A method for analyzing intersection errors and rapidly optimizing and fusing intersection results using photoelectric theodolites

Abstract

This invention proposes a method for analyzing intersection errors and rapidly optimizing and fusing intersection results using photoelectric theodolites. The method includes steps such as generating intersection results and initial error values, iteratively classifying the measurement accuracy of individual devices, recursively solving for the angle measurement errors of individual devices, optimizing the positioning results, and fusing them for output. This solves the problem of being unable to accurately analyze theodolite measurement errors and generate accurate measurement points when there are few photoelectric theodolites participating in the intersection, or when there is no other measurement data as an auxiliary benchmark for error identification. By analyzing the angle measurement data and intersection result generation of multiple photoelectric theodolites at a single moment, this invention can identify the measurement errors of all photoelectric theodolites in the system and classify the intersection priorities, provided that at least two photoelectric theodolites have high accuracy. Then, it selects the positioning points generated by the intersection of high-priority measurement devices as candidate output results, and finally generates the output intersection positioning points through weighted fusion of error parameters.

Description

Technical Field

[0001] This invention relates to the field of optical measurement data processing technology, specifically to a method for analyzing intersection errors and rapidly optimizing and fusing intersection results using a photoelectric theodolite. Background Technology

[0002] With the accelerated advancement of equipment testing in my country, there is a greater demand for stable tracking and precise positioning of space targets and atmospheric targets during range tests. Optical measurement, with its advantages of high precision, strong intuitiveness, and immunity to "blackout" and ground clutter interference, is increasingly being used in range tests. However, conventional rendezvous using data from photoelectric theodolites has certain inherent flaws. If one or more of the equipment involved in the rendezvous tracks the wrong target or if the measurement system has significant errors, it will affect the accuracy of the rendezvous trajectory and may even lead to incorrect target positioning.

[0003] Traditional methods typically eliminate data with poor rendezvous accuracy by comprehensively comparing rendezvous tracks, high-precision radar measurement tracks, and target cooperative track information. Multi-source optical rendezvous results are then fused using a master station and multiple slave stations to remove error measurement sources and improve rendezvous positioning accuracy. However, this method has significant limitations. For example, without high-precision radar or cooperative track information, if n electro-optical theodolites are simultaneously tracking the target, and m of them have low tracking accuracy or are tracking the wrong target, then... The intersection results have a large error, and if When the number of intersection results containing errors exceeds half of the total number of intersection results, traditional methods cannot effectively remove errors and may even misclassify high-precision intersection results as low-precision ones. Furthermore, even if the number of intersection results containing errors is less than half of the total number of intersection results, traditional methods cannot quantitatively analyze the magnitude of measurement errors of each device, and involve secondary fusion after removing out-of-tolerance device sources, resulting in poor computational complexity and real-time performance. To address these issues, some scholars have proposed using a method that judges the continuity of the intersection sequence to continuously assess the status of each photoelectric theodolite within the system, thereby optimizing the intersection results. This method is effective, but it requires a relatively long period of data accumulation to establish a stable and accurate output. Therefore, how to accurately identify out-of-tolerance data sources and quickly generate high-precision intersection results using only photoelectric latitude and longitude angle measurement data at a single moment, when there are few photoelectric theodolites participating in the intersection or when there is no other measurement data as an auxiliary benchmark for error identification, is a technical problem that needs to be solved. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes a method for analyzing intersection errors and rapidly optimizing and fusing intersection results using photoelectric theodolites, comprising the following steps:

[0005] Step 1: Perform pairwise intersections on n photoelectric theodolites tracking the target at the same time to generate a total of For each intersection positioning point, an error information vector Evec is established. i ,

[0006] Evec i =(X i Elp i Elm i ,a i ,b i Eam a,i Eam b,i ,r a,i ,r b,i )

[0007] Where a i b i The photoelectric theodolite equipment number for forming the i-th intersection positioning point, X i For device a i With device b i Interactive localization results in the geocentric system; Elp i Elm i For intersection measurement error, Eam a,i With Eam b,i r represents the angle measurement error of the corresponding device. a,i With r b,i This represents the distance between the corresponding device and the target;

[0008] The rendezvous positioning accuracy error Elp i Intersection measurement error Elm i Based on this, the positioning error index El is designed. i :

[0009]

[0010] Press El i Sort the error information vectors in Evec in ascending order to establish an error information vector set G. E :

[0011]

[0012] Step 2: Establish the equipment error statistics vector Eequip and the equipment error statistics vector set G for each device. Eequ :

[0013] Eequip k =(Ea k Cjoin k Prio k )

[0014] G Eequ ={Eequip k |k∈[1,n]}

[0015] Among them, Ea k The mean angle measurement error of device k is initialized to 0; Cjoin k Prio represents the total weighting coefficients of all intersections involving device k at this moment, initialized to 0. k The priority of device k is initialized to 1 if the device has measurement data at the current time, and to 0 if there is no measurement data at the current time.

[0016] Establish a vector D of size n×1 for each priority device. PPEN =0 n×1 With PrioroNow=1 as the current priority, the following steps are followed to begin iteratively classifying the measurement accuracy of a single device:

[0017] Step 2.1: Calculate the error of a single measuring device with the current priority.

[0018] Press i from 1 to For the error information vector set G E Search, if Evec i Corresponding device a i Priority Prio a and equipment b i Priority Prio b The following conditions must be met:

[0019]

[0020] Then update device a i b i Error statistics vector Eequip a Eequip b The process is as follows:

[0021]

[0022] Ea a =Ea a,new

[0023]

[0024] Ea b=Ea b,new

[0025]

[0026]

[0027] After the search is completed, count the number of devices with the current priority participating in the rendezvous, and denote this as N. EQ Update the device number vector D for each priority level. PPEN Record the number of devices currently participating in the rendezvous at the current priority level: D PPEN (PrioNow) = N EQ

[0028] For the devices participating in the rendezvous at the current priority, the corresponding device error statistics vector Eequip is... k Ea k The reassignment process is as follows:

[0029]

[0030]

[0031] If N EQ If the value is less than 3, it means that there are fewer than 3 devices intersecting at this moment, and the data accuracy cannot be determined. Therefore, the iteration loop is exited and the process proceeds to step 3; otherwise, the process proceeds to step 2.2.

