Search

CN-121995312-A - TDOA/FDOA passive positioning method based on alternate direction multiplier method

CN121995312ACN 121995312 ACN121995312 ACN 121995312ACN-121995312-A

Abstract

A TDOA/FDOA passive positioning method based on the alternate direction multiplier method comprises the steps of firstly, utilizing a weighted least square method to initially estimate the target position and speed; then, carrying out first-order Taylor expansion on the nonlinear geometric constraint at the initial point, and reconstructing the original non-convex optimization problem into a constraint weighted least square model with linear coupling constraint; finally, introducing an ADMM frame, and realizing efficient decoupling solution of position and speed variables by alternately updating the target position, the speed and the Lagrange multiplier; the system, the equipment and the medium are used for realizing the TDOA/FDOA passive positioning method based on the alternate direction multiplier method; the method effectively solves the problem that the traditional nonlinear optimization is easy to be trapped in local optimization, remarkably improves the positioning precision, greatly reduces the calculation complexity, and enhances the robustness and the instantaneity of the algorithm under the conditions of low signal-to-noise ratio and complex observation.

Inventors

  • HAO BENJIAN
  • WU KEHAO
  • WANG YUXUAN
  • WANG XINLEI
  • RONG FEI
  • LIU BENHU
  • Luo Jiashen
  • CHEN XIAOJUN
  • LI ZAN

Assignees

  • 西安电子科技大学

Dates

Publication Date
20260508
Application Date
20260128

Claims (10)

  1. 1. The TDOA/FDOA passive positioning method based on the alternate direction multiplier method is characterized by comprising the following steps of: step 1, arranging at least 5 observation stations in a three-dimensional space, initializing, and determining position coordinates, motion speed vectors, signal propagation speeds and iteration termination thresholds of the observation stations; Step 2, all the observation stations synchronously receive the target signal, and acquire an arrival time difference TDOA measured value and an arrival frequency difference FDOA measured value of the target signal between each observation station and the reference station; Step 3, introducing distance and distance change rate auxiliary variables, and converting a nonlinear TDOA/FDOA equation into a pseudo-linear equation set; step 4, performing first-order Taylor series expansion on nonlinear geometric constraints at the initial position and the speed estimated value, and reconstructing the original non-convex optimization problem into a constraint weighted least square model with linear coupling constraints; And 5, solving the constraint weighted least square model by using an alternating direction multiplier method ADMM framework, and updating the target position, the target speed and the Lagrange multiplier alternately until convergence conditions are met, so as to finally output an accurate estimation result of the target position coordinate and the speed vector.
  2. 2. The TDOA/FDOA passive positioning method of claim 1, wherein the number of observation stations in step 1 is set to be First, the The position coordinates of each observation station are The motion velocity vector is The target position to be estimated is The velocity vector is The true distance between the target and the observation station is The change rate of the distance is 。
  3. 3. A TDOA/FDOA passive positioning method according to claim 1, wherein in step 2 zero mean gaussian white noise is added to the TDOA and FDOA measurements to simulate an actual measurement environment: without loss of generality, the first observation station is set as the reference station wherein, And The gaussian measurement noise with the mean value of zero respectively, And Respectively, are observation stations And the distance difference and the distance change rate difference between the reference stations 1, squaring the two sides of the reference stations and ignoring the second-order noise item to obtain the following TDOA/FDOA positioning equation: 。
  4. 4. The TDOA/FDOA passive localization method of claim 1, wherein in step 3, the set of pseudo-linear equations is Wherein the estimated quantity to be measured is Matrix of (a) And The structure of (2) is as follows: Weighting matrix used by weighted least square method Determined from a noise covariance matrix of the time difference of arrival, TDOA, measurements and the frequency difference of arrival, FDOA, measurements; obtaining an initial solution by using a weighted least square method: due to intermediate variables And And unknown quantity And There is a nonlinear relationship between them, thus resulting in the following constrained weighted least squares problem: 。
  5. 5. The TDOA/FDOA passive localization method of claim 1, wherein in step 4 the linear coupling constraint is derived by defining a jacobian matrix for the target position and velocity and performing a first order taylor expansion at the initial estimated point; At the initial point Deployment of the site The method comprises the following steps: Definition of the definition And The corresponding constraints are expressed as: Wherein, the , The constraint weighted least squares problem after reconstruction is therefore restated as: Wherein, the 。
  6. 6. The TDOA/FDOA passive localization method of claim 1, wherein in step 5, the solving using the ADMM framework specifically comprises: Constructing an augmented lagrangian function; Wherein, the To correspond to constraint conditions Is a product of the lagrangian multipliers of (c), Is a penalty coefficient; by the ADMM method, the following three iterative updates are derived: Under the condition of fixed target speed and Lagrangian multiplier, solving closed-form solution about target position, firstly, under the condition of fixed variable And On the premise of (1), the constraint condition is converted into Definition of And Augmenting the Lagrangian equation and retaining the inclusion Is obtained by: Are arranged as about Is of the standard convex quadratic form Wherein the matrix And (3) with The specific forms of (a) are as follows: Thus, the following is obtained Is estimated as a weighted least squares of ; Under the condition of fixing the target position and Lagrangian multiplier, solving a closed solution about the target speed; Updating Lagrangian multipliers; Similarly, at the fixing of And Is converted into constraint conditions under the condition of (1) Wherein And Augmenting the Lagrangian equation and retaining the inclusion Is obtained by: Are arranged as about Is a standard convex quadratic form of (a): wherein the matrix And (3) with The specific forms of (a) are as follows: Thus, the following is obtained Is estimated as a weighted least squares of Wherein, the After completing the alternate update of position and velocity, the lagrangian multiplier is updated to Repeatedly executing the iterative process until the convergence condition is satisfied, and finally outputting the target position And a target speed 。
  7. 7. A TDOA/FDOA passive positioning method according to claim 6 wherein the convergence condition is that the amount of change in the target position and velocity estimates obtained in two consecutive iterations is less than a predetermined iteration termination threshold.
  8. 8. A TDOA/FDOA passive location system based on an alternate direction multiplier method, implementing the TDOA/FDOA passive location method based on an alternate direction multiplier method of any one of claims 1 to 7, comprising: the data acquisition module is used for controlling at least 5 observation stations arranged in the three-dimensional space to synchronously receive the target signals and acquiring an arrival time difference TDOA measured value and an arrival frequency difference FDOA measured value of the target signals between each observation station and the reference station; the initial estimation module is used for introducing distance and distance change rate auxiliary variables, converting a nonlinear TDOA/FDOA equation into a pseudo-linear equation set, and calculating an initial position and a speed estimation value of the target by using a weighted least square method; the model reconstruction module is used for performing first-order Taylor series expansion on the nonlinear geometric constraint at the initial position and the speed estimation value, and reconstructing the original non-convex optimization problem into a constraint weighted least square model with linear coupling constraint; and the iteration solving module is used for solving the constraint weighted least square model by utilizing an alternating direction multiplier method ADMM framework, and outputting the accurate estimation result of the target position coordinate and the speed vector by alternately updating the target position, the target speed and the Lagrange multiplier until the convergence condition is met.
  9. 9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the TDOA/FDOA passive localization method based on the alternating direction multiplier method as claimed in any one of claims 1 to 7 when the program is executed by the processor.
  10. 10. A computer readable storage medium having stored thereon a computer program which when executed by a processor implements a TDOA/FDOA passive localization method based on the alternating direction multiplier method as claimed in any one of claims 1 to 7.

