A Fast Time Synchronization Method for Radar Measurement Data Based on Error Modeling

Abstract

This invention proposes a rapid time synchronization method for radar measurement data based on error modeling, including steps such as data preprocessing and coordinate transformation, time inconsistency error analysis, point weight calculation, and iterative calculation of time alignment correction. Based on the analysis of radar measurement principles, this invention effectively avoids the increased error caused by using positioning information for time alignment by modeling the distance measurement error; it designs a point weight index and analyzes the factors affecting error, improving the reliability of the time alignment index; and it establishes a gradient function to rapidly iteratively solve for the globally optimal solution of the time offset correction value within the data segment. This invention solves the problem of reduced accuracy or even errors in multi-radar nR intersection trajectory calculation caused by inconsistencies in the clock systems of radar measurement data within a measurement system. It is suitable not only for clock synchronization between radar and reference track data but also for clock synchronization between multiple radar data.

Description

Technical Field

[0001] This invention relates to the field of radar measurement data processing technology, specifically to a method for rapid time synchronization of radar measurement data based on error modeling. Background Technology

[0002] With the accelerated development of national defense equipment systems, there are higher requirements for the accuracy of external ballistic measurements of space targets and targets flying within the atmosphere during equipment type approval tests. Among existing external ballistic measurement methods, multi-radar ranging crosstalk (nR system crosstalk) is the most accurate measurement method besides continuous wave velocity crosstalk. Radars commonly used for external ballistic measurements, when calibrated to meet the required accuracy, typically have a ranging error better than 10 meters, and this error does not increase with the distance to the measured target. Therefore, with a reasonable multi-station layout, measurement results with an error better than 20 meters can generally be generated through multi-radar ranging crosstalk.

[0003] The most significant factor affecting the accuracy of multi-radar ranging and rendezvous is the inconsistency in radar data timing, especially for radars using different clock systems for synchronization and small mobile radars. Taking tracking low-Earth orbit satellites as an example, with a satellite speed of approximately 7.9 km / s, if the radar timing error reaches the order of 0.01 s, the positioning error will reach 79 meters. Using such a data source for multi-radar rendezvous will drastically impact the rendezvous accuracy.

[0004] The main problem this invention addresses is how to improve the accuracy of multi-radar nR rendezvous by completing time correction and synchronization between devices at the central level without relying entirely on the radar equipment's own clock synchronization system. Summary of the Invention

[0005] The purpose of this invention is to solve the problem of asynchronous and inconsistent radar data clock systems participating in ranging and rendezvous, and to achieve clock synchronization between radars and between radars and the central computer by means of mutual calibration between radars or calibration from radar to reference track at the central computer level, without over-reliance on the equipment's own clock system, thereby ensuring the accuracy of rendezvous track generation.

[0006] The technical solution of this invention is as follows:

[0007] A method for fast time synchronization of radar measurement data based on error modeling includes the following steps:

[0008] Step 1: Acquire the radar measurement data X to be corrected so,T

[0009] X so,T =[x so,t1 ,…,x so,tn ]

[0010] x so,t =(r so,t ,a so,t ,e so,t ) T

[0011] Where r so,t a so,t e so,t Let X be the distance, azimuth, and elevation angles in the spherical coordinate system of the station measured by the radar at time t; the radar measurement data to be corrected has already undergone radio wave refraction correction; so,T The corresponding time series is

[0012] T = {t1,…,t} n …,}

[0013] t∈T

[0014] And obtain the reference data X as the time correction alignment reference. sc,T' The sampling time series T' of the reference data is continuous and covers the time series T of the data to be corrected, and satisfies the following conditions:

[0015] T = {t1,…,t} n}, n∈R

[0016] T'={t1',…,t m '},M∈R

[0017]

[0018] Where et is the maximum value of the timing error;

[0019] Through interpolation and coordinate transformation, X sc,T' Transform to the spherical coordinate system of the radar station to be corrected to obtain the reference data X. sco,T ;

[0020] x sco,t =(r sco,t ,a sco,t ,e sco,t ) T

[0021] X sco,T =[x sco,t1 ,…,x sco,tn ]

[0022] Step 2: Calculate the time alignment accuracy index Pt:

[0023]

[0024] Among them, Pr m For the ranging accuracy index of the radar to be corrected, ErTime,t Er is the sequence of maximum ranging errors caused by time inconsistency. Time,T The elements in; the maximum range error sequence Er caused by time inconsistency. Time,T Based on benchmark data X sco,T The maximum value of the time-stamping error et is calculated.

[0025] Step 3: Calculate point weights:

[0026] Step 3.1: Initialize point weights

[0027] Point weight sequence W point,T The definition is as follows:

[0028] W point,T =[w point,t1 ,…,w point,tn ]

[0029] Weight w at time t point,t Initialization assignment is as follows:

[0030]

[0031] In the formula, r so,t Let r be the radar range measurement value to be corrected at time t. sco,t Let Er be the range reference value of the radar station in the spherical coordinate system to be corrected at time t. thre,t It is the ranging error threshold;

[0032] Step 3.2: Assigning pitch angle weights:

[0033] Pitch angle error weight sequence W eo,T The definition is as follows:

[0034] W eo,T =[w eo,t1 ,…,w eo,tn ]

[0035] The assignment process is as follows:

[0036]

[0037] In the formula e so,t The radar elevation angle measurement value to be corrected at time t;

[0038] Step 3.3: Distance weight assignment:

[0039] Distance error weight sequence W ro,T The definition is as follows:

[0040] W ro,T =[w ro,t1 ,…,w ro,tn ]

[0041] The assignment process is as follows:

[0042]

[0043] In the formula r so,t Let r be the radar range measurement value to be corrected at time t. so,max For the radar measurement data sequence X to be corrected so,T The maximum range value in the range, r so,min For the radar measurement data sequence X to be corrected so,T The minimum distance measurement value; and the X value used in the process of finding the maximum and minimum distance measurement values. so,T The data needs to be filtered through the initial point weight assignment in step 3.1, using data with an initial point weight of 1; c ro This refers to the distance weighting coefficient.

[0044] Step 3.4: Assigning accuracy weights to the reference radar data

[0045] If the reference data is satellite precision orbit data, target telemetry self-positioning data, or GNSS data, it is assumed that the reference data has no error; if the reference data is radar measurement data, then the reference radar data accuracy weight sequence W... cd,T The definition is as follows:

[0046] W ecd,T =[w ecd,t1 ,…,w ecd,tn ]

[0047] The assignment process is as follows:

[0048]

[0049] e cd,t =||X ecd,t

[0050] e min =min(e r,t ,e a,t ,e e,t )

[0051] e max =max(e r,t ,e a,t ,e e,t )

[0052] Where c ecd ∈[0,1] represents the accuracy weighting coefficient of the baseline radar data; (e r,t ,e a,t ,e e,t ) and e cd,t and X ecd,tIt is obtained through the following process:

[0053] An error analysis coordinate system is established with the location point of the reference data as the origin o. The x-axis is the beam direction of the reference radar, the y-axis is perpendicular to the x-axis and vertically upward, and the z-axis conforms to the right-hand rule and is perpendicular to both the y-axis and x-axis. A reference radar positioning error ellipsoid is established with the origin of the error analysis coordinate system as the center.

