Research On Moving Transmitter Direct Tracking Based On Delay And Doppler

Passive direct tracking based on time delay and Doppler effect attracts much interest in radar,sonar,satellite positioning and navigation.Under the Bayesian filtering framework,a particle filter has been proposed for passive direct tracking which is a single step tracking of a moving emitter.The single step tracking methods generally outperform the traditional two-step methods because the single step approaches include the constraint that all measurements must be consistent with a geolocation of a single point emitter.However,the existing particle filter algorithms for direct tracking would reduce the diversity of particles during resampling,and therefore lose the tracking performance.In addition,the complexity analysis shows that the complexity of the algorithm increases dramatically when the number of particles and sampling of the particle filter is high,which is not suitable to real-time target tracking.In this paper,a Markov Chain Monte Carlo(MCMC)direct tracking algorithm and a direct Kalman filter tracking algorithm based on Laplace approximation are proposed to address the above problems,respectively.The main contents of this paper are given as follows.1.The existing direct particle filter tracking algorithms are reviewed and then the posterior Cramér-Rao lower bound(PCRLB)of the target tracking error is deduced.After that,the computational complexity is analyzed and simulation experiments are carried out.The simulation results show that the target tracking error decreases with the increase of SNR,the number of particles,and the number of sampling snapshots.However,the running time of the algorithm increases sharply when the number of particles and the number of sampling snapshots are large.2.A direct tracking algorithm based on MCMC is proposed.First of all,we introduce the Metropolis-Hasting sampling technique during the Bayesian filtering iterations.A set of samples that match the rejection-reception rate is selected as a set of Markov chains,which approximately obey the posterior probability density function of the target.Then the samples are averaged to estimate the state parameters such as the position and velocity of the target at each moment.Since the constructed Markov chains have good convergence characteristics,it avoids the problem of reduced convergence caused by particle depletion in the above mentioned particle filtering algorithm.Simulation results show that the tracking error of MCMC-based direct tracking algorithm decreases with the increase of SNR,Markov chain length,and the number of sample,and it is closer to PCRLB than the direct particle filter tracking algorithm under the same number of particles.3.A direct Kalman filter tracking algorithm based on Laplace approximation is proposed.This algorithm uses deterministic Laplace approximation to approximate the highly nonlinear posterior probability density function to a Gaussian distribution,and then performs real-time tracking via Kalman filter.Since the proposed algorithm belongs to the deterministic approximation domain,the computational complexity can be reduced compared with the particle filtering method.The simulation results show that the direct Kalman filter tracking algorithm based on Laplace approximation has less computational complexity than the standard particle filter.Moreover,the tracking error of the proposed method decreases with the increase of SNR and the number of sample,and it has much less computation time compared with the particle filter algorithm in the case of achieving the same tracking accuracy.