[0032] Step 2.2: Determine whether the current highest accuracy level meets the accuracy requirements.

[0033] Count all those that satisfy Prio k For devices ≥PrioNow, create a set Gp, where the mean angular error of all devices in the set is . The maximum angle error is Eam; the angle measurement accuracy of all devices is Pam. k Geometric superposition is performed as a precision criterion to determine whether the angular errors of all devices within the set are better than the precision criterion, and whether the precision of all devices within the set is at a relatively close level.

[0034]

[0035] If the above conditions are met, it is assumed that all devices with the current accuracy priority meet the accuracy requirements, and the iteration loop is exited, proceeding to step 3; otherwise, proceed to step 2.3.

[0036] Step 2.3: Identify devices with higher measurement accuracy and assign them higher priority.

[0037] Higher priority is defined as PrioNext = PrioNow + 1, which filters devices within the current priority set Gp, and prioritizes those with angular measurement errors Ea. k Superior Device k is given higher priority, among which The mean angle measurement error of all devices in the current set Gp; devices k that meet the criteria are given higher priority, and the error statistics vector Eequip is... k Device Priority Prio k Updated: Prio k =PrioNext;

[0038] Step 2.4: Determine whether the priority can be further subdivided in the next iteration.

[0039] The number of devices of each priority is recounted. If the number of devices of the current priority is 0, it means that the corner error of the devices currently in the next priority is too large. In this case, the priority of these devices is reduced to the current priority, and the iteration loop is exited, and the process proceeds to step 3.

[0040] Search error information vector set G E If at least one intersection point is generated entirely by a intersection of devices with PriorityNext, then continue with the subsequent steps; otherwise, exit the iteration loop and go to step 3.

[0041] Step 2.5: Reset the error statistics of the devices with elevated priority to zero.

[0042] Establish a set G for devices with elevated priority. PNE Set the mean angle measurement error Ea of these devices to zero, and the total weighting coefficient Cjoin to zero;

[0043] Increase the current priority by setting PrioNow = PrioNext, and jump to step 2.1 for iteration;

[0044] Step 3: Recursively solve for the angle measurement error of a single device

[0045] Record the highest priority PrioMax = PrioNow obtained after step 2. If PrioMax = 1, it means that step 2 did not complete the iterative classification of the measurement accuracy of a single device, and skip directly to step 4; otherwise, iteratively solve the angle measurement error of a single device through the following steps:

[0046] Step 3.1: Recursively calculate the angle measurement error of the lower-level equipment.

[0047] For the error information vector set G E Perform a search: i∈G EAnd for the equipment error statistical vector set G Eequ Perform a search: k∈G Eequ If both conditions are met:

[0048] 1) The accuracy class of device k is PrioNow.

[0049] 2) Device k participated in point X i The intersection

[0050] 3) Participation point X i The accuracy class of the other device l at the intersection is less than that of PrioNow.

[0051] Then for X i The error information vector Evec i The angle measurement error Eam of equipment k and equipment l k,i Eam l,i Make corrections

[0052] Eam k,i =Ea k

[0053] Eam l,i =(Elm) i -Ea k ·r k,i ) / r l,i

[0054] In the formula Ea k Elm is the mean angle measurement error of device k. i Let X be the point i The intersection measurement error, r k,i Let X be the point i The distance measurement value of the corresponding device k, r l,i Let X be the point i The distance measurement value of the corresponding device l;

[0055] Each time a G is completed E and G Eequ If the search is incomplete, let PrioNow = PrioNow-1, repeat step 3.1 until PrioNow equals 1, then exit the iteration and proceed to step 3.2;

[0056] Step 3.2: Update equipment error statistics

[0057] Traversing the error information vector set G E For each device, calculate the weighted average of the angle measurement error and update the device error statistics vector Eequip. k Mean angle measurement error Ea k :

[0058]

[0059] In the formula Elm is the set of all error information vectors Evec from which device k participates in the intersection. i The error information vector Evec i The intersection measurement error in Eam k,i The error information vector Evec i The angle measurement error of the device k in the middle;

[0060] Step 4: Optimize and fuse the localization results for output.

[0061] Use the priority device number vector D obtained in step 2. PPEN The number N of photoelectric theodolites participating in the intersection is counted in order of priority from low to high. UE :

[0062]

[0063] In the formula, PrioMax is the highest priority obtained in step 2, Ps is the precision level of the initial statistics, and N is the highest priority obtained in step 2. UE Maximum Ps ≥ 3; sequentially search error information vector set G E Query each error information vector Evec i The equipment accuracy levels corresponding to the two intersection sources like If all values ​​are not less than Ps, then Evec will be... i The intersection and localization result X i As alternative output results; the final output result is obtained by weighting all alternative output results.

[0064] Furthermore, in step 1, for device a i With device b i The following process is used to obtain: Device a i With device b i Interactive localization result X in the geocentric system i Rendezvous and positioning accuracy error Elp i Intersection measurement error Elm i The corresponding angle measurement error of the equipment, Eam a,i With Eam b,i The distance r between the corresponding device and the target a,i With r b,i ;

[0065] Acquire device a i With device b i The measured values ​​are denoted as (A) a,i E a,i ) and (Ab,i E b,i A is the azimuth angle being measured, and E is the elevation angle being measured.