[0054]

[0055] Among them, Pr mc Pe serves as the benchmark for radar ranging accuracy. mc Pa is the accuracy index for the elevation angle measurement of the reference radar. mc As the reference radar azimuth angle measurement accuracy index, r sc,t The distance measured by the reference radar at time t;

[0056] The geocentric coordinates of the radar to be corrected are Sg o Its coordinates in the error analysis coordinate system are Se. o,t :

[0057] Sg o =(x go ,y go ,z go ) T

[0058] Se o,t =Mge c,t ·Sg o +Vge c,t

[0059] Se o,t =(x eo,t ,y eo,t ,z eo,t ) T

[0060] Among them Mge c,t Vge is the transformation matrix from the geocentric coordinate system to the error analysis coordinate system. c,t For the corresponding transformation vector; (x eo,t ,y eo,t ,z eo,t Let t be the coordinates of the radar site to be corrected at time t in the error analysis coordinate system; X be the coordinates of the intersection point X of the radar beamline to be corrected and the reference radar positioning error ellipsoid at time t. ecd,t The calculation is as follows:

[0061] X ecd,t =(x ecd,t ,y ecd,t ,z ecd,t ) T

[0062]

[0063] y ecd,t =k yx x ecd,t

[0064] z ecd,t =k zx x ecd,t

[0065] in:

[0066]

[0067]

[0068] Step 3.5: Complete the point weight assignment

[0069] When the reference data is radar measurement data, the point weight assignment process is as follows:

[0070] W pointNew,T =W point,T ·W eo,T ·W ro,T ·W ecd,T ,t∈T

[0071] W point,T =W pointNew,T

[0072] When the reference data is telemetry self-positioning, GNSS data, or precision orbit data, the point weight assignment process is as follows:

[0073] W pointNew,T =W point,T ·W eo,T ·W ro,T ,t∈T

[0074] W point,T =W pointNew,T

[0075] Step 4: Iteratively calculate the time alignment correction.

[0076] Establish initial values ​​for the iteration, including the range value sequence R of the radar measurement data to be corrected. so,T The distance measurement sequence R of the reference measurement data sco,T Step 3 finally obtains the point weight W point,T Current time correction amount dt, time correction step size st, time precision alignment index Pt;

[0077] Step 4.1: Solve for the current correction error

[0078] The ranging value sequence R of the radar measurement data to be corrected so,T Add the timestamp to the current time correction factor dt to obtain the corrected ranging data sequence R. so,T+dt Then, using the time series T as the interpolation point, R is... so,T+dt Interpolation was performed to obtain the range value sequence R of the current corrected data, which is aligned with the time series of the original radar measurement data to be corrected. so,T (dt), current weighted error variance E d,T (dt) is:

[0079]

[0080] Step 4.2: Solve for the maximum correction error

[0081] The ranging value sequence R of the radar measurement data to be corrected so,T By adding the time correction factor and the time correction step size to the time axis, we obtain the corrected distance value sequence R of the ranging data. so,T+dt+st Then, using the time series T as the interpolation point, R is... so,T+dt+st Interpolation was performed to obtain a positive offset corrected distance value sequence R that was aligned with the original measurement data time series. so,T (dt+st); R so,T Adding the time correction amount to the time axis and subtracting the time correction step size, and then performing the same operation as above, yields the negative offset corrected data distance value sequence R. so,T (dt-st);

[0082] Calculate the weighted error variance E of the positive offset correction data d,T (dt+st) is:

[0083]

[0084] Calculate the weighted error variance E of the negative offset correction data d,T (dt-st) is:

[0085]

[0086] Step 4.3: Solve for the error gradient

[0087] Based on the current weighted error variance, the weighted error variance of the positive offset correction data, and the weighted error variance of the negative offset correction data, solve for the time offset dt at the gradient minimum. new

[0088]

[0089]

[0090]

[0091] The step size st is then updated as follows:

[0092] st = dt new

[0093] Update time correction amount dt:

[0094] dt=dt+st

[0095] Step 4.4: Iteration Termination Decision

[0096] The conditions for terminating the iteration are as follows:

[0097]

[0098] If the decision condition is not met, skip to step 4.1 for iteration; if the condition is met, output dt, add dt to the time axis of the measurement data to be corrected, and the result is the time-aligned measurement data.

[0099] Furthermore, in step 1, X is transformed through interpolation and coordinate transformation. sc,T' Transform to the spherical coordinate system of the radar station to be corrected to obtain the reference data X. sco,T The process is as follows:

[0100] Step 1.1: If X sc,T' If the data is in the spherical coordinate system of the reference radar station, then it must first be transformed from the spherical coordinate system of the reference radar station to the geocentric rectangular coordinate system:

[0101] X sc,T' =[x sc,t1' ,…,x sc,tm' ]

[0102] x sc,t =(r sc,t ,a sc,t ,e sc,t ) T

[0103] (x c,t ,y c,t ,z c,t ) T =r sc,t M sg,c (cose sc,t cosa sc,t ,sine sc,t ,cose sc,t sina sc,t ) T +V sg,c

[0104] x gc,t =(xc,t ,y c,t ,z c,t ) T

[0105] X gc,T' =[x gc,t1' ,…,x gc,tm' ]

[0106] In the formula (x c,t ,y c,t ,z c,t Let X be the coordinate position of the reference data in the geocentric rectangular coordinate system at time t. gc,T' Reference data sequence in geocentric rectangular coordinate system; M sg,c V is the transformation matrix from the reference radar station system to the geocentric rectangular coordinate system. sg,c This is the corresponding transformation vector;

[0107] If X sc,T' If the data is already in a geocentric rectangular coordinate system, proceed directly to step 1.2;

[0108] Step 1.2: Place X gc,T' Smooth the data, then use the time series T as the interpolation point in the smoothed data X. gc,T' Interpolation is performed to obtain the geocentric rectangular coordinate system reference measurement data X at the smoothed and interpolated interpolation points. gc,T :

[0109] X gc,T =[x gc,t1 ,…,x gc,tn ]

[0110] Step 1.3: Convert the reference radar measurement data X in the geocentric rectangular coordinate system gc,T Transform to the Cartesian coordinate system of the radar station to be corrected:

[0111] X scso,T =M gs,o X gc,T +V gs,o

[0112] X scso,T =[x scso,t1 ,…,x scso,tn ]

[0113] x scso,t =(x sco,t ,y sco,t ,z sco,t ) T

[0114] In the formula (x sco,t ,y sco,t ,z sco,tX represents the coordinates of the reference data at time t in the Cartesian coordinate system of the radar station to be corrected. scso,T M is the reference data sequence in the rectangular coordinate system of the radar station to be corrected. gs,o V is the transformation matrix from the geocentric rectangular coordinate system to the radar station system to be corrected. gs,o This is the corresponding transformation vector;

[0115] Step 1.4: Convert the reference data of the radar station to be corrected from the rectangular coordinate system to the spherical coordinate system of the radar station to be corrected:

[0116]

[0117]

[0118]

[0119] x sco,t =(r sco,t ,a sco,t ,e sco,t ) T

[0120] X sco,T =[x sco,t1 ,…,x sco,tn ]

[0121] In the formula (r sco,t ,a sco,t ,e sco,t X represents the coordinates of the reference data at time t in the spherical coordinate system of the radar station to be corrected; sco,T This is the reference data sequence in the spherical coordinate system of the radar station to be corrected.

[0122] Furthermore, in step 2, the maximum range error sequence Er caused by time inconsistency is... Time,T for

[0123]

[0124] Er Time,T =[Er Time,t1 ,…,Er Time,tn ]

[0125] Where R sco,T For the baseline data X sco,T The distance value sequence, R sc o, T (-et) represents the negative offset reference data X. sc o, T The distance value sequence of (-et), R sco,T (+et) represents the positive offset reference data X. sco,TA sequence of distance values ​​for (+et);

[0126] Among them, the negative offset reference data X sco,T (-et) is obtained through the following process:

[0127] Use the baseline data X sco,T Subtracting the maximum time-of-facts error et from the timestamp yields the offset baseline data X. sco,T-et Then, using the baseline data X sco,T Using the time series T as the interpolation point, for X sco,T-et Interpolation is performed to obtain negative offset reference data X aligned with the reference data time series. sco,T (-et);

[0128] Positive offset reference data X sco,T (+et) is obtained through the following process:

[0129] Use the baseline data X sco,T By adding the time axis to the maximum value of the timing error et, the offset baseline data X is obtained. sco,T+et Then, using the baseline data X sco,T Using the time series T as the interpolation point, for X sco,T+et Interpolation was performed to obtain positive offset reference data X aligned with the reference data time series. sco,T (+et).

[0130] Furthermore, in step 3.1, the ranging error threshold Er thre,t According to the formula

[0131]

[0132] Calculate, where Er ref To correct the maximum residual error of the radar ranging radio wave refraction, Pr m For the ranging accuracy index of the radar to be corrected, Er Time,t Let t be the maximum distance measurement error at time t.

[0133] Furthermore, in step 3.4, the transformation matrix Mge c,t for:

[0134]

[0135] m 11 =-cos E sin L sin A-cos E cos L sin B cos A+sin E cos L cos B

[0136] m 21=sin E sin L sin A+sin E cos L sin B cos A+cos E cos L cos B

[0137] m 31 =-sin L cos A+cos L sin B sin A

[0138] m 12 =cos E cos L sin A-cos E sin L sin B cos A+sin E sin L cos B

[0139] m 22 =-sin E cos L sin A+sin E sin L sin B cos A+cos E sin L cos B

[0140] m 32 =cosLcosA+sinLsinBsinA

[0141] m 13 =cosEcosBcosA+sinEsinB

[0142] m 23 = -sinEcosBcosA + cosEsinB

[0143] m 33 = -cosBsinA

[0144] A = a c,t

[0145] E = e c,t

[0146] Where L is the longitude coordinate of the reference radar station, B is the latitude coordinate of the reference radar station, A is the elevation angle of the reference radar relative to the origin of the error analysis coordinate system at time t, and E is the azimuth angle of the reference radar relative to the origin of the error analysis coordinate system at time t.

[0147] Transformation vector Vge c,t for:

[0148]

[0149] Where x gc,t =(x c,t ,y c,t ,z c,t ) T The coordinates are the geocentric coordinates of the origin of the error analysis coordinate system.

[0150] Beneficial effects

[0151] This invention solves the problem that inconsistencies in the clock systems of measurement data from different radars within a measurement system lead to reduced accuracy or even errors in multi-radar nR intersection trajectory calculation.

[0152] The present invention has the following advantages:

[0153] 1. Based on the analysis of radar measurement principles, by modeling the distance measurement error, the increase in error caused by using positioning information for time alignment is effectively avoided;

[0154] 2. By designing point weight indicators and analyzing factors affecting errors, the reliability of time alignment indicators has been improved.

[0155] 3. By establishing a gradient function, the global optimal solution for the time offset correction value within the data segment is quickly obtained through iterative solutions.

[0156] This invention is not only suitable for clock synchronization between radar and reference track data, but also for clock synchronization between multiple radar data.

[0157] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0158] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0159] Figure 1 : Reference radar positioning error ellipsoid

[0160] Figure 2 Flowchart of the method steps in the invention

[0161] Figure 3 Calculate the initial point weights based on the self-localization track.

[0162] Figure 4 : Calculation of point weights based on self-localization track

[0163] Figure 5 Iteratively solve for the time correction based on the self-localization trajectory.

[0164] Figure 6 The time correction is iteratively solved based on the self-localization trajectory (local).

[0165] Figure 7 Comparison of errors before and after correction based on the self-localization track.

[0166] Figure 8 Comparison of ranging values ​​before and after correction based on the self-localization track.

[0167] Figure 9 Calculate the initial point weights based on radar data.

[0168] Figure 10 Point weight calculation is completed based on radar data.

[0169] Figure 11 Iteratively solve for the time correction based on radar data.

[0170] Figure 12 Comparison of errors before and after correction based on radar data.

[0171] Figure 13 Comparison of ranging values ​​before and after correction based on radar data. Detailed Implementation

[0172] This invention aims to solve the problem of asynchronous and inconsistent radar data clock systems participating in ranging and rendezvous. It proposes a method for rapid synchronization of radar measurement data time based on error modeling. This method achieves clock synchronization between radars and between radars and the central computer at the central computer level without over-reliance on the device clock system. This is accomplished through inter-radar calibration or radar-to-reference track calibration, thereby ensuring the accuracy of rendezvous track generation.

[0173] Specifically, the following steps are included:

[0174] Step 1: Data preprocessing and coordinate transformation:

[0175] Acquire radar measurement data X, which has already undergone radio wave refraction correction, to be corrected. so，T :

[0176]

[0177] Where r so,t a so,t e so,t Let t be the distance, azimuth, and elevation angles of the station in the spherical coordinate system measured by the radar at time t (all are results after refraction correction).

