having problems

designing a Kalman filter for inertial position and velocity

estimation.

Given the state and measurement Kalman equations:

X(t+1) = A(t)X(t) + w(t)

Y(t) = H(t)X(t) + v(t)

What I want is position and velocity estimates for x,y,z,roll,pitch

and yaw. I have measurements for roll,pitch and yaw and their rates so

the state and measurement equations are fairly obvious given the state

vector being position and velocity. For x,y and z axis, I want the

estimate for the inertial position and velocities. The measurements I

have are x,y in body frame and z in inertial frame, the 3 velocities

and accelerations in body frame with the gravity vector added in for

z. Given that I have the roll, pitch and yaw, I have the direction

cosine available to convert from body to inertial(world) frame. The

problem I am having is that given that X(t) is in inertial frame and

Y(t) is in body frame I am having trouble coming up with a H(t)

matrix. Also I am having trouble subtracting out the gravity vector in

the context of the measurement equation.

There must be some examples of something similar that is done in

aircraft navigation. If someone can point me to a simple description

of this, it would be helpful.

- bijtaj