[0066] First, select an initial distance value r. a,i With r b,i The size is not less than the measurement baseline length ||S a -S b || That's it, where device a i With device b i The station coordinates are S a =(x a ,y a ,z a ) and S b =(x b ,y b ,z b );

[0067] According to the formula

[0068] (x a,i ,y a,i ,z a,i ) T =r a,i M sg,a (cosE a,i cosA a,i sinE a,i ,cosE a,i sinA a,i ) T +V sg,a

[0069] (x b,i ,y b,i ,z b,i ) T =r b,i M sg,b (cosE b,i cosA b,i sinE b,i ,cosE b,i sinA b,i ) T +V sg,b

[0070] Computing device a i With device b i Initial positioning result X in the geocentric system a,i =(x a,i ,y a,i ,z a,i ) and X b,i =(x b,i ,y b,i ,zb,i M sg,a M sg,b V is the transformation matrix. sg,a V sg,b Transformation vector;

[0071] According to the formula

[0072]

[0073]

[0074] Computing device a i With device b i The angle between the optical path and the measurement baseline is measured, and the formula θ is used. i =π-θ a,i -θ b,i Calculate the theoretical optical intersection angle θ i ;

[0075] Reuse formula

[0076]

[0077]

[0078] Inversely calculate the distance r between the corresponding device and the target. a,i With r b,i The calculated r a,i With r b,i Substitution

[0079] (x a,i ,y a,i ,z a,i ) T =r a,i M sg,a (cosE a,i cosA a,i sinE a,i ,cosE a,i sinA a,i ) T +V sg,a

[0080] (x b,i ,y b,i ,z b,i ) T =r b,i M sg,b (cosE b,i cosA b,i sinE b,i ,cosE b,i sinA b,i ) T+V sg,b

[0081] Resolve X a,i With X b,i X i =(X a,i +X b,i ) / 2 represents the current time of device a i With device b i Inter-location results in the geocentric system; intersection measurement error Elm i =||X a,i -X b,i ||;Angle measurement error Eam a,i and Eam b,i The initial value calculation results are as follows:

[0082]

[0083] Rendezvous positioning accuracy error Elp i for:

[0084]

[0085] in

[0086] El' a,i =El a,i / sinθ i

[0087] El' b,i =El b,i / sinθ i

[0088] El' ab,i =min(El' a,i ,El' b,i )

[0089] El a,i =Pam a ·r a,i

[0090] El b,i =Pam b ·r b,i

[0091] Pam a Pam b For device a i With device b i Its own angular measurement accuracy.

[0092] Furthermore, in step 1, if the theoretical optical intersection angle θ corresponding to a certain intersection positioning point... iIf the value is less than π / 12 or greater than π·11 / 12, it is considered that the measurement data of the pair of devices corresponding to the intersection positioning point do not meet the intersection conditions and cannot generate accurate results.

[0093] Furthermore, in step 4, the process of weighting and averaging all candidate outputs is as follows:

[0094] The error information vector Evec for each device whose accuracy level corresponding to the two internal intersection sources is not less than Ps is defined. i Establish set G OT The set contains N vectors. OT The final output result is

[0095]

[0096] El is the positioning error index corresponding to the error information vector Evec.

[0097] Beneficial effects

[0098] This invention solves the problem of accurately analyzing theodolite measurement errors and generating accurate measurement points when there are few photoelectric theodolites participating in the intersection, or when there is no other measurement data as an auxiliary reference for error identification. By analyzing the angle measurement data of multiple photoelectric theodolites at a single moment and the generation of intersection results, this invention can identify the measurement errors of all photoelectric theodolites in the system and classify the intersection priority (relative accuracy level) by ensuring that at least two photoelectric theodolites have high accuracy. Then, it selects the positioning points generated by the intersection of high-priority measurement devices as candidate output results, and finally generates the output intersection positioning points through weighted fusion of error parameters.

[0099] 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

[0100] 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:

[0101] Figure 1 Schematic diagram of intersection plane error projection

[0102] Figure 2 Flowchart of the method steps in the invention

[0103] Figure 3 The process by which the relative accuracy level of a device changes during iteration at a certain moment.

[0104] Figure 4The process by which the error of the device changes during the iterative-recursive solution at a certain moment.

[0105] Figure 5 Analysis results of equipment angle measurement error

[0106] Figure 6 Comparison of intersection results errors Detailed Implementation

[0107] The purpose of this invention is to solve the problem of how to accurately identify out-of-tolerance data sources and quickly generate high-precision intersection results using only photoelectric theodolite angle measurement data at a single moment when there are few photoelectric theodolites participating in the intersection or when there is no other measurement data as an auxiliary reference for error identification.

[0108] To solve the above-mentioned technical problems, the present invention adopts the following steps:

[0109] Step 1: Generate intersection results and initial error values

[0110] First, pairwise intersections are performed on n photoelectric theodolites tracking the target simultaneously. The classical optical intersection refraction correction method is used to calculate the refraction-corrected measurements of the two devices in each intersection. The relevant algorithm is a classical algorithm and will not be elaborated further in this embodiment. The refraction-corrected device measurements are denoted as (A... a,i E a,i ) and (A b,i E b,i A represents the measured azimuth angle, and E represents the measured elevation angle. The subscripts a and b are the equipment numbers, and their value ranges are as follows:

[0111] a,b∈[1,n] (1)

[0112] The subscript i represents the sequence number of the intersection point generated by devices a and b at the current time, and its value range is as follows:

[0113]

[0114] The coordinates of the two equipment sites are S a =(x a ,y a ,z a ) and S b =(x b ,y b ,z b ), which augments its current measurement value to (r) a,i A a,i E a,i ) and (r b,i A a,i E a,i ), where r at this time a,iWith r b,i The initial distance value can be a larger fixed value during the calculation process, and its magnitude must not be less than the measurement baseline length ||S a -S b This effectively avoids errors in results caused by errors in the Earth model and site location.