[0178] The time series corresponding to this data segment is as follows:

[0179]

[0180] The radar measurement data used as the time correction alignment reference is denoted as X. sc,T' The transformation matrix from the reference radar station system to the geocentric rectangular coordinate system is M. sg,c The transformed vector is V sg,c M sg,c With V sg,cThe calculation method is a widely used algorithm in the industry, and will not be elaborated here. The data from the reference radar station in spherical coordinates is then transformed to a geocentric rectangular coordinate system:

[0181] X sc,T' =[x sc,t1' ,…,x sc,tm' ]

[0182] x sc,t =(r sc,t ,a sc,t ,e sc,t ) T

[0183] (x c,t ,y c,t ,z c,t ) T =r sc,t M sg,c (cose sc,t cosa sc,t ,sine sc,t ,cose sc,t sina sc,t ) T +V sg,c (3)

[0184] x gc,t =(x c,t ,y c,t ,z c,t ) T

[0185] X gc,T' =[x gc,t1' ,…,x gc,tm' ]

[0186] In the formula (x c,t ,y c,t ,z c,t Let X be the coordinate position of the reference data in the geocentric rectangular coordinate system at time t. gc,T' Reference data sequence in geocentric rectangular coordinate system.

[0187] The sampling time period T' of the reference data is continuous and covers the time period T of the data to be corrected. Let et be the maximum value of the timing error (this value is an empirical value, obtained statistically for each device based on actual conditions), which satisfies the following formula:

[0188] T = {t1,…,t} n}, n∈R

[0189] T'={t1',…,t m '},M∈R

[0190]

[0191] X gc,T' Smoothing is typically performed using a cubic B-spline smoothing algorithm. This avoids endpoint errors introduced by the smoothing model. Then, the radar data segment X to be corrected is used. so,T Using the time series T as the interpolation point, interpolation is performed on the smoothed geocentric reference radar data to obtain the smoothed and interpolated geocentric reference measurement data X at the interpolation point. gc,T :

[0192] X gc,T =[x gc,t1 ,…,x gc,tn (5)

[0193] The transformation matrix from the geocentric system to the radar station system to be corrected is M. gs,o The transformed vector is V gs,o M gs,o With V gs,o The calculation method is a widely used algorithm in the industry, and will not be elaborated here. The reference radar measurement data under the geocentric system X... gc,T Transform to the Cartesian coordinate system of the radar station to be corrected:

[0194] X scso,T =M gs,o X gc,T +V gs,o

[0195] X scso,T =[x scso,t1 ,…,x scso,tn (6)

[0196] x scso,t =(x sco,t ,y sco,t ,z sco,t ) T

[0197] In the formula (x sco,t ,y sco,t ,z sc,o ) t X represents the coordinates of the reference data at time t in the Cartesian coordinate system of the radar station to be corrected. scso,T This is the reference data sequence in the rectangular coordinate system of the radar station to be corrected.

[0198] Then, the reference data in the rectangular coordinate system of the radar station to be corrected is transformed to the spherical coordinate system of the radar station to be corrected:

[0199]

[0200]

[0201]

[0202] x sco,t =(r sco,t ,a sco,t ,e sco,t ) T

[0203] X sco,T =[x sco,t1 ,…,x sco,tn ]

[0204] In the formula (r sco,t ,a sco,t ,e sco,t X represents the coordinates of the reference data at time t in the spherical coordinate system of the radar station to be corrected; sco,T This is the reference data sequence in the spherical coordinate system of the radar station to be corrected.

[0205] Of course, if the reference data uses geocentric data and also meets the conditions described in formula (4), then formulas (5), (6), and (7) are used directly to smooth and interpolate it, and then convert it to the spherical coordinate system of the radar station to be corrected. This completes the preparation of the reference data.

[0206] Step 2: Time Inconsistency Error Analysis

[0207] Step 2.1: Calculate the maximum distance measurement error caused by time inconsistency.

[0208] The baseline data X processed in step 1 sco,T Subtracting the maximum time-of-facts error et from the timestamp yields the offset baseline data X. sco,T-et Then, using the baseline data X sco,T Using the time series T as the interpolation point, for X sco,T-et Interpolation is performed to obtain negative offset reference data X aligned with the reference data time series. sco,T (-et);

[0209] The baseline data X processed in step 1 sco,T By adding the time axis to the maximum value of the timing error et, the offset baseline data X is obtained. sco,T+et Then, using the baseline data X sco,T Using the time series T as the interpolation point, for X sco,T+et Interpolation was performed to obtain positive offset reference data X aligned with the reference data time series. sco,T (+et);

[0210] Use the baseline data X sco,T The distance value sequence is denoted as R. sco,TThe distance value sequence of the negative offset reference data is denoted as R. sco,T (-et), denoted as R, represents the distance value sequence of the positive offset reference data. sco,T If (+et), then in the time series T, the sequence of maximum ranging errors caused by time inconsistency is:

[0211]

[0212] Er Time,T =[Er Time,t1 ,…,Er Time,tn ]

[0213] Since the selection of the reference data satisfies formula (4), the error introduced by the above calculation and interpolation can be ignored.

[0214] Step 2.2: Calculate the time alignment accuracy index

[0215] Let Pt be the time alignment accuracy metric. Pt is the maximum acceptable time correction residual after completing time consistency correction, and the ranging error caused by this residual must be one order of magnitude better than the device's ranging accuracy metric. Based on the above definition, Pt can be expressed as:

[0216]

[0217] In the formula, n represents the sequence of maximum ranging errors Er caused by time inconsistency. Time,T The data length, et is the value used to calculate Er. Time,T The maximum value of the timing error used, Pr m The ranging accuracy specification for the radar to be corrected is (obtained from the equipment manual, typically 7m to 10m).

[0218] Step 3: Point Weight Calculation

[0219] When performing clock system error estimation, since the measurement accuracy is different at each sampling time, the accuracy of the reference data at each point is also different. Therefore, it is necessary to assign different alignment weights to each point of the reference data and the data to be corrected. First, the point weights need to be initially assigned.

[0220] Step 3.1: Initialize point weights

[0221] Point weight sequence W point,T The definition is as follows:

[0222] W point,T =[w point,t1 ,…,w point,tn (10)

[0223] Weight w at time t point,t Initialization assignment is as follows:

[0224]

[0225] In the formula, r so,t Let r be the radar range measurement value to be corrected at time t. sco,t Let Er be the range reference value of the radar station in the spherical coordinate system to be corrected at time t. thre,t This is the ranging error threshold. The above formula means that when the error between the ranging result of a certain point in the radar measurement data to be corrected and the distance value of the corresponding point in the reference data exceeds a certain threshold, the two points are considered not to be the same target, and the threshold for that point is set to 0; otherwise, it is set to 1.

