The exact Direct Maximum Likelihood Position Determination (ML-DPD) of multiple emitters requires a multidimensional searching with exponential complexity. The subspace-based DPD technique and the filtering-based DPD technique are recently proposed to reduce the complexity by transforming the original high-dimensional optimization problem into several low-dimensional ones. However, these techniques approximate the exact ML solution only if the measurements are assumed infinite. In this paper, we model the received signals in the nonlinear regression form and resort to the multidimensional optimization framework, consisting of the Pincus’ theorem and the Importance Sampling (IS) technique, to approximate the exact ML solution using finite measurements. The proposed IS based ML DPD approach also reduces the complexity by decoupling the multidimensional optimization problem into several three-dimensional ones. Moreover, the new non-iterative ML DPD approach guarantees global optimality and does not suffer from the off-grid problems inherent to most DPD techniques. The numerical simulations show that the proposed ML DPD estimator acquires the exact multidimensional ML solution even using a narrow bandwidth or being at low Signal to Noise Ratio (SNR).

多个发射器的精确直接最大似然位置确定（ML-DPD）需要具有指数复杂度的多维搜索。最近提出了基于子空间的DPD技术和基于过滤的DPD技术，通过将原始的高维优化问题转换为几个低维问题来降低复杂度。但是，这些技术仅在假设测量值无限大的情况下才近似精确的ML解决方案。在本文中，我们以非线性回归形式对接收到的信号进行建模，并诉诸于由Pincus定理和重要性采样（IS）技术组成的多维优化框架，以使用有限度量来逼近精确的ML解。所提出的基于IS的ML DPD方法还通过将多维优化问题解耦为几个三维问题来降低了复杂性。此外，新的非迭代ML DPD方法可确保全局最优，并且不会遭受大多数DPD技术固有的离网问题的困扰。数值仿真表明，即使使用窄带宽或处于低信噪比（SNR）时，所提出的ML DPD估计器也可以获得精确的多维ML解决方案。