## 1 Introduction  
The techniques of emitter localization using direction of arrival (DOA) measurements [1; 2; 3; 4; 5] play an important role in many areas, including vehicle navigation, localization and tracking of acoustic sources, and location services of satellite communications. In such localization systems, a single moving observer or multiple stationary observers are used to determinate the positions of the emitters. Generally, each observer is equipped with an antenna array for measuring the DOAs of the transmitted sources, and the emitter can then be located at the intersection of a set of lines of bearing [6; 7; 8]. The location procedure described above is typically called the two-step method. In the first step, the signal parameters (e.g., DOA [1; 2; 3; 4; 5], time difference of arrival (TDOA) [9; 10], time of arrival (TOA) [11; 12], frequency difference of arrival (FDOA) [13; 14], frequency of arrival (FOA) [15], and received signal strength (RSS) [16; 17]) are separately measured at several stations. In the second step, a central station uses the measurements to estimate the position coordinates of the sources. The two-step procedure is also known as the decentralized approach [18]. Note that although the two-step procedure is widely applied to the modern localization system, it is difficult to yield the optimal position estimate from the point of view of statistical characteristics. The reason is that the signal parameters are obtained by ignoring the constraint that all measurements must correspond to a common source position. As a result, information loss between the two steps is unavoidable. Althoughit can be proved by the extended invariance principle (EXIP) [19] that the two-step method provides an asymptotically efficient estimate under certain conditions, these requirements cannot be easily met in practical scenarios. To improve the accuracy of two-step location methods, a promising technique, called the direct position determination (DPD) approach, is proposed over the past few years. DPD is a centralized and single-step estimation technique in which the estimator uses exactly the same data as classical two-step methods but searches for the source location directly. Generally, the DPD method outperforms conventional two-step methods under low-signal-to-noise conditions and when there are relatively few samples; moreover, it does not encounter the association problem. More importantly, the DPD technique can be applied to many wireless positioning systems. Specifically, the DPD method for locating a narrowband radio emitter based on a Doppler shift is presented in [20; 21], and DPD methods for locating a wideband source based on a time delay metric are proposed in [22; 23; 24]. Furthermore, DPD estimators using both the Doppler frequency and time delay are developed in [25; 26; 27; 28]. Note that in the DPD methods mentioned above, multiple platforms each equipped with a single-antenna receiver are used for position determination, and as a result, the DOA information of the impinging signals cannot be exploited. In [29], a DPD method based on multiple static stations each equipped with an antenna array is first proposed. In this single-step location method, the array response is modeled as a function of the source position, and only a two-dimensional search is required although there are many stray parameters in the array signal model. Following the work of [29], other DPD estimators for special localization scenarios are developed in the literature. In particular, DPD methods for multiple radio emitters are presented in [30; 31], and some high-resolution DPD methods are given in [32; 33]. DPD estimators for the cases of known waveforms and multipath environments are developed in [34] and [35; 36], respectively. In addition, DPD methods tailored to special signals (e.g., orthogonal frequency division multiplexing signals, cyclostationary signals, and intermittent emissions) are proposed in [37; 38; 39].