[0115] Transformation matrix M from the station system to the geocentric system sg,a M sg,b and transformation vector V sg,a V sg,b Solve for the initial positioning results X of photoelectric theodolites a and b in the geocentric system. a,i =(x a,i ,y a,i ,z a,i ) and X b,i =(x b,i ,y b,i ,z b,i The method is as follows:

[0116] (x a,i ,y a,i ,z a,i ) T =r a,i M sg,a (cosE a,i cosA a,i sinE a,i ,cosE a,i sinA a,i ) T +V sg,a (3)

[0117] (x b,i ,y b,i ,z b,i ) T =r b,i M sg,b (cosE b,i cosA b,i sinE b,i ,cosE b,i sinA b,i ) T +V sg,b (4)

[0118] Where the transformation matrix M sg,a M sg,b and transformation vector V sg,a V sg,b The solution method is a traditional algorithm commonly used in the industry, which will not be elaborated here.

[0119] The angles between the measuring optical paths of the photoelectric theodolite a and b and the measuring baseline are respectively:

[0120]

[0121]

[0122] Theoretical optical intersection angle (not the actual intersection angle, used for error analysis):

[0123] θ i =π-θ a,i -θ b,i (7)

[0124] It should be noted that in this embodiment, when the theoretical optical intersection angle is less than π / 12 or greater than π·11 / 12, the measurement data of this group of devices is considered to lack the conditions for intersection and cannot generate accurate results. Therefore, the intersection calculation should be performed on the next group of devices.

[0125] Then the distance r between the photoelectric theodolite a, b and the target can be calculated. a,i r b,i They are respectively:

[0126]

[0127]

[0128] Then r a,i r b,i Substitute the values ​​into formulas (3) and (4), keeping other parameters unchanged, and solve for X again. a,i With X b,i , let X i =(X a,i +X b,i ) / 2 represents the geocentric positioning results of devices a and b at the current moment.

[0129] The rendezvous measurement error Elm i The definition is as follows:

[0130] Elm i =||X a,i -X b,i || (10)

[0131] Assume that in this intersection, photoelectric theodolites a and b have the same angle measurement error Eam a,i Eam b,i The calculation method is as follows:

[0132]

[0133] Eam a,i Eamb,i The iterative correction will be completed in subsequent steps; this is only the result of the initial value calculation.

[0134] The angle measurement accuracy of the photoelectric theodolite at points a and b is Pam. a Pam b The theoretical positioning accuracy errors can be obtained by consulting the equipment manual:

[0135] El a,i =Pam a ·r a,i (12)

[0136] El b,i =Pam b ·r b,i (13)

[0137] The intersection of two devices will produce an error scattering envelope sphere diameter Elp i The calculation formula is as follows:

[0138]

[0139] In the formula El a,i El b,i The definitions are given in formulas (12) and (13), θ i For the intersection angle, Elp i This refers to the diameter of the intersection positioning accuracy error. (See the attached diagram in the instruction manual.) Figure 1 The diagram shows the intersection plane error. The narrower area represents the error range caused by the angular measurement error of device a in the direction of light wave propagation, and the wider area represents the error range caused by the angular measurement error of device b in the direction of light wave propagation. The overlapping area represents the positioning error distribution area of ​​the intersection plane. The diameter of the circumcircle of this area is compared with the error El' perpendicular to the intersection plane direction. ab,i The geometric sum is the diameter of the accuracy error of this intersection.

[0140] Repeat the above steps to pair up and rendezvous n photoelectric theodolites, generating a total of There are 10 intersection positioning points, and each intersection positioning point has a corresponding geocentric intersection positioning result X. i Rendezvous and positioning accuracy error Elp i Intersection measurement error Elm i Equipment No. a i Equipment No. b i Equipment angle measurement error Eam a,i With Eam b,i Distance r between equipment and target a,i With r b,i .

[0141] An error information vector Evec is established for each positioning point. i :

[0142] Evec i =(X i Elp i Elm i ,a i ,b i Eam a,i Eam b,i ,r a,i ,r b,i (15)

[0143] The rendezvous positioning accuracy error Elp i Intersection measurement error Elm i Based on this, the positioning error index El is designed. i :

[0144]

[0145] Press El i Sort Evec in ascending order to establish an error information vector set G. E :

[0146]

[0147] Step 2: Iterative grading of measurement accuracy for individual devices

[0148] For each device, establish a device error statistical vector Eequip and a device error statistical vector set G. Eequ :

[0149]

[0150] Among them, Ea k The mean angle measurement error of device k is initialized to 0; Cjoin k Prio represents the total weighting coefficients of all intersections involving device k at this moment, initialized to 0. k This is the priority (and accuracy level) of device k. It is initialized to 1 if the device has measurement data at the current moment, and initialized to 0 if there is no measurement data at the current moment.

[0151] Establish a vector D of size n×1 for each priority device. PPEN =0 n×1 PrioroNow=1 indicates the current priority; begin iterative device precision grading.

[0152] Step 2.1: Calculate the error of a single measuring device with the current priority.

[0153] Press i from 1 to For the error information vector set G E Search and determine if Evec i Corresponding device a i Priority Prio a and equipment b i Priority Prio b The following conditions must be met:

[0154]

[0155] Then update device a i b i Error statistics vector Eequip a Eequip b The process is as follows:

[0156]

[0157] After the search is completed, count the number of devices with the current priority participating in the intersection (devices that meet condition (19)) and record it as N. EQ Update the device number vector D for each priority level. PPEN Record the number of devices currently participating in the rendezvous at the current priority level:

[0158] D PPEN (PrioNow) = N EQ (twenty one)

[0159] For equipment that meets condition (19), the corresponding equipment error statistics vector Eequip k Ea k The reassignment process is as follows:

[0160]

[0161] Equations (20) and (22) with respect to Ea k The operation essentially obtains the weighted average of the angle measurement errors of the device k with the current priority (accuracy level), and the intersection measurement error Elm of the relevant intersection points. i The smaller the value, the higher its weight.

