Design And Hardware Acceleration Of Algorithms For Elliptic Localization With Sensor Position Uncertainty

Wireless location technology is profoundly influencing the way humans live and work.Elliptic Localization,one of the ways in which wireless positioning systems work,has received a lot of attention.Researchers at home and abroad have conducted extensive research on measurement techniques,noise models and positioning algorithms in elliptic localization systems and have continued to develop target positioning algorithms with high accuracy,stability and real-time performance.Among the algorithms studied so far,the arrival time difference-based and angle-based observations are mostly used to estimate the position of the target,while the Doppler shift-based observations are used to estimate the velocity of the moving target.Most of these algorithms assume that the base station of the positioning system is free of sensor position uncertainty.In this paper,for an elliptic localization system with multiple transmitting base stations and multiple receiving base stations with sensor position uncertainty,the target is located using two observation quantities,the time difference of arrival and the Doppler frequency shift.In order to reduce the impact of sensor position uncertainty on positioning accuracy,two different positioning algorithms are designed in this paper,and a hardware-based computing acceleration structure is designed for the large number of matrix multiplication operations involved in the algorithms.Firstly,this paper considers the use of an elliptic localization system with sensor position uncertainty for the localization of moving targets.The system combines observations of time difference of arrival and Doppler shift for joint estimation of target position and velocity.The hybrid Cramer-Rao lower bound for the system was analyzed according to parameter estimation theory to provide an indicator for the assessment of localization performance.A non-iterative estimator that treats sensor position uncertainty as equivalent to observation errors is designed through a two-stage process of parameter transformation and model linearization,and a detailed derivation of the algorithm is given.The effect of sensor position uncertainty on the performance of the algorithm is investigated experimentally.The results show that the noniterative estimator designed in this paper outperforms the commonly used closed-form solution algorithm in terms of estimation performance,and that the algorithm can reach the mixed Cramer-Rao lower bound under small noise conditions.It is also demonstrated through largescale simulation experiments that the proposed estimator has low bias and is less computationally intensive.Secondly,for elliptic localization systems where the receiving base station is affected by the environment and generates sensor position uncertainty,this paper reduces the negative impact of sensor position uncertainty on positioning performance by introducing a calibration source(a transmitter source whose position is known with certainty).The feasibility of the introduction of the calibration source is first illustrated by the analysis of the Cramer-Rao lower bound.The calibration source is then used to derive a linear minimum mean square error estimate of the sensor position uncertainty to obtain improved station coordinates.Finally,a two-step weighted least squares algorithm based on corrected station locations is proposed to obtain accurate target position estimates.The experiments consider the effects of observation error and sensor position uncertainty on positioning accuracy separately,and compare the root mean square error of different estimation quantities.The experiments show that the use of calibration sources can reduce the loss of positioning accuracy due to sensor position uncertainty and improve the positioning performance.Moreover,the smaller the observation error,the more significant the performance improvement of the calibration source.Finally,considering the increased size of the correlation matrix in the algorithm when the number of base stations in the localization scenario increases,this paper designs a hardware acceleration scheme for the key part of the algorithm.In order to solve the problem of slow solution of large scale matrix computation by Central Processing Unit(CPU),a Field Programmable Gate Array(FPGA)based platform proposes a high-speed parallel hardware acceleration architecture with multiple Process Element(PE).The triangular matrix is obtained by LU decomposition of the large-scale matrix,and the sparsity of the triangular matrix is analyzed and the matrix is blocked.A processing unit is built on the FPGA side for each block to carry out operations,realizing a two-dimensional unidirectional ring network structure with multiple processing units operating in parallel.Experimental results show that the proposed hardware-accelerated architecture provides good acceleration for large-scale matrix multiplication operations and outperforms general-purpose CPUs and Graphics Processing Units(GPUs).