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I've been asked to design a Kalman Filter where we can observe several states of a process (some of which being related to each other) and to use the Kalman filter to combine related observations to get a better estimate of each.

Some texts I've been reading seem to indicate instead of making a prediction and measurement and using these to form the best estimate, two measurements are combined to form the best estimate (of one of the measurements). In examples, the two measurements seem to be usually a state and its derivative.

I find all of this quite confusing - is this a proper technique?

Let's say, for example, we can measure

[tex] u,\ v,\ w,\ V_{tot} [/tex]

where [tex]u,\ v\ and\ w[/tex] represent the speed in 3 dimensions and [tex]V_{tot}[/tex] is the total velocity - i.e. [tex]V_{tot}=\sqrt{(u^2+v^2+w^2)}[/tex]

I guess the rates of change of these variables are also observable. How could the Kalman filter be used here (where functions to make predictions of the next step are unknown)...

Something else that would really be terrific would be a worked example of an ekf with a nonlinear system - many people seem to have difficulty understanding this (myself included, and I've been reading about them for over a year now!).

Some texts I've been reading seem to indicate instead of making a prediction and measurement and using these to form the best estimate, two measurements are combined to form the best estimate (of one of the measurements). In examples, the two measurements seem to be usually a state and its derivative.

I find all of this quite confusing - is this a proper technique?

Let's say, for example, we can measure

[tex] u,\ v,\ w,\ V_{tot} [/tex]

where [tex]u,\ v\ and\ w[/tex] represent the speed in 3 dimensions and [tex]V_{tot}[/tex] is the total velocity - i.e. [tex]V_{tot}=\sqrt{(u^2+v^2+w^2)}[/tex]

I guess the rates of change of these variables are also observable. How could the Kalman filter be used here (where functions to make predictions of the next step are unknown)...

Something else that would really be terrific would be a worked example of an ekf with a nonlinear system - many people seem to have difficulty understanding this (myself included, and I've been reading about them for over a year now!).

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