Design And Hardware Acceleration Of Low-bias Wireless Positioning Algorithm

The development of wireless positioning technology is accompanied by the continuous optimization of positioning algorithms to improve the positioning accuracy.The design of classical algorithms sets many idealized assumptions for the positioning scene.In the actual positioning scene,there are common obstacles,crowd activities and non-ideal channel environment,resulting in a series of interference errors.If these interference errors are not processed by optimizing the positioning algorithm,the positioning accuracy will be seriously affected.One of the main indicators to measure the positioning accuracy is the positioning bias.Therefore,this thesis mainly studies the design and implementation of low bias wireless location algorithm.This thesis first analyzes the positioning algorithm error in the positioning system,and provides a theoretical basis for the design of low bias positioning algorithm.Theoretical analysis shows that the positioning algorithm error can be divided into iterative algorithm error and closed algorithm error.Convergence threshold and the accuracy of iterative initial value determine the error of iterative algorithm.The error of the closed-form algorithm comes from the simple linearization of the nonlinear observation model.The commonly used pseudo-linear model ignores the high-order error term and the correlation between the observation error vectors,resulting in a large positioning bias.In this thesis,the low bias algorithms of elliptic and hyperbolic positioning are studied to reduce the positioning bias caused by the high-order error term and the correlation between the observation error vectors.Based on the analysis of the bias of pseudo linear observation model in the positioning algorithm error,this thesis first proposes a low bias ellipse positioning algorithm based on semidefinite programming(SDP).In the elliptical positioning model,the position estimation problem is transformed into the minimization problem of negative log-likelihood(NLL)function,and it is transformed into a quadratic programming problem with multiple quadratic equality / inequality constraints.By equivalent transformation and relaxation of the non-convex rank 1 constraint,the quadratic programming problem with multiple quadratic equality /inequality constraints is transformed into a semidefinite programming problem and the final closed-form positioning solution is calculated.Starting from the original likelihood function,the scheme achieves a balance between the nonlinear observation model and the pseudo-linear observation model.It not only avoids the iterative solution of nonlinear observation model,but also avoids the pseudo-linear observation model error caused by ignoring the high-order error term because of the need for linearization.At the same time,it ensures the positioning accuracy and the calculation efficiency of positioning algorithm.This thesis not only gives the detailed derivation process of the algorithm,but also analyzes and compares the estimation performance of the positioning estimator under different noise levels through Monte Carlo simulation experiments.Simulation results show that under different noise levels,the algorithm does not need post-processing,and gives the minimum variance unbiased estimation of the location estimator.Different from the above algorithm to avoid the use of pseudo linear observation model,this thesis proposes a low bias hyperbolic positioning algorithm based on constrained total least squares(CTLS).In this algorithm,the pseudo-linear observation model of hyperbolic positioning problem is first given.According to the bias analysis of pseudo linear observation model,considering the quadratic error term and the correlation between observation errors,the positioning model based on CTLS estimation theory is given,and the iterative solution of the positioning problem is obtained by Newton iterative method.Next,the quadratic error term and the correlation between observation errors are also considered.In order to maintain the estimation performance of position parameters under the general observation error model,a positioning model based on generalized total least squares(GTLS)estimation theory is proposed.The closed-form solution of the positioning problem is obtained by matrix decomposition and matrix transformation.The calculation is simple,and the matrix square and inversion are avoided and has strong numerical stability.Simulation results show that under different noise levels,CTLS estimator and GTLS estimator almost achieve the optimal statistical performance,effectively reducing the positioning bias caused by ignoring the correlation between observation error vectors and quadratic error terms.In the design of low bias positioning algorithm based on GTLS,the iterative solution of positioning problem is avoided by matrix transformation and decomposition,and the convergence of the algorithm is ensured.At the same time,the calculation bottleneck in the process of solving is introduced: Singular Value Decomposition(SVD).Therefore,at the end of this thesis,the hardware acceleration of singular value decomposition on FPGA heterogeneous platform is realized,and the parallel algorithm of singular value decomposition is realized on the hardware platform.The experimental results show that the proposed singular value decomposition acceleration scheme consumes less hardware resources and the calculation error is within the allowable range.Compared with the calculation time of singular value decomposition on MATLAB,the calculation time is significantly reduced and the acceleration effect is obvious.