[0226] Ranging error threshold Er thre,t It can be calculated according to formula (12), where Er thre,t It is the geometric sum of the current maximum ranging error, the maximum residual error after refraction correction, and the ranging accuracy index, defined as follows:

[0227]

[0228] In the formula Er ref To correct the maximum residual error of the radar ranging radio wave refraction correction (this value is an empirical value of the equipment, generally less than 5m), Pr m For ranging accuracy specifications (this value is obtained from the equipment manual), Er Time,t Let t be the maximum distance measurement error at time t.

[0229] Step 3.2: Assigning Pitch Angle Weights

[0230] Radar measurements are often affected by factors such as radio wave refraction and multipath propagation errors, resulting in errors. These errors decrease as the elevation angle increases. At elevation angles above 10°, the residual error after radio wave refraction correction becomes negligible. Therefore, an elevation angle error weighting sequence W is designed. eo,T The definition is as follows:

[0231] W eo,T =[w eo,t1 ,…,w eo,tn (13)

[0232] The assignment process is as follows:

[0233]

[0234] In the formula e so,t Let t be the radar elevation angle measurement value to be corrected at time t. The assignment process is to make the weight of the equipment measurement value 0 when the elevation angle is 0° or below, and the weight increases continuously as the elevation angle increases, reaching 1 when the elevation angle is 10° or above.

[0235] Step 3.3: Assigning Distance Weights

[0236] Radar measurement electromagnetic waves are affected by electromagnetic refraction, and the refraction error increases with distance. Therefore, a distance error weighting system is designed. The distance error weighting sequence W... ro,T The definition is as follows:

[0237] W ro,T =[w ro,t1 ,…,w ro,tn (15)

[0238] The assignment process is as follows:

[0239]

[0240] In the formula r so,t Let r be the radar range measurement value to be corrected at time t. so,max For the radar measurement data sequence X to be corrected so,T The maximum range value in the range, r so,min For the radar measurement data sequence X to be corrected so,T The minimum distance measurement value. And the X value used in the process of finding the maximum and minimum distance measurement values. so,T The data needs to be filtered through the initial point weight assignment in step 3.1, using data with an initial point weight of 1, which is data tracking the same target.

[0241] In formula (16) c ro This is the distance weighting coefficient, with a value between 0 and 1, typically obtained experimentally. This assignment process ensures that the weight of the device's measured value is adjusted as the distance value approaches r. so,min The closer the time is to 1, the closer it is to r. so,max The closer it gets to 1-c ro .

[0242] Step 3.4: Assigning accuracy weights to the reference radar data

[0243] If the reference data is satellite precision orbit data or target telemetry self-positioning data, the difference in its positioning error is usually much lower than the order of magnitude of radar measurement accuracy and the error is stable. In this case, the reference data can be considered to have no error. However, if the reference data is radar measurement data, the positioning error of the reference data and the positioning error of the radar to be corrected are generally on the same order of magnitude. Therefore, it is necessary to consider the positioning error existing in the reference data and its variation.

[0244] As is known from the principles of radar measurement, the positioning error differs depending on whether it is parallel to or perpendicular to the radar beam direction. The error parallel to the radar beam direction is equal to the radar ranging accuracy error, while the error perpendicular to the radar beam direction is equal to the product of the radar angle measurement accuracy error and the distance. Therefore, for a given positioning point, the relationship between the reference radar beam direction and the radar beam direction to be corrected needs to be considered.

[0245] like Figure 1 As shown, a rectangular coordinate system is established with the positioning point of the reference data as the origin o. The x-axis is the beam direction of the reference radar, the y-axis is perpendicular to the x-axis and vertically upward (the xy plane is perpendicular to the horizontal plane where the origin is located), and the z-axis conforms to the right-hand rule and is perpendicular to both the y-axis and x-axis. This coordinate system is referred to as the error analysis coordinate system below. A positioning error ellipsoid of the reference radar is established with the origin of the error analysis coordinate system as its center:

[0246]

[0247] Among them, Pr mc Pe serves as the benchmark for radar ranging accuracy. mc Pa is the accuracy index for the elevation angle measurement of the reference radar. mc The above-mentioned azimuth angle measurement accuracy indicators are the benchmark radar indicators, which can be obtained by consulting the equipment manual; r sc,t The distance measured by the reference radar at time t is denoted as t.

[0248] The length e of the measurement beam from the radar to be corrected within the error sphere cd,t This refers to the ranging accuracy index of the reference data relative to the radar to be corrected. By transforming the geocentric coordinates of the radar to be corrected to the error analysis coordinate system, and solving for the intersection of the radar beam direction (the line connecting the origin of the error analysis coordinate system and the radar site coordinates) with the positioning error ellipsoid, the accuracy of the ranging accuracy can be determined. cd,t The solution is as follows:

[0249] First, establish the transformation matrix Mge from the geocentric fixed coordinate system to the error analysis coordinate system mentioned above. c,t :

[0250]

[0251] m 11 =-cosEsinLsinA-cosEcosLsinBcosA+sinEcosLcosB

[0252] m 21 =sinEsinLsinA+sinEcosLsinBcosA+cosEcosLcosB

[0253] m31 = -sinLcosA + cosLsinBsinA

[0254] m 12 =cosEcosLsinA-cosEsinLsinBcosA+sinEsinLcosB

[0255] m 22 =-sinEcosLsinA+sinEsinLsinBcosA+cosEsinLcosB (18)

[0256] m 32 =cosLcosA+sinLsinBsinA

[0257] m 13 =cosEcosBcosA+sinEsinB

[0258] m 23 = -sinEcosBcosA + cosEsinB

[0259] m 33 = -cosBsinA

[0260] A = a c,t

[0261] E = e c,t

[0262] Where L is the longitude coordinate of the reference radar site, B is the latitude coordinate of the reference radar site, A is the elevation angle of the reference radar relative to the origin of the error analysis coordinate system at time t, and E is the azimuth angle of the reference radar relative to the origin of the error analysis coordinate system at time t.