Description

TDOA/FDOA passive positioning method based on alternate direction multiplier method Technical Field The invention belongs to the technical field of communication, and particularly relates to a TDOA/FDOA passive positioning method based on an alternate direction multiplier method. Background The Alternate Direction Multiplier Method (ADMM) combines parallelism of the dual decomposition method with good convergence performance of the augmented lagrangian method. The framework decomposes a complex original problem into a series of easily processed sub-problems by utilizing a separable structure of an objective function to carry out alternate iteration, effectively relieves the calculation burden of a large-scale and complex constraint optimization problem, shows great application potential in the field of optimization algorithms, and has been tried to be introduced into a positioning problem. For example, patent application CN120595232a entitled "positioning method and system based on differential time delay and alternate direction multiplier method" proposes a passive target positioning method based on ADMM, which uses Differential Time Delay (DTD) to jointly estimate the positions of a stationary target and an unknown transmitter. The method embodies the effectiveness of ADMM in solving the positioning problem. However, the method and the existing ADMM positioning scheme represented by the method have the fundamental limitations that the model is only designed for a static target, utilization and modeling of FDOA observables are completely lacking, so that the target speed cannot be estimated in principle, and the processing constraint is only a static geometric constraint, so that the dynamic coupling relation between the position and the speed cannot be described. This results in the existing ADMM positioning framework not being directly applicable to the more challenging dynamic scenario of joint positioning and velocity measurement of mobile radiation sources. In order to meet the positioning requirement of a moving target, the prior art mainly searches along two paths, but has obvious defects that a closed solution or a two-step optimization framework based on the traditional Lagrangian multiplier method is adopted in the first scheme. For example, the patent application, "improved constrained weighted least squares TDOA/FDOA passive location method based on Lagrangian multiplier" (CN 119471565A) proposes a two-step solution strategy by first obtaining an initial closed solution through pseudo-linearization and constraint simplification, and then establishing a nonlinear equation set based on the original constraint for iterative optimization. Although the method can obtain the analytic primary solution, the process of step-by-step solving and iterative correction still has the obvious defects that the model error introduced by constraint simplification in the first step is transferred to the second step to influence convergence accuracy and stability, and the nonlinear iterative optimization in the second step is still possibly influenced by initial value quality, and the whole calculation process still has a lifting space in the aspect of efficiency and accuracy balance. The second category of schemes turns to heuristic global optimization algorithms based on random search. The improved heuristic search is adopted to solve the problem of non-convex optimization as in the patent application 'a time-frequency difference passive positioning method based on a self-adaptive step-size cuckoo search algorithm' (CN 121299583A). However, such methods generally have problems of low convergence speed, high calculation cost, large influence of parameter setting and randomness on the quality of solutions, and the like, and in scenes with high noise or strict real-time requirements, the robustness and engineering practicability of the method are often insufficient. In summary, the prior art has obvious capability fault and performance bottleneck in the aspect of the combined positioning of the mobile radiation source TDOA/FDOA, namely, on one hand, an ADMM frame with high efficiency and good convergence is only suitable for static scenes and has incomplete functions, and on the other hand, a closed solution method and a heuristic algorithm capable of processing dynamic problems have limitations in error transfer, calculation efficiency or convergence reliability respectively. The concrete steps are as follows: 1. Functional limitations and model deficiencies the existing ADMM positioning framework (such as CN 120595232A) is designed only for static targets, lacks modeling of FDOA observables and speed estimation, and cannot meet the estimation requirements of the complete motion state (position and speed) of the targets in dynamic scenes. 2. The existing method capable of processing dynamic positioning, such as an algorithm based on two-step closed solution or heuristic search, often has the problems of error accum