Method for solving least square grid search of multi-base joint positioning of external radiation source radar

Abstract

The present application belongs to the field of radar technology, and relates to a multi-base joint positioning least square grid search solving method of an external radiation source radar, comprising the following steps: establishing an observation equation according to a multi-station external radiation source positioning principle; performing parameter substitution and parameter separation processing on to-be-estimated parameters (target position); converting the multi-dimensional to-be-estimated parameters into one-dimensional to-be-estimated parameters; and obtaining the least square estimation of the target position through a grid search method. The present application reduces the complexity of the grid search least square estimation, and has higher positioning precision and smaller calculation amount.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radars. BACKGROUND

[0002] Passive radar can use civil or commercial radiation sources in the environment as opportunity illuminators to detect and locate targets, and is a special kind of bistatic radar. It has the advantages of high concealment, anti-electronic interference, anti-anti-radiation missile, good coverage, low operation and maintenance cost, and does not occupy spectrum resources, etc., and in recent years has attracted widespread interest from scholars in various fields.

[0003] At present, the external radiation source positioning problem has been widely studied, and various algorithms have been developed. The commonly used positioning solving methods have their own advantages and disadvantages: the weighted least squares positioning method introduces auxiliary parameters, but ignores the dependence of the estimated parameters and the auxiliary parameters, so it is not optimal; the distributed weighted least squares method has large calculation amount and complex model; and the extreme value search method will decrease the search efficiency with the increase of the estimated parameters. Therefore, it is a direction worth studying to find a positioning algorithm with small calculation amount and high precision. SUMMARY

[0004] In order to solve the problem that the existing positioning solving method ignores the dependence of the estimated parameters and the auxiliary parameters, resulting in a non-optimal solution, the application provides a least squares grid search solving method for external radiation source radar multi-base joint positioning.

[0005] The application is implemented through the following technical solutions:

[0006] Step 1: according to the position [x T ,y T ] T of the external radiation source, the position of N receiving stations and the position [x,y] T of the target, an observation equation is established:

[0007]

[0008] wherein, is the receiving station observation quantity, c is the speed of light, Δτ is the time difference between the direct wave signal of the external radiation source and the signal reflected by the target to the receiving station n, x, y and are unknown parameters.

[0009] Step 2: variable substitution is made on the unknown parameters x=r T cosθ+x T , y=r T sinθ+y T , and the observation equation is:

[0010]

[0011] Step 3: find the least square estimate of r T

[0012]

[0013] Where:

[0014]

[0015]

[0016] Step 4: find the estimate of theta in [0, 2pi] using grid search method Minimize the error e:

[0017] e = X T H(theta) (H T (theta) H(theta)) -1 H T (theta) X

[0018] The target unknown estimate is

[0019]

[0020] The beneficial effects of the present application are: the multi-parameter nonlinear least square positioning problem is converted into a single-parameter nonlinear least square positioning problem through variable substitution and parameter separation, the complexity of grid search least square estimation is reduced, and the positioning accuracy is high and the calculation amount is small. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 is a multi-station external radiation source positioning schematic diagram. DETAILED DESCRIPTION

[0022] The technical solutions of the present application will be further explained and described below in combination with the drawings and examples.

[0023] The preferred embodiments of the present application are as follows:

[0024] Step 1: as shown in Figure 1 , the external radiation source position is [x T , y T ] T , the position of N receiving stations is The target position is [x, y] T , and the observation equation is established:

[0025]

[0026] Wherein, ​For the observed quantities at the receiving stations, c is the speed of light, Δτ is the time difference between the direct signal from the source and the signal reflected from the target to the receiving station n, x, y and are the unknown parameters.

[0027] Step 2: Make a variable substitution x = r cos θ T and y = r sin θ T The observation equations become: T T

[0028]

[0029] The observation equations can be written as:

[0030] H(θ) r T = X

[0031] where

[0032]

[0033] Step 3: Find the least squares estimate of r T

[0034]

[0035] Step 4: Use a grid search to find the estimate of θ in [0, 2π] to minimize the error e:

[0036] e = X T H(θ) (H T (θ) H(θ)) -1 H T (θ) X

[0037] The target unknown estimate is:

[0038]

[0039] ​​​

Claims

1. A method for solving the least squares grid search of multi-base joint positioning of an external radiation source radar, characterized in that: Step 1: Establish observation equation according to external radiation source position [x T ,y T ] T and N receiving station position and target position [x,y] T ​ wherein is the observed quantity at the receiving station, c is the speed of light, Δτ is the time difference between the direct signal and the signal reflected by the target arriving at the receiving station n, x, y and are unknown parameters; Step 2: Substitute the unknown parameters as variables x = r T cos θ + x T , y = r T sin θ + y T The observation equation is: Step 3: Solve for r T least squares estimate of wherein: Step 4: Estimate of θ in [0, 2π] using grid search method Minimize error e: e = X T H(θ) (H T (θ) H(θ)) -1 H T (θ) X the unknown target estimate is:

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