[0162] At this point, a judgment is made: if N... EQ If the value is less than 3, it means that there are fewer than 3 devices intersecting at this moment, making it impossible to determine the data accuracy. Therefore, the iteration loop will be terminated, and the process will proceed to step 3.

[0163] Step 2.2: Determine whether the current highest accuracy level meets the accuracy requirements.

[0164] Count all those that satisfy Prio kFor devices with a priority greater than or equal to PrioroNow (device priority not lower than the current priority), create a set Gp, where the mean angular error of all devices in the set is [value missing]. The maximum angular error is Eam. The angular measurement accuracy Pam for all devices is also considered. k Geometric superposition is performed as a precision criterion to determine whether the angular errors of all devices within the set are better than the precision criterion, and whether the precision of all devices within the set is at a relatively close level. Based on this, the design criteria are as follows:

[0165]

[0166] If the above conditions are met, it is assumed that all devices with the current accuracy priority meet the accuracy requirements, and the iteration loop is exited, proceeding to step 3.

[0167] Step 2.3: Identify devices with higher measurement accuracy and assign them higher priority.

[0168] Higher priority is defined as PrioNext = PrioNow + 1, which filters devices within the current priority set Gp, and prioritizes those with angular measurement errors Ea. k Superior The device k is prioritized, and the criterion is designed as follows:

[0169]

[0170] in This is the mean angle measurement error of all devices within the current set Gp. Devices k that meet the criteria are assigned higher priority, and the error statistics vector Eequip is calculated accordingly. k Device Priority Prio k Update:

[0171] Prio k =PrioNext (25)

[0172] The purpose of the above calculations is to assign higher priority to devices with smaller angular errors among the current priority devices, so as to facilitate the continuous subdivision of device priorities through iteration and ensure that there are intersection results in the next iteration as much as possible.

[0173] Step 2.4: Determine whether the priority can be further subdivided in the next iteration.

[0174] The number of devices for each priority level is recounted. If the current number of priority devices is 0, then the following condition is met:

[0175] D PPEN (PrioNow) == 0 (26)

[0176] This means that the corner errors of the devices currently at the next priority level are generally large and the number is similar, meaning that the priority cannot be further subdivided in the next iteration. At this point, the priority of these devices is reduced to the current priority, and the iteration loop is exited, proceeding to step 3.

[0177] Search error information vector set G E If at least one intersection point is generated entirely by intersection of devices with Priority Next, then continue with the subsequent steps; otherwise, exit the iteration loop and go to step 3. The criteria for continuing with the subsequent steps are as follows:

[0178]

[0179] Step 2.5: Reset the error statistics of the devices with elevated priority to zero.

[0180] Establish a set G for devices with elevated priority. PNE Set the mean angle measurement error Ea of these devices to zero, and the total weighting coefficient Cjoin to zero:

[0181]

[0182] Increase the current priority by setting PrioNow = PrioNext, and jump to step 2.1 to iterate until you exit the iteration loop of step 2 and enter step 3.

[0183] Step 3: Recursively solve for the angle measurement error of a single device

[0184] After completing step 2 of the calculation, the error information vector Eequip for each device is... k All assignments have been completed, and Prio in the vector... k To classify the accuracy level of device k (also as the priority classification of intersection sources), a larger number indicates higher accuracy, and a value of 0 means that the device failed to acquire target measurement data at this moment; Ea k This is the statistical mean of the angle measurement error that would occur if device k interacted with a device of at least the same accuracy level as itself at the current moment.

[0185] It is easy to see that only the devices marked as having the highest priority have the highest mean angle measurement error Ea. k Only the value that is close to its true value is obtained. Therefore, it is necessary to solve the angle measurement error of other accuracy level devices by recursive calculation.

[0186] Record the highest priority (precision level) PrioMax obtained after calculation in step 2:

[0187] PrioMax = PrioNow (29)

[0188] If PrioMax = 1, it means that step 2 did not complete the iterative classification of the measurement accuracy of a single device (or the device accuracy is very high), and we skip directly to step 4; otherwise, we begin iteratively solving for the angle measurement error of each device:

[0189] Step 3.1: Recursively calculate the angle measurement error of the lower-level equipment.

[0190] Using the PrioroNow priority device as a benchmark, the angle measurement error of lower priority devices that have intersected with the PrioroNow priority device is recursively calculated.

[0191] For the error information vector set G E Perform a search (i∈G) E ), and for the equipment error statistical vector set G Eequ Perform a search (k∈G) Eequ If the following conditions are met simultaneously:

[0192] 1) The accuracy class of device k is PrioNow.

[0193] 2) Device k participated in point X i The intersection

[0194] 3) Participation point X i The accuracy class of the other device l at the intersection is less than that of PrioNow.

[0195] It is possible to target X i The error information vector Evec i The angle measurement error Eam of equipment k and equipment l k,i Eam l,i The correction steps are as follows:

[0196]

[0197] In the formula Ea k Elm is the mean angle measurement error of device k. i Let X be the point i The intersection measurement error, r k,i Let X be the point i The distance measurement value of the corresponding device k, r l,i Let X be the point i The corresponding distance measurement value of device l. Each time a distance measurement of G is completed... E and G Eequ If the search is complete, let PrioNow = PrioNow-1, repeat step 3.1 until PrioNow equals 1, then exit the iteration and proceed to step 3.2.

[0198] Step 3.2: Update equipment error statistics

[0199] Traversing the error information vector set G E For each device, calculate the weighted average of the angle measurement error and update the device error statistics vector Eequip. k Mean angle measurement error Ea k The specific algorithm is as follows:

[0200]

[0201] In the formula Elm is the set of all error information vectors Evec from which device k participates in the intersection. i The error information vector Evec i The intersection measurement error in Eam k,i The error information vector Evec i The angle measurement error of the device k.

[0202] This completes the solution for the angle measurement error of a single device.

[0203] Step 4: Optimize and fuse the localization results for output.

