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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:

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

and are the initial conditions.

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

2) Give the estimate of 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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