KR102218229B1 - Method and system for launch vehicle location determination - Google Patents

Abstract

The present invention relates to a method and system for positioning a launch vehicle. The method comprises the steps of: obtaining a TDOA-AOA-based launch vehicle location estimate by using a TDOA hyperbolic equation obtained by measuring the difference between times of arrival of radio waves at first and second ground stations with respect to a signal transmitted from a launch vehicle, a first AOA straight line equation corresponding to an angle of arrival of the radio waves from the launch vehicle to the first ground station, and a second AOA straight line equation corresponding to an angle of arrival of the radio waves from the launch vehicle to the second ground station; dividing the TDOA-AOA-based launch vehicle location estimate into a plurality of time slots having predetermined time intervals, and obtaining respective regression model result equations by calculating regression coefficients and standard deviations for the plurality of time slots; and obtaining a regression model result equation with the smallest estimation error by moving the regression model result equations respectively obtained for the plurality of time slots. Therefore, the method and the system can increase the estimation accuracy of TDOA-AOA.

Description

TECHNICAL FIELD [Method and system for launch vehicle location determination}

The present invention relates to a projectile positioning system and method.

In general, a location estimation algorithm for a signal source estimates location information by combining information such as a signal arrival time (TOA), a difference in arrival time (TDOA), and an angle of arrival (AOA). The TOA-AOA algorithm can estimate the location information by using only one ground station, but it cannot obtain location information unless the launch vehicle-mounted transmitter transmits the data transmission time. The AOA-AOA and TDOA-AOA algorithms acquire location information using two ground stations. In this case, even if there is no data transmission time information of the onboard transmitter, location information can be obtained only with information obtained from the ground station. Among the above algorithms, the estimation accuracy of TDOA-AOA is the closest to the GPS measurement information. However, when the tracking elevation of the ground station antenna is low, the variation width and bias of the estimation error of TDOA-AOA increase due to the influence of the multipath signal.

Accordingly, a technical problem to be solved by the present invention is to provide a method and system for positioning a projectile to improve the estimation accuracy of TDOA-AOA by minimizing the variation of the estimation error and removing the bias.

The projectile position positioning method according to the present invention for solving the above technical problem is a TDOA hyperbolic equation obtained by measuring the difference in radio wave arrival time between the first and second ground stations of the signal transmitted from the projectile, and the first Obtaining a TDOA-AOA based projectile position estimate using a first AOA linear equation corresponding to a radio wave arrival angle to a ground station and a second AOA linear equation corresponding to a radio wave arrival angle from the launch vehicle to the second ground station, the TDOA- Dividing the AOA-based projectile position estimate into a plurality of time slots having a predetermined time interval, calculating a regression coefficient and a standard deviation for the plurality of time slots to obtain a regression model result equation, and the plurality of time slots And obtaining a regression model result equation obtained by shifting each obtained regression model result equation so that the estimation error is the smallest.

The TDOA-AOA-based projectile position estimate value is obtained as the location of the projectile from the intersection of the second AOA straight line and the small angle between the two