Ie, if you have as state variables position (**p**) and velocity (**v**), and I make low-frequency measurements of **p**, this also indirectly gives me information about **v** (since it's the derivative of **p**). What is the best way to to handle such a relationship?

A) At the update step, should I only say I've measured **p**, and rely on the filtering process, and my accumulated state-covariance matrix (**P**), to correct **v**?

B) Should I create an "extra" prediction step, either after or before my update step for the measurement of **p**, that uses my measured **p** and (relatively large) delta-time to make a high-variance prediction of **v**?

C) In my update/measurement step, should I say I've made a measurement of both **p** and 
**v**, and then somehow encode information about their interdependence into the measurement co-variance matrix (**R**)?

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For a little more background, here's the specific situation in which I've run into the problem:

I'm working with a system where I want to estimate the position (**p**) of an object, and I make frequent measurements of acceleration (**a**) and infrequent, high-noise measurements of **p**.

I'm currently working with a codebase that does this with an Extended Kalman Filter, where it keeps as state variables **p** and **v**. It runs a "prediction" step after every acceleration measurement, in which it uses the measured **a** and delta-time to integrate and predict new **p** and **v**.  It then runs an "update"/"measurement" step for every (infrequent) **p** measurement.

The problem is this - I get occasional high-error measurements of **a**, which result in highly-erroneous **v**.  Obviously, further measurements of **a** will never correct this, but measurements of **p** should get rid of this.  And, in fact, this does seem to happen... but VERY slowly.

I was thinking that this may be partially because the only way **p** affects **v** in this system is through the covariance matrix **P** - ie, method A) from above - which seems fairly indirect.  I was wondering if there would be a better way to incorporate our knowledge of this relationship between **p** and **v** into the model, so that measurements of **p** would correct **v** faster.

Thanks!