       constraints in EKF

• To: mathgroup at smc.vnet.net
• Subject: [mg33309] constraints in EKF
• From: "Tobias Wahl" <enxtw1 at nottingham.ac.uk>
• Date: Thu, 14 Mar 2002 19:51:09 -0500 (EST)
• Organization: ACS, The University of Nottingham
• Sender: owner-wri-mathgroup at wolfram.com

```Dear All,

I want to introduce equality and inequality constraints in a discrete
extended Kalman filter (I programmed it myself and DON'T use the Mathematica
one if there is one). Unfortunately I cannot find any real detailed and
target oriented approach to that. Any hint would be very much appreciated.

For your information: I aim to estimate the plants state and unknown
parameters (fa0,fb0,fc0,fI0) on which I have one inequality constraint
(fa0<=fb0) and one equality constraint (f0-fa0-fb0-fc0-fI0=0) where f0 is a
variable passed on to the filter at every sample instant. If I cannot
implement the equality constraint never mind, but the inequality constraint
is important since it resolves an ambiguity problem between fa0 and fb0 and
makes the system observable.

Furthermore I am working with an discrete perturbation-around-working point
model. There are several way of doing what I want:
1.) setting initial covariances (I don't want to do that because they change
when iterating the filter?)
2.) truncation of covariances?
3.) introduce slack variables (that's what I want!): fa0 - fb0 - s^2 = 0
Here I also need to estimate the slack variable s? But how to
implement that in my filter matrices and vectors? Where can I get a detailed
description from?
How can I introduce the equality constraint?

Any hints would be very much appreciated? Thank you very much in advance.

Tobias

```

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