[0263] Establish the transformation vector Vge c,t :

[0264]

[0265] Where x gc,t =(x c,t ,y c,t ,z c,t ) T Let Sg be the geocentric coordinates of the origin of the error analysis coordinate system (the location point of the reference data at time t in the geocentric rectangular coordinate system). The geocentric station coordinates of the radar to be corrected are Sg. o Its coordinates in the error analysis coordinate system are Se. o,t :

[0266] Sg o =(x go ,y go ,zgo ) T

[0267] Se o,t =Mge c,t ·Sg o +Vge c,t (20)

[0268] Se o,t =(x eo,t ,y eo,t ,z eo,t ) T

[0269] In the formula (x eo,t ,y eo,t ,z eo,t Let X be the coordinates of the radar site to be corrected at time t in the error analysis coordinate system. Let X be the coordinates of the intersection point X of the radar beamline to be corrected and the reference radar positioning error ellipsoid at time t. ecd,t The calculation is as follows:

[0270] X ecd,t =(x ecd,t ,y ecd,t ,z ecd,t ) T

[0271]

[0272] y ecd,t =k yx x ecd,t

[0273] z ecd,t =k zx x ecd,t

[0274] in:

[0275]

[0276] Reference radar data accuracy weight sequence W cd,T The definition is as follows:

[0277] W ecd,T =[w ecd,t1 ,…,w ecd,tn ] (twenty three)

[0278] The assignment process is as follows:

[0279]

[0280] e cd,t =||X ecd,t || (24)

[0281] e min =min(e r,t ,e a,t ,e e,t )

[0282] e max =max(e r,t ,e a,t ,e e,t )

[0283] Where c ecd ∈[0,1] represents the accuracy weighting coefficients of the baseline radar data, obtained through experiments. (e r,t ,e a,t ,e e,t The definition of ) is given in formula (17).

[0284] Step 3.5: Complete the point weight assignment

[0285] After completing steps 3.1 to 3.4, the weights of each point need to be reassigned. When the reference data is radar measurement data, the point weight assignment process is as follows:

[0286]

[0287] When the reference data is telemetry self-positioning, GNSS data, or precision orbit data, the point weight assignment process is as follows:

[0288]

[0289] This completes the calculation of the point weights.

[0290] Step 4: Iteratively calculate the time alignment correction.

[0291] An error gradient function is established to solve the relative change relationship between the time correction direction and the total error, and the optimal solution of the time correction amount in the corrected data segment is obtained through iteration.

[0292] The initial values ​​for iteration include the ranging sequence R of the radar measurement data to be corrected. so,T The distance measurement sequence R of the reference measurement data sco,T (Radar station system to be corrected), the final point weight W obtained in step 3 point,T Current time correction amount dt, time correction step size st, time precision alignment index Pt:

[0293]

[0294] The maximum value of the timing error et is defined in step 1, and the value of the timing accuracy alignment index Pt is determined in step 2.2. so,T R sco,TSee step 1 for the value, point weight W point,T The calculation method is shown in step 3.

[0295] Step 4.1: Solving for the current correction error

[0296] The ranging value sequence R of the radar measurement data to be corrected so,T Add the timestamp to the current time correction factor dt to obtain the corrected ranging data sequence R. so,T+dt Then, using the time series T as the interpolation point, R is... so,T+dt Interpolation was performed to obtain the range value sequence R of the current corrected data, which is aligned with the time series of the original radar measurement data to be corrected. so,T (dt). Current weighted error variance E d,T The solution method for (dt) is as follows:

[0297]

[0298] Step 4.2: Solving for the maximum correction error

[0299] The ranging value sequence R of the radar measurement data to be corrected so,T By adding the time correction factor and the time correction step size to the time axis, we obtain the corrected distance value sequence R of the ranging data. so,T+dt+st Then, using the time series T as the interpolation point, R is... so,T+dt+st Interpolation was performed to obtain a positive offset corrected distance value sequence R that was aligned with the original measurement data time series. so,T (dt+st).

[0300] R so,T Adding the time correction amount to the time axis and subtracting the time correction step size, and then performing the same operation as above, yields the negative offset corrected data distance value sequence R. so,T (dt-st).

[0301] Calculate the weighted error variance E of the positive offset correction data d,T (dt+st) is as follows:

[0302]

[0303] Calculate the weighted error variance E of the negative offset correction data d,T (dt-st) is as follows:

[0304]

[0305] Step 4.3: Solving for the error gradient

[0306] Since the weighted error variance function is a quadratic function, the time offset dt at the minimum gradient can be directly solved. new :

[0307]

[0308]

[0309]

[0310] Since the independent variable in the weighted error variance function is not linear, it is only a quadratic function, not a true quadratic function. Therefore, iterative searching is needed to find the true minimum gradient point within the data segment. To avoid getting trapped in local optima, the function values ​​within the feature point region need to be recalculated during iteration. Therefore, the corrected step size *st* is updated as follows:

[0311] st = dt new (32)

[0312] Update time correction amount dt:

[0313] dt=dt+st (33)

[0314] Step 4.4: Iteration Termination Decision

[0315] The conditions for terminating the iteration are as follows:

[0316]

[0317] This condition is to determine whether the time correction step size st is less than half of the time precision alignment index Pt. If the judgment condition is not met, the process jumps to step 4.1 for iteration.

[0318] If the condition is met, it means that the impact of the remaining error of the current correction amount is better than the maximum error allowed by the time accuracy alignment index Pt. Output dt, add dt to the time axis of the measurement data to be corrected, and you will get the time-aligned measurement data.

[0319] This completes the work of aligning the radar measurement data with the reference data time axis in this invention. The flowchart of the method steps of this invention is shown in the attached figure. Figure 2 .

[0320] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0321] This embodiment serves as a joint tracking and measurement system for an aircraft using multiple radars. In this embodiment, a small mobile radar (hereinafter referred to as the small radar) and a large fixed precision measurement radar (hereinafter referred to as the large radar) track and measure an aircraft. The aircraft is equipped with a GNSS self-positioning device, and the ground-based central computer can receive the radar's measurement data and the aircraft's real-time self-positioning data in real time. The aircraft's self-positioning device uses a GPS positioning system, which has high time accuracy. However, due to the aircraft's angular obstruction of the GPS antenna, its satellite signal reception is unstable, resulting in some jumps in the self-positioning data. The small radar's time synchronization system has lower accuracy but continuous tracking. The large radar has high time synchronization accuracy and continuous, stable tracking.

[0322] In this embodiment, the measurement data from a small radar is used as the data to be corrected, and the aircraft self-localization data and the measurement data from a large radar are used as reference data, respectively. This allows for simultaneous verification of the time alignment of the radar measurement data to the reference track data and the alignment of the radar measurement data to the reference radar measurement data.

[0323] Time alignment of radar measurement data with reference track data:

[0324] First, the small radar measurement data is time-synchronized and corrected to the flight track data. The small radar measurement data is then corrected for radio wave refraction using a classic refraction correction algorithm, which will not be elaborated here. Using the method described in step 1, the aircraft's positioning flight track data is converted to the small radar station system, and the self-positioning flight track segment corresponding to the small radar measurement data is extracted. The ranging error Er caused by time misalignment at each moment is calculated using the method described in step 2. Time,t Let Pt be the maximum time misalignment value, et, be 1 second. Then, the average time misalignment error and time alignment accuracy index for this data segment can be calculated from the data as follows:

[0325]

[0326] Using the method in step 3.1, the maximum residual error Er is corrected for refraction. ref Take 5m as the distance measurement accuracy index Pr m Using 7m, the point weight initialization can be completed, such as... Figure 3 As shown in the figure, the small dots represent the deviation between the radar ranging value and the reference ranging value at each moment, and the dashed line represents the ranging error threshold Er at each moment. thre,t The large dot trace represents the initial point weight w at each time step. point,t As can be seen, the initial point weights set the weights of the measured arc segments that exceed the error threshold to 0, and the weights of other arc segments to 1.

