By using two rotating noncollinear antennas or three spatially fixed noncoplanar antennas on a spacecraft, full information on the polarization and the direction of arrival of an electromagnetic wave can be obtained by measuring the voltages created by the electric field of the incident wave. The physical parameters (polarization and direction of arrival) of the incoming wave are related to the received voltages on the antenna system by the so-called direction-finding equations. Since the used antennas are generally of small directivity (electrically short monopoles or dipoles), the resulting system of equations is numerically close to singular, and generally no unique solution can be obtained for the physical parameters of the wave throughout the inversion process. However, there exists a very powerful tool for dealing with sets of equations that are singular or close to singular, known as singular-value decomposition (SVD), which precisely focuses the problem. For illustration, this paper analyzes the direction-finding equations for the Radio and Plasma Wave Science (RPWS) experiment on the Cassini spacecraft by using SVD techniques. It also compares the expected performances of RPWS with those of the Ulysses Unified Radio and Plasma Wave (URAP) experiment achieved at Jupiter for the kilometer and hectometer emissions. The RPWS experiment on Cassini, which will be launched in 1997, is supposed to observe wave phenomena between a few hundred Hertz and 16 MHz in the Saturnian magnetosphere.