[0204] Use the priority device number vector D obtained in step 2. PPEN The number N of photoelectric theodolites participating in the intersection is counted in order of priority from low to high. UE :

[0205]

[0206] In the formula, PrioMax is the highest priority obtained in step 2, and Ps is the precision level of the initial statistics. Find the N... UE The maximum Ps is ≥3. The purpose of this is to ensure that there are at least two intersection results for fusion.

[0207] Search the error information vector set G in sequence E Query each error information vector Evec i The equipment accuracy levels corresponding to the two intersection sources like If all values ​​are not less than Ps, then Evec will be... i The intersection and localization result X i As alternative output results, the final output result is obtained by weighting all alternative output results, with the weights being negatively correlated with the intersection positioning error.

[0208] The specific steps are as follows: First, define the conditions:

[0209]

[0210] Each error information vector Evec that satisfies condition (33)i Establish set G OT The set contains N vectors. OT The output result is:

[0211]

[0212] Where El is the positioning error index corresponding to the error information vector Evec, and its definition is given in formula (16).

[0213] This completes the error identification, accuracy grading, and fusion intersection point output of the measurement equipment of this invention. See the flowchart below. Figure 2 .

[0214] 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.

[0215] This embodiment serves the trajectory measurement of targets flying within the atmosphere. It uses 11 photoelectric theodolites deployed in the area where the target aircraft's flight path is located to track and measure the target. It can use the angle measurement data of the photoelectric theodolites to generate high-precision trajectories in real time. It uses the measurement data at a single moment to complete the equipment measurement accuracy analysis and eliminate the influence of low-precision measurement equipment on the rendezvous results.

[0216] In this embodiment, following the principle of intersection before identification, at each moment, all positioning points meeting the generation conditions are first intersected, and an initial error value is generated along with the intersection result. Subsequently, the measurement accuracy of individual measuring devices is statistically analyzed by examining the intersection points and the initial error value to find the device with the highest accuracy. Using the device with the highest accuracy as the benchmark, the measurement accuracy of devices with lower accuracy is recursively calculated to obtain the measurement accuracy analysis results of each device at the same moment. Referring to the accuracy analysis results, the positioning points generated by the intersection of devices with high measurement accuracy (high intersection priority) are finally weighted and fused to generate the output positioning result.

[0217] Generation of intersection results and initial error values:

[0218] The angle measurement data sent to the central computer by the photoelectric theodolite is processed in real time at a frequency of 20 Hz. Due to the impact of data transmission delay of each device, and taking into account the timeliness of the intersection data and the validity of the measurement data, the current Beijing time is subtracted by a small fixed delay (usually 0.5 seconds) as the alignment time. The measured data of each photoelectric theodolite are interpolated to obtain the alignment time measurement data.

[0219] The tracking status of the equipment is determined. If the equipment is in self-tracking or semi-automatic tracking mode, it is considered to be in an effective tracking state of the target aircraft; otherwise, it is considered that the target has not been acquired. Using the method described in step 1, the intersection points are generated by pairing two devices together, and initial values ​​for the positioning error and equipment angle measurement error are generated. Cases where the intersection angle is less than π / 12 or greater than π·11 / 12 are excluded, as the error spread caused by the intersection angle is too large, and it is considered that the two optical devices cannot achieve intersection in this case.

[0220] Iterative grading of measurement accuracy for individual measuring devices:

[0221] For each device that tracks the aircraft at the same moment, establish a device error statistics vector. The vector includes the device's angular error statistics, the total weight ratio coefficient of the rendezvous that the device is participating in at the same moment, the number of rendezvous points generated at the moment, and the device's current accuracy level (rendezvous priority).

[0222] Using the method described in step 2, analyze whether the angular errors of all devices are better than the accuracy judgment index of the current accuracy level. Assign a higher accuracy level to devices that are better than the accuracy judgment index. Repeat step 2 iteratively until the devices at the current highest accuracy level are insufficient to generate at least one intersection point, or the errors of the devices at the current highest accuracy level are very close (the difference between devices is less than one-tenth), and there is no need to further refine the accuracy level iteratively. Then, terminate the iteration.

[0223] like Figure 3 As shown in the figure, the relative accuracy level of the measuring device changes during the iteration at a certain moment in this embodiment. It can be observed that at this moment, theodolites 4 to 10 have achieved tracking of the target. The final iteration result classifies theodolites 5 and 7 as accuracy level 4, theodolite 4 as accuracy level 3, theodolites 6 and 10 as accuracy level 2, and theodolites 8 and 9 as accuracy level 1. The accuracy level of other theodolites is 0, which means that the theodolite has not achieved tracking of the target aircraft at the current moment.

[0224] Recursively solve for the angle measurement error of a single device:

[0225] After completing the accuracy classification of each device at the current moment, the device with the highest accuracy level is used as the benchmark. The angle measurement error of the low-accuracy devices is corrected by using the intersection measurement error value generated during intersection. This process is repeated until the angle measurement error correction of all devices is completed.

[0226] like Figure 4 As shown, at a certain moment in this embodiment (and Figure 3The changes in measurement errors of the measuring devices (at the same time) during the iteration and recursion process show that, after iteration, the angle measurement errors of theodolites 7 and 5, which have the highest accuracy levels, were confirmed. Using these two devices as benchmarks, the measurement accuracy corrections for other devices were completed. Ordinary electric theodolites typically have an angle measurement accuracy of 10" (0.04848 mrad). Observing the statistical results of the device angle measurement errors after the recursion, it can be analyzed that theodolite 9 exhibits a slight out-of-tolerance phenomenon at the current time, while theodolite 8 has an incorrect tracking status or is tracking the wrong target.

[0227] Figure 5 The figure shows the angle measurement error calculation results of each photoelectric theodolite in the telemetry and control section during the entire flight of the aircraft. It can be observed that theodolites 2, 3, and 8 have large errors throughout the tracking process, which should be caused by inaccurate calibration or tracking of the wrong target. Theodolite 10 has an error exceeding the tolerance in some time periods. Through elevation angle analysis, it can be seen that the error is caused by overhead measurement.