[0327] Using the methods shown in steps 3.2 and 3.3 (step 3.4 is not required for track data), complete the pitch weight assignment and range weight assignment, with the range weight coefficient c. ro Set the value to 0.1. Use the method shown in step 3.5 to reassign the point weights. The final point weights are as follows: Figure 4 As shown in the figure. The large dots in the graph represent the final point weights, and... Figure 3 Compared with the initial point weights, it can be observed that the point weights changed significantly after reassignment. The radar navigation point is at approximately 68360s in the data. At this point, the radar is closest to the aircraft and the elevation angle is the highest. It can be seen that the weight is the largest near this point. The farther away from this point, the lower the elevation angle, and therefore the lower the point weight.

[0328] Using the method shown in step 4, the time alignment correction is calculated iteratively: in the first iteration, dt is set to 0, st = et is set to 1, and st is obtained. new =0.4454; In the second iteration, dt = 0.4454, st = 0.4454, and we can solve for st. new = -0.0028; 3rd iteration st = 0.0028, solving for st gives st new = -0.0056; In the 3rd iteration, dt = 0.4369, st = 0.0056, and we can solve for st. new = -1.06 × 10 -12 The iteration termination condition is met, and the final correction amount dt = 0.4369 is output.

[0329] Iterative process as follows Figure 5 As shown in the figure, the midpoint of the inflection line is the current correction error point (dt, E) for each iteration. d,T (dt)), the two endpoints of the broken line are (dt-st, E) d,T (dt-st)) and (dt+st,E) d,T (dt+st)), where the circle represents the final correction value of the output. The continuous dots in the figure represent the weighted error variance obtained by iterating through the time correction values ​​from -1 to 1, which can be used to check whether the time correction value calculated by this method is accurate.

[0330] Figure 6 for Figure 5 The magnified view shows that this algorithm effectively avoids outputting local optima.

[0331] Add dt to the time axis of the original radar data to obtain time-aligned data. Figure 7 To compare the ranging error with the reference data before and after correction, Figure 8 By comparing the distance measurement values ​​before and after correction with the benchmark data, the effectiveness and accuracy of this patented method can be clearly seen.

[0332] Time alignment of radar measurement data with reference radar measurement data:

[0333] Synchronize the time of the small radar measurement data with that of the large radar. Perform radio wave refraction correction on the raw measurement data from both radars using a classic refraction correction algorithm, which will not be elaborated here. Using the method described in step 1, convert the large radar measurement data to the small radar station system, and extract the large radar measurement data segment corresponding to the small radar measurement data. Calculate the ranging error Er caused by time misalignment at each moment using the method described in step 2. Time,t Pt. The maximum time misalignment, et, is taken as 1 second, and the maximum residual error after refraction correction, Er, is also taken as Pt. ref Take 5m as the distance measurement accuracy index Pr m Taking 7m as an example, the average misalignment error and time alignment accuracy index for this data period can be calculated as follows:

[0334]

[0335]

[0336] Using the method in step 3.1, the point weight initialization assignment can be completed, such as... Figure 9 As shown in the figure, the small dots represent the deviation between the radar ranging value and the reference ranging value at each moment, and the dashed line represents the ranging error threshold Er at each moment. thre,t The large dot trace represents the initial point weight w at each time step. point,t As can be seen, the initial point weights set the weights of the measured arc segments that exceed the error threshold to 0, and the weights of other arc segments to 1.

[0337] Using the methods shown in steps 3.2, 3.3, and 3.4, the elevation weight, range weight, and reference radar data accuracy weight are assigned. The range weight coefficient c... ro Taking 0.1, the radar angle measurement accuracy index Pe mc With Pa mc All values ​​are taken as 0.14 mrad, and the reference radar data accuracy weighting coefficient is c. ecd Set the value to 0.5. Use the method shown in step 3.5 to reassign the point weights. The final point weights are as follows: Figure 10 As shown in the figure. The large dots in the graph represent the final point weights, and... Figure 3Compared to the initial point weights, a significant change in point weights after reassignment can be observed. Around 68360s, the small radar's approach point is closest to the aircraft and has the highest elevation angle. The overall trend of point weights is that they are higher near this point, and decrease further away with decreasing elevation angles. At 68330s and 6841s, the beams of the small radar and the large radar are nearly perpendicular. Analyzing the error causes as described in step 3.4, the ranging error of the small radar at this time is close to the latitudinal positioning error Pe of the large radar at that moment. mc ·r sc,t With the longitudinal positioning error Pa mc ·r sc,t And at this moment Pe mc ·r sc,t With Pa mc ·r sc,t The magnitude is extremely large, therefore the weight of points near that moment is reduced.

[0338] Using the method shown in step 4, the time alignment correction is calculated iteratively: in the first iteration, dt is set to 0, st = et is set to 1, and st is obtained. new =0.4367; In the second iteration, dt = 0.4367, st = 0.4367, and we can solve for st. new = -0.00016, which satisfies the iteration termination judgment condition, and the final correction amount dt = 0.4365 is output.

[0339] Iterative process as follows Figure 11 As shown in the figure, the midpoint of the inflection line is the current correction error point (dt, E) for each iteration. d,T (dt)), the two endpoints of the broken line are (dt-st, E) d,T (dt-st)) and (dt+st,E) d,T (dt+st)), where the circle represents the final correction value of the output. The continuous dots in the figure represent the weighted error variance obtained by traversing the time correction values ​​from -1 to 1, which can be used to check whether the time correction value calculated by the method of this patent is accurate.

[0340] Add dt to the time axis of the original radar data to obtain time-aligned data. Figure 12 To compare the ranging error with the reference data before and after correction, Figure 13 By comparing the distance measurement values ​​before and after correction with the benchmark data, the effectiveness and accuracy of this patented method can be clearly seen.

[0341] Aligning the small radar with the self-localization track and the measurement data of the large radar respectively, the time corrections obtained were 0.4369s and 0.4365s, respectively. The difference between the two corrections was about 0.0004s, which is less than one order of magnitude of the time alignment accuracy index Pt, further proving the effectiveness of this patent.

