Question

Explain with necessary system / control equations how Kalman filtering can be used in guiding an unmanned aircraft.

Answer 1

Kalman filtering is a form of optimal estimation characterized by recursive evaluation, and an internal model of the dynamics of the system being estimated. Kalman filter has the ability to combine the subsystems, on the knowledge of the measurements noise covariance (GPS measurements noise covariance) and the process noise covariance.

The Kalman filter assumes that the random process which has to be estimated is of the form:

dx/dt = Fx+Bu+Gw

where x is a state value, u is a control effort, w is white noise with known covariance.

When measurements are taken of the process at discrete moments in time , they occur according to the following relationship:

Hx+Du+v= z

where z is a noisy sample, D is the direct transmission of the input to the output,

H is the ideal (noiseless) connection between the measurement and the state, and ν is measurement error.

This process can be modeled discretely in the following form, assuming there are not control inputs u to the system.

The system error is defined as: Ek =Xk-X^k

Xk is the best estimate prior to receiving a measurement at time K t .

The disadvantage of the Navigation Linear Error Kalman Filter is that the assumption of linearity for the error estimates is not always valid. Also, the unbounded error in the uncorrected INS output can cause numerical problems if the algorithm will run for a long time.