[0228] Optimize and fuse the output positioning results:

[0229] The accuracy levels of each device are analyzed to determine the highest initial fusion accuracy level that satisfies at least three devices. This ensures that at least two intersection results are available for fusion. An error information vector set is searched, and intersection results where the accuracy levels of the devices corresponding to the two intersection sources are both at least equal to the highest initial fusion accuracy level are considered as candidate outputs. The candidate outputs are then weighted and fused using the reciprocal of the positioning error index as the weight, resulting in the final positioning output. Experiments have shown that this method guarantees high stability in the output value while maintaining accuracy.

[0230] In the embodiments used in this invention, the aircraft is equipped with a GPS positioning system. By comparing the measured GPS track with the rendezvous results, the accuracy of the output rendezvous results can be analyzed. Figure 6 As shown, the position difference between the rendezvous track generated using the method of this invention and the rendezvous track generated using the traditional method and the measured GPS track can be seen. It can be seen that the method described in this invention has higher accuracy than the traditional method and effectively eliminates the interference of error data sources on the overall rendezvous results.

[0231] 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 analyzing intersection errors and rapidly optimizing and fusing intersection results using a photoelectric theodolite, characterized in that: Includes the following steps: Step 1: Perform pairwise intersections on n photoelectric theodolites tracking the target at the same time to generate a total of For each intersection positioning point, an error information vector Evec is established. i , Evec i =(X i ,Elp i ,Elm i ,a i ,b i ,Eam a,i ,Eam b,i ,r a,i ,r b,i ) Where a i b i The photoelectric theodolite equipment number for forming the i-th intersection positioning point, X i For device a i With device b i Interactive localization results in the geocentric system; Elp i Elm i For intersection measurement error, Eam a,i With Eam b,i r represents the angle measurement error of the corresponding device. a,i With r b,i This represents the distance between the corresponding device and the target; The rendezvous positioning accuracy error Elp i Intersection measurement error Elm i Based on this, the positioning error index El is designed. i : Press El i Sort the error information vectors in Evec in ascending order to establish an error information vector set G. E : Step 2: Establish the equipment error statistical vector Eequip and the equipment error statistical vector set G for each device. Eequ : Eequip k =(Ea k ,Cjoin k ,Prio k ) G Eequ ={Eequip k / k∈[1,n]} Among them, Ea k The mean angle measurement error of device k is initialized to 0; Cjoin k Prio represents the total weighting coefficients of all intersections involving device k at this moment, initialized to 0. k The priority of device k is initialized to 1 if the device has measurement data at the current time, and to 0 if there is no measurement data at the current time. Establish a vector D of size n×1 for each priority device. PPEN =0 n×1 With PrioroNow=1 as the current priority, the following steps are followed to begin iteratively classifying the measurement accuracy of a single device: Step 2.1: Calculate the error of a single measuring device with the current priority. Press i from 1 to For the error information vector set G E Search, if Evec i Corresponding device a i Priority Prio a and equipment b i Priority Prio b The following conditions must be met: Then update device a i b i Error statistics vector Eequip a Eequip b The process is as follows: Yes a =Yes a,new Yes b =Yes b,new After the search is completed, count the number of devices with the current priority participating in the rendezvous, and denote this as N. EQ Update the device number vector D for each priority level. PPEN Record the number of devices currently participating in the rendezvous at the current priority level: D PPEN (PrioNow) = N EQ For the devices participating in the rendezvous at the current priority, the corresponding device error statistics vector Eequip is... k Ea k The reassignment process is as follows: If N EQ If the value is less than 3, it means that there are fewer than 3 devices intersecting at this moment, and the data accuracy cannot be determined. Therefore, the iteration loop is exited and the process proceeds to step 3; otherwise, the process proceeds to step 2.

2. Step 2.2: Determine whether the current highest accuracy level meets the accuracy requirements. Count all those that satisfy Prio k For devices ≥PrioNow, create a set Gp, where the mean angular error of all devices in the set is . The maximum angle error is Eam; the angle measurement accuracy of all devices is Pam. k Geometric superposition is performed as a precision criterion to determine whether the angular errors of all devices within the set are better than the precision criterion, and whether the precision of all devices within the set is at a relatively close level. If the above conditions are met, it is assumed that all devices with the current accuracy priority meet the accuracy requirements, and the iteration loop is exited, proceeding to step 3; otherwise, proceed to step 2.

