A Computationally Effective SDP Solution for Target Localization Using DTD and DFS Measurements in Multistatic Systems With Unknown Signal Propagation Speed

This paper investigates the moving target localization in multistatic systems for unknown signal propagation speed environments and presents a semi-definite programming (SDP) solution with reduced computational complexity by differential time delay (DTD) and differential frequency shift (DFS) measurements. Existing research on this problem defines numerous auxiliary variables to pseudo-linearize measurement models, proposing high requirement related to the number of transmitters/receivers for effective localization performance of the solution or causing the computationally demanding solution. To address the aforementioned shortcomings, the auxiliary variables introduced when constructing pseudo-linear equations from the measurement models are minimized as much as possible. After that, based on the weighted least squares (WLS) criterion, a constrained WLS formulation of reducing the number of constraints is proposed, as the constraints included are formulated according to the relationships among auxiliary variables. Considering the non-convexity of the formulation, semi-definite relaxation (SDR) is applied to transform the constrained WLS problem into its SDP form for the global optimum. Besides, the mean square error (MSE) and complexity analyses are conducted to validate the performance of the proposed method from two perspectives. Both analyses and simulation results demonstrate that the method has the ability to balance the localization accuracy and computational load.