[0342] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for fast time synchronization of radar measurement data based on error modeling, characterized in that: Includes the following steps: Step 1: Acquire the radar measurement data to be corrected in , , for The radar range measurement, azimuth measurement, and elevation measurement values ​​to be corrected are located in the station's spherical coordinate system at all times; the radar measurement data to be corrected has been corrected for radio wave refraction. The corresponding time series is And obtain the reference data as the time correction alignment reference. Sampling time series of benchmark data Time series that are continuous and cover the data to be corrected And satisfy in This represents the maximum value of the timing error; Through interpolation and coordinate transformation, Transform to the spherical coordinate system of the radar station to be corrected to obtain the reference data. ; In the formula for The coordinates of the time reference data in the spherical coordinate system of the radar station to be corrected; Step 2: Calculate the time alignment accuracy index : in The ranging accuracy index of the radar to be corrected. The sequence of maximum ranging errors caused by time inconsistency The elements in; the sequence of maximum ranging errors caused by time inconsistency. Based on benchmark data Maximum value of summation error Calculated; Step 3: Calculate point weights: Step 3.1: Initialize point weights Point weight sequence The definition is as follows: Time point weight Initialization assignment is as follows: In the formula, for The radar range measurement value to be corrected in the station's spherical coordinate system at any given time. for The distance reference value in the spherical coordinate system of the radar station needs to be corrected at all times. It is the ranging error threshold; Step 3.2: Assigning pitch angle weights: Pitch angle error weight sequence The definition is as follows: The assignment process is as follows: In the formula for The measured radar elevation angle to be corrected in the station's spherical coordinate system at all times; Step 3.3: Distance weight assignment: Distance Error Weight Sequence The definition is as follows: The assignment process is as follows: In the formula for The radar range measurement value to be corrected in the station's spherical coordinate system at any given time. Radar measurement data sequence to be corrected The maximum range in the range, Radar measurement data sequence to be corrected The minimum distance measurement value; and the values ​​used in the process of finding the maximum and minimum distance measurement values. The data needs to be filtered through the initial point weight assignment in step 3.1, using data with an initial point weight of 1; This refers to the distance weighting coefficient. Step 3.4: Assigning accuracy weights to the reference radar data If the reference data is satellite precision orbit data, target telemetry self-positioning data, or GNSS data, it is assumed that the reference data has no error; if the reference data is radar measurement data, then the reference radar data accuracy weight sequence is... The definition is as follows: The assignment process is as follows: in The accuracy weighting coefficient for the baseline radar data; as well as and It is obtained through the following process: The origin is the location point of the reference data. Establish an error analysis coordinate system. The axial direction is the beam direction of the reference radar. Axis perpendicular to And vertically upward, The axis conforms to the right-hand rule and is perpendicular to axis, Axis; Establish a reference radar positioning error ellipsoid centered on the origin of the error analysis coordinate system: in As a benchmark for radar ranging accuracy, As a benchmark for radar elevation angle measurement accuracy, As a benchmark for radar azimuth angle measurement accuracy, For reference radar The distance measured at that moment; The geocentric coordinates of the radar to be corrected are: Its coordinates in the error analysis coordinate system are : in This is the transformation matrix from the geocentric coordinate system to the error analysis coordinate system. This is the corresponding transformation vector; for The coordinates of the radar station site to be corrected in the error analysis coordinate system at all times; The coordinates of the intersection point between the radar beamline to be corrected and the reference radar positioning error ellipsoid at any given time. The calculation is as follows: in: Step 3.5: Complete the point weight assignment When the reference data is radar measurement data, the point weight assignment process is as follows: When the reference data is telemetry self-positioning, GNSS data, or precision orbit data, the point weight assignment process is as follows: Step 4: Iteratively calculate the time alignment correction. Establish initial values ​​for the iteration, including a sequence of range values ​​from the radar measurement data to be corrected. Distance value sequence of reference measurement data The final point weights obtained in step 3 Current time correction amount Time correction step size Time accuracy alignment index ; Step 4.1: Solve for the current correction error The range value sequence of the radar measurement data to be corrected timestamp plus current time correction Obtain the corrected ranging data sequence Then, in time series As interpolation points, for Interpolation was performed to obtain a range value sequence of the current corrected data aligned with the time series of the original radar measurement data to be corrected. Current weighted error variance for: Step 4.2: Solve for the maximum correction error The range value sequence of the radar measurement data to be corrected By adding the time correction factor and the time correction step size to the time axis, we obtain the corrected distance value sequence of the ranging data. Then, in time series As interpolation points, for Interpolation was performed to obtain a positive offset corrected distance value sequence aligned with the original measurement data time series. ;Will Adding the time correction amount to the time axis and subtracting the time correction step size, and then performing the same operation as above, yields the negative offset corrected data distance value sequence. ; Calculate the weighted error variance of the positive offset correction data for: Calculate the weighted error variance of the negative offset correction data for: Step 4.3: Solve for the error gradient Based on the current weighted error variance, the weighted error variance of the positive offset correction data, and the weighted error variance of the negative offset correction data, solve for the time offset at the gradient minimum. Then adjust the step size The update is as follows: Update time correction : Step 4.4: Iteration Termination Decision The conditions for terminating the iteration are as follows: If the decision condition is not met, skip to step 4.1 for iteration; if the condition is met, output the result. Add the time axis of the measurement data to be corrected Then, the measurement data is time-aligned.

2. The method for fast time synchronization of radar measurement data based on error modeling according to claim 1, characterized in that: In step 2, the sequence of maximum ranging errors caused by time inconsistency for in For benchmark data The distance value sequence, negative offset reference data The distance value sequence, Positive offset reference data The distance value sequence; Negative offset reference data It is obtained through the following process: benchmark data The maximum value of the time stamp minus the time statistics error Obtain the offset baseline data Then, based on the baseline data time series As interpolation points, for Interpolation is performed to obtain negative offset reference data aligned with the reference data time series. ; Positive offset reference data It is obtained through the following process: benchmark data Time axis plus maximum time error Obtain the offset baseline data Then, based on the baseline data time series As interpolation points, for Interpolation was performed to obtain positive offset reference data aligned with the reference data time series. .

3. The method for fast time synchronization of radar measurement data based on error modeling according to claim 1, characterized in that: In step 3.1, the ranging error threshold According to the formula Calculation, where To correct the maximum residual error caused by the refraction of the radar ranging radio waves, The ranging accuracy index of the radar to be corrected. for The maximum distance measurement error at any given time.

4. The method for fast time synchronization of radar measurement data based on error modeling according to claim 1, characterized in that: In step 3.4, the transformation matrix for: in The longitude coordinates of the reference radar station site, The latitude coordinates of the reference radar station site for The elevation angle measured by the time-reference radar relative to the origin of the error analysis coordinate system. for The azimuth angle of the time reference radar relative to the origin of the error analysis coordinate system; Transformation vector for: in The coordinates are the geocentric coordinates of the origin of the error analysis coordinate system.

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