Research On Passive Location And Velocity Measurement Technology By TDOA And FDOA Of Multiple Stations Under Atmospheric Refraction Conditions

Passive interception of signals from receiving radiation sources such as radars and communications and measurement of time difference of arrival(TDOA)and arrival frequency difference(FDOA)can achieve passive location and velocity measurement of radiation source,in electronic reconnaissance,electromagnetic situational awareness,it has a wide range of applications in the field of rescue search.Because of the atmospheric inhomogeneity,especially at low elevation angles and long distances,the refraction effect occurs during the propagation process of radio waves,the propagation path bends,and the propagation speed is less than the speed of light.Futhermore,the measured TDOA and FDOA are deviated from TDOA and FDOA under the linear condition,and the positioning and velocity measurement results obtained by TDOA and FDOA positioning algorithm under the condition of the linear propagation model also cause large deviation.Aiming at this problem,this paper focuses on the passive location and velocity correction algorithm of TDOA and FDOA under atmospheric refraction.The main contents of this paper are as follows:(1)Three-dimensional TDOA location error correction algorithm under atmospheric refraction is studied.A correction model of atmospheric refraction TDOA location error is established.Aiming at the phenomenon the initial location point can not be iterated,a grid search and iteration two-step correction algorithm is proposed,and the Cramer-Rao Lower Bound(CRLB)of three-dimensional TDOA location under atmospheric refraction is derived.The simulation results show that in the case of small random noise,the correction effect is very obvious,and CRLB can be achieved.with the increase of random noise,positioning effect is less and less obvious,atmospheric refraction error will be submerged in the random noise.And there is a small deviation,so the positioning root mean square error is lower than CRLB.(2)The altitude-constrained TDOA location error correction algorithm under atmospheric refraction is studied.It is proved that the iterative correction algorithm can not reach the optimum when the elevation constraint is redundant,and the validity of the demonstration is verified by simulation analysis.Furthermore,a two-step correction algorithm based on iterative and improved particle swarm optimization is proposed,and the CRLB for elevation-constrained TDOA localization under atmospheric refraction is derived.The simulation results show that the modified algorithm achieves the CRLB compared with the iterative method,and greatly improves the operation speed compared with the improved particle swarm optimization algorithm.(3)The error correction algorithm of TDOA and FDOA passive location for air-toground bistatic stations under atmospheric refraction is studied.An error correction model for air-to-ground atmospheric refraction is established,and an iterative error correction algorithm is proposed.The CRLB for TDOA and FDOA location under atmospheric refraction is derived.Using the control variable method,the positioning accuracy of the modified algorithm is analyzed under difference TDOA and FDOA random noises.The simulation results show that the modified algorithm can reach the CRLB,which illustrates the effectiveness of the modified algorithm.(4)Three-station TDOA and FDOA location and velocity error correction algorithm under atmospheric refraction are studied.The model of atmospheric refraction TDOA and FDOA positioning and velocity measurement error correction is established.A two-step method is proposed to correct the positioning and velocity measurement errors respectively.The first step is to iteratively correct the positioning errors by two TDOA equations and one elevation constraint equation.The second step is based on the first step,the equations of velocity measurement under atmospheric refraction are established and solved directly.The CRLB for TDOA and FDOA location and velocity measurement at three stations under atmospheric refraction are derived respectively.The simulation results show that the modified algorithm can reach the CRLB,which illustrates the effectiveness of the modified algorithm.