3. Step 2.3: Identify devices with higher measurement accuracy and assign them higher priority. Higher priority is defined as PriorNext = PriorNow + 1, which filters devices within the current priority set Gp, and prioritizes those with angular measurement error Ea. k Superior Device k is given higher priority, among which The mean angle measurement error of all devices in the current set Gp; devices k that meet the criteria are given higher priority, and the error statistics vector Eequip is... k Device Priority Prio k Updated: Prio k =PrioNext; Step 2.4: Determine whether the priority can be further subdivided in the next iteration. The number of devices of each priority is recounted. If the number of devices of the current priority is 0, it means that the corner error of the devices currently in the next priority is too large. In this case, the priority of these devices is reduced to the current priority, and the iteration loop is exited, and the process proceeds to step 3. Search error information vector set G E If at least one intersection point is generated entirely by a intersection of devices with PriorityNext, then continue with the subsequent steps; otherwise, exit the iteration loop and go to step 3. Step 2.5: Reset the error statistics of the devices with elevated priority to zero. Establish a set G for devices with elevated priority. PNE Set the mean angle measurement error Ea of these devices to zero, and the total weighting coefficient Cjoin to zero; Increase the current priority by setting PrioNow = PrioNext, and jump to step 2.1 for iteration; Step 3: Recursively solve for the angle measurement error of a single device Record the highest priority PrioMax = PrioNow obtained after step 2. If PrioMax = 1, it means that step 2 did not complete the iterative classification of the measurement accuracy of a single device, and skip directly to step 4; otherwise, iteratively solve the angle measurement error of a single device through the following steps: Step 3.1: Recursively calculate the angle measurement error of the lower-level equipment. For the error information vector set G E Perform a search: i∈G E And for the equipment error statistical vector set G Eequ Perform a search: k∈G Eequ If both conditions are met: 1) The accuracy class of device k is PrioNow. 2) Device k participated in point X i The intersection 3) Participation point X i The accuracy class of the other device l at the intersection is less than that of PrioNow. Then for X i The error information vector Evec i The angle measurement error Eam of equipment k and equipment l k,i Eam l,i Make corrections It k,i =It k Eam l,i =(Elm i -Ea k ·r k,i ) / r l,i In the formula Ea k Elm is the mean angle measurement error of device k. i Let X be the point i The intersection measurement error, r k,i Let X be the point i The distance measurement value of the corresponding device k, r l,i Let X be the point i The distance measurement value of the corresponding device l; Each time a G is completed E and G Eequ If the search is incomplete, let PrioNow = PrioNow-1, repeat step 3.1 until PrioNow equals 1, then exit the iteration and proceed to step 3.2; Step 3.2: Update equipment error statistics Traversing the error information vector set G E For each device, calculate the weighted average of the angle measurement error and update the device error statistics vector Eequip. k Mean angle measurement error Ea k : In the formula Elm is the set of all error information vectors Evec from which device k participates in the intersection. i The error information vector Evec i The intersection measurement error in Eam k,i The error information vector Evec i The angle measurement error of the device k in the middle; Step 4: Optimize and fuse the localization results for output. Use the priority device number vector D obtained in step 2. PPEN The number N of photoelectric theodolites participating in the intersection is counted in order of priority from low to high. UE : In the formula, PrioMax is the highest priority obtained in step 2, Ps is the precision level of the initial statistics, and N is the highest priority obtained in step 2. UE Maximum Ps ≥ 3; sequentially search error information vector set G E Query each error information vector Evec i The equipment accuracy levels corresponding to the two intersection sources like If all values ​​are not less than Ps, then Evec will be... i The intersection and localization result X i As alternative output results; the final output result is obtained by weighting all alternative output results.

2. The method for analyzing intersection errors and rapidly optimizing and fusing intersection results using a photoelectric theodolite according to claim 1, characterized in that: In step 1, for device a i With device b i The following process is used to obtain: Device a i With device b i Interactive localization result X in the geocentric system i Rendezvous and positioning accuracy error Elp i Intersection measurement error Elm i The corresponding angle measurement error of the equipment, Eam a,i With Eam b,i The distance r between the corresponding device and the target a,i With r b,i ; Acquire device a i With device b i The measured values ​​are denoted as (A) a,i E a,i ) and (A b,i E b,i A is the azimuth angle being measured, and E is the elevation angle being measured. First, select an initial distance value r. a,i With r b,i The size is not less than the measurement baseline length ||S a -S b || That's it, where device a i With device b i The station coordinates are S a =(x a ,y a ,z a ) and S b =(x b ,y b ,z b ); According to the formula (x a,i ,y a,i ,z a,i ) T =r a,i M sg,a (things a,i What a,i ,sinE a,i ,things a,i sinA a,i ) T +V sg,a (x b,i ,y b,i ,z b,i ) T =r b,i M sg,b (things b,i What b,i ,sinE b,i ,things b,i sinA b,i ) T +V sg,b Computing device a i With device b i Initial positioning result X in the geocentric system a,i =(x a,i ,y a,i ,z a,i ) and X b,i =(x b,i ,y b,i ,z b,i M sg,a M sg,b V is the transformation matrix. sg,a V sg,b Transformation vector; According to the formula Computing device a i With device b i The angle between the optical path and the measurement baseline is measured, and the formula θ is used. i =π-θ a,i -θ b,i Calculate the theoretical optical intersection angle θ i ; Reuse formula Inversely calculate the distance r between the corresponding device and the target. a,i With r b,i The calculated r a,i With r b,i Substitution (x a,i ,y a,i ,z a,i ) T =r a,i M sg,a (things a,i What a,i ,sinE a,i ,things a,i sinA a,i ) T +V sg,a (x b,i ,y b,i ,z b,i ) T =r b,i M sg,b (things b,i What b,i ,sinE b,i ,things b,i sinA b,i ) T +V sg,b Resolve X a,i With X b,i X i =(X a,i +X b,i ) / 2 represents the current time of device a i With device b i Inter-location results in the geocentric system; intersection measurement error Elm i =||X a,i -X b,i ||;Angle measurement error Eam a,i and Eam b,i The initial value calculation results are as follows: Rendezvous positioning accuracy error Elp i for: in He' a,i =The a,i / sinθ i He' b,i =The b,i / sinθ i He' ab,i =min(El' a,i ,He' b,i ) He a,i =Pam a ·r a,i He b,i =Pam b ·r b,i Pam a Pam b For device a i With device b i Its own angular measurement accuracy.

3. The method for analyzing intersection errors and rapidly optimizing and fusing intersection results using a photoelectric theodolite according to claim 2, characterized in that: In step 1, if the theoretical optical intersection angle θ corresponding to a certain intersection positioning point... i If the value is less than π / 12 or greater than π·11 / 12, it is considered that the measurement data of the pair of devices corresponding to the intersection positioning point do not meet the intersection conditions and cannot generate accurate results.

4. The method for analyzing intersection errors and rapidly optimizing and fusing intersection results using a photoelectric theodolite according to claim 1, characterized in that: In step 4, the process of weighting and averaging all the alternative output results is as follows: The error information vector Evec for each device whose accuracy level corresponding to the two internal intersection sources is not less than Ps is defined. i Establish set G OT The set contains N vectors. OT The final output result is El is the positioning error index corresponding to the error information vector Evec.

Images