Generalized Cramer-Rao Bound in the Case of Azimuth and Elevation Direction Finding
M. P. Slichenko, Olga Zavalishina, Ekaterina Artemova · 2023
The paper proposes a generalized Cramer-Rao bound for the case of joint azimuth and elevation direction finding of a radio emission source by a multichannel direction finder with an antenna system of arbitrary structure and directivity characteristics. A theorem is formulated for the Fisher information of joint azimuth and elevation estimates in the case of a multichannel detector-direction finder with an antenna system described in the chosen coordinate system by a vector complex radiation pattern. The dependences of the root mean square error of direction finding in azimuth and in elevation angle on the signal-to-noise ratio are obtained, calculated from the used and generalized expressions for the Cramer-Rao lower bound. The applicability condition for the existing and proposed in the paper expressions for the Fisher information matrix is obtained. The concept of the energy center of the antenna system is given. To confirm the validity of the generalized expression of the Cramer-Rao lower bound, statistical modeling was carried out.