A passive positioning method based on maximum likelihood estimation

Abstract

The present invention relates to a passive positioning method based on maximum likelihood estimation, which includes: establishing an observation model of the azimuth data of each observation radar with respect to the target position, obtaining the azimuth angle probability density model of each node radar through mathematical derivation, establishing a multi-station radar angle measurement joint probability density model, processing to obtain the joint probability density logarithmic likelihood function, and finally solving the maximum likelihood estimation of the logarithmic likelihood function.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar. Background Art

[0002] Radar uses the target radiation signal and its characteristics to detect the target. It has the characteristics of high radar concealment and large applicable range, and has become a main radar type or a main working mode of radar. A single radar can obtain target parameters and target angle information for detecting radiation source targets. For target positioning, it is commonly used to perform collaborative processing on the radiation source target angle measurement information based on multi-radar detection to obtain the position information of the target and achieve target positioning.

[0003] The positioning accuracy of the target positioning method is related to many factors, such as angle measurement error, relative spatial position between the target and the passive sensor, etc. At present, the positioning methods are divided into dual-radar positioning and multi-radar collaborative positioning from the number of parameters of the positioning platform. From the perspective of positioning methods, there are azimuth intersection positioning, time difference positioning, azimuth-time difference joint positioning, etc. Most of the above methods are based on the premise of planar positioning. However, due to the influence of the earth's curvature, when the positioning stations are far apart or high-precision positioning of the target is required, the planar positioning model no longer conforms to the actual earth's surface situation, which will cause positioning errors.

[0004] Conventional passive positioning methods considering the earth's curvature. "A Dual-Base Three-Dimensional Passive Positioning Method Considering the Earth's Curvature" (CN110******91A) discloses a dual-base three-dimensional passive positioning method considering the earth's curvature. This method first establishes the motion equations of the target and the external radiation source considering the earth's curvature, then establishes the likelihood function, and solves the extreme value of the likelihood function through the genetic algorithm, taking it as the initial motion state of the target. However, the genetic algorithm has the disadvantage of large computational complexity. "A Passive Cooperative Positioning Method for Radar Beyond the Horizon Baseline" (CN104******48B) discloses a method for realizing passive cooperative positioning of marine radiation source targets based on the observations of dual-station radar in the case of beyond-the-horizon baseline. Aiming at the problem of poor positioning accuracy caused by the earth's curvature in the beyond-the-horizon case, by adopting a passive cooperative positioning method applicable to the beyond-the-horizon baseline case, the radar measurement error introduced by the earth's curvature is corrected to achieve positioning. However, the error correction value is affected by the positions of the target and the radar. Each time the position changes, the correction amount needs to be recalculated. Summary of the Invention

[0005] Aiming at the problem that when performing dual / multi-station pure azimuth passive positioning, when the positioning stations are far apart, affected by the earth's curvature, the planar positioning model no longer conforms to the actual earth's surface situation, which will cause positioning errors, the present invention provides a maximum likelihood estimation passive positioning method considering the earth's curvature.

[0006] The technical solution adopted by the present invention is as follows:

[0007] Step 1: The radar GPS coordinates of each node and the target GPS coordinates are converted through coordinate transformation to obtain the azimuth angle observation data model of the target in radar i:

[0008]

[0009] where (B t , L t , H t ) are the parameters to be estimated;

[0010] Step 2: Substitute the azimuth angle observation model and the angle measurement accuracy of each node radar into the Gaussian probability density model to obtain the probability density model of the azimuth angle measurement of the target by each node radar:

[0011]

[0012] Step 3: Under the assumption that the azimuth angle probability density of each node radar for the target is independent of each other, multiply them to obtain the joint probability density function of multi-station radar angle measurement:

[0013]

[0014] Step 4: Take the logarithm of the joint probability density function to obtain the log-likelihood function:

[0015]

[0016] Step 5: Find the maximum value of the log-likelihood function to obtain the maximum likelihood estimate of the parameter to be estimated.

