*Introduction*

In this appendix, we present the Carew and Belanger approach [1] as an alternative to the Mehra method to obtain the optimal Kalman gain. This approach is based on the prediction of the state vector using a sub-optimal gain. We first present some basic definitions and notations, used in the rest of the appendix; then, we consider the calculation of the innovation sequence's autocorrelation function for the sub-optimal case; and finally, using this calculation, we establish the relation between the optimal and sub-optimal cases.

*Notations and definitions*

The superscript * denotes the sub-optimal case and the superscript ^ denotes the optimal case. Thus, for example, *(*k/k*–1) is the *a priori* estimation of the state vector (*k*) when the gain *K*^{*} is sub-optimal whereas (*k/k* – 1) denotes the *a priori* estimation of (*k*) for optimal Kalman gain .

We now introduce the following notations:

*P**(*k/k*-1) denotes the autocorrelation ...

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