| Compared to active positioning,passive positioning technology has gained increasing attention in recent years because it does not actively send electromagnetic signals to the outside world and has higher concealment,security and resistance to interference.Passive positioning based on external radiation sources does not rely on the signals radiated by the target itself,but rather uses a large number of third party signals in the air(e.g.FM radio signals,mobile phone base station signals,WIFI signals,etc.)to locate the target,which makes passive positioning techniques more widely available.There are various observation parameters that can be used in passive positioning,and literature has shown that passive positioning algorithms using Bistatic Range(BR)and Bistatic Range Rate(BRR)have better positioning accuracy.Therefore,this paper focuses on the BR/BRR-based passive positioning technique for external radiation sources and its main contributions are as follows:(1)Through the simulation analysis of an algebraic solution for multi-station passive coherent localization based on BR/BRR,it was found that there is still room for improvement in the localization accuracy.To address this issue,a multi-station and multi-external radiation source iterative algorithm based on BR/BRR is proposed.The algorithm first establishes a maximum likelihood estimation model through BR/BRR observation equations,and then pseudo-linearizes the model to obtain iterative expressions.The iterative expressions are solved by weighted least squares with the introduction of auxiliary parameters multiple times to obtain the initial value of the iterative expressions.Finally,the initial value is substituted into the iterative expressions to obtain estimates of the target position and velocity parameters.Simulation results show that within a certain level of observation error,the position and velocity deviation curves of the proposed algorithm are lower than existing algorithms,and the root mean square error curves of position and velocity can approach or even reach the Cramer-Rao Lower Bound(CRLB),indicating that the proposed algorithm outperforms existing algorithms in terms of localization accuracy.(2)Although the positioning accuracy of the multi-station,multi-external radiation source iterative algorithm based on BR/BRR has been further improved,the use of iteration increases the algorithm’s computational complexity,which can affect the real-time performance of the positioning algorithm.To address this issue,an error estimation-based multi-station BR/BRR external radiation source positioning algorithm is proposed.First,the observation equation is established by introducing an auxiliary vector,which provides an initial rough estimate of the target’s position and velocity.Unlike classical algorithms,this algorithm estimates the positioning error of the rough estimate,thereby obtaining the final estimate of the target’s position and velocity.Unlike iterative algorithms,this algorithm belongs to an analytical algorithm,and no initial value is required,nor is there a need to consider convergence issues during the solving process.Compared to the existing Three-step Weighted Least Squares(3WLS)algorithm,this algorithm simplifies the calculation steps while avoiding the problem of sign ambiguity.Combining simulation results with computational complexity analysis,this algorithm’s positioning accuracy is not only superior to the existing 3WLS algorithm,but the computational complexity is also further reduced.In addition,when the observation error is less than 32 d B,although this algorithm’s positioning accuracy is slightly lower than the previously proposed iterative algorithm,the computational complexity of this algorithm is reduced by 33.35%,greatly improving the algorithm’s positioning real-time performance.When the observation error gradually exceeds 32 d B,the analytical algorithm’s positioning accuracy begins to surpass the iterative algorithm due to the gradually emerging drawbacks of the iterative algorithm’s dependence on initial values. |
