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Discrete Stochastic Processes and Optimal Filtering by Roger Ceschi, Jean-Claude Bertein

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7.4. Exercises for Chapter 7

Exercise 7.1.

Given the state equation XK+1 = A XK + NK

where the state matrix A is the “identity” matrix of dimension 2 and NK the system noise whose covariance matrix is written Q = σ2Id (Id : identity matrix).

The system is observed by the scalar equation:

images where images and images are the components of the vector XK and where WK is the measurement noise of the variance images.

images and images are the initial conditions.

1) Give the expression of the Kalman gain K(1) at instant “1” according to σ2 and images.

2) Give the estimate of images of X1 at instant “1” according to the first measurement of K(1) and the first measurement Y1.

Solution 7.1

1)

2)

Exercise 7.2.

We are considering the movement of a ...

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