[0017] The beneficial effects of the present invention are as follows: The present invention preferably solves the calculation problem of the influence of the earth curvature on the positioning accuracy under long baselines and long positioning distances. The calculation of the likelihood function is not limited to bistatic positioning and is also applicable to multi-station bearing-only positioning problems, and is universal for the number of positioning stations. Brief Description of the Drawings

[0018] Figure 1 is the flowchart of the present invention. Detailed Embodiment

[0019] The technical solution will be further explained below in conjunction with the drawings and embodiments of the present invention.

[0020] A passive positioning method of maximum likelihood estimation proposed by the present invention:

[0021] Step 1: A and B are the positions where the passive sensors are located, and the coordinates are G i =(B i , L i , H i)(i = 1, 2), where Bi, Li, and Hi are the latitude, longitude, and altitude of the sensor respectively. The measured azimuth angles of the target are respectively The variances of the angle measurement accuracies are respectively The direction-finding error of the sensor follows a normal distribution. The angle measurement accuracy, GPS coordinates, and ECEF coordinates of the radar are all known. Denote the parameter vector to be estimated as the latitude and longitude of the target θ = (B t , L t , H t ). Assume the target altitude is a sea surface target, 20 meters. The azimuth angle observation data model of the target in radar i is obtained as:

[0022]

[0023] where, where w i is Gaussian white noise with a mean of 0 and a variance of [X t , Y t , Z t are the ECEF coordinate values of the target, which can be calculated from the parameters to be estimated through coordinate transformation:

[0024]

[0025] In the formula, the first eccentricity is the radius of curvature of the prime vertical; a is the semi-major axis of the ellipsoid; b is the semi-minor axis of the ellipsoid.

[0026] Step 2: Denote:

[0027]

[0028] The probability density function of

[0029]

[0030] Step 3: Since the angle measurements of the bistatic radar are independent of each other, the probability density function of the bistatic radar angle measurement is:

[0031]

[0032] Step 4: Take the logarithm of to obtain the log-likelihood function as:

[0033]

[0034] Step 5: Solve the maximum likelihood estimate of the parameters to be estimated (B t , L t , H t ) The specific solution methods include the Newton - Raphson iteration method, the scoring method, and the grid search method. Taking the Newton - Raphson iteration method as an example, the maximum likelihood estimation solution process is as follows:

[0035]

[0036] In the formula

[0037]

[0038] The iteration converges at θ k+1 = θ k here.

Claims

1. A passive positioning method based on maximum likelihood estimation, characterized in that: Step 1: The radar GPS coordinates of each node and the target GPS coordinates are subjected to coordinate transformation to obtain the azimuth angle observation data model of the target in radar i: Among them, (B t , L t , H t ) are the parameters to be estimated. B i are the latitude of the sensor respectively; L i is the longitude of the sensor; X t is the coordinate value of the target in the X-axis direction in the ECEF coordinate system; X i is the coordinate value of the sensor in the X direction in the ECEF coordinate system; Y t is the coordinate value of the target in the Y direction in the ECEF coordinate system; Y i is the coordinate value of the sensor in the Y direction in the ECEF coordinate system; Z t is the coordinate value of the target in the Z direction in the ECEF coordinate system; w i is Gaussian white noise with a mean of 0 and a variance of , is the variance of the azimuth angle measurement of the sensor; H t is the target height; The first eccentricity is the radius of curvature of the prime vertical; a is the semi-major axis of the earth ellipsoid, and b is the semi-minor axis of the earth ellipsoid; is the observed azimuth angle of the sensor to the target; Φ i is denoted as θ is a convenient notation for the parameter to be estimated, θ = (B t , L t , H t ); where i = 1, 2; Step 2: Substitute the azimuth observation data model and the angle measurement accuracy of each node radar into the Gaussian probability density model to obtain the probability density model of the azimuth angle measurement of the target by each node radar: Step 3: Under the assumption that the azimuth angle probability density of each node radar for the target is independent of each other, multiply them to obtain the joint probability density function of multi-station radar angle measurement: Step 4: Take the logarithm of the joint probability density function to obtain the log-likelihood function: Step 5: Maximize the log-likelihood function to obtain the maximum likelihood estimates of the parameters to be estimated (B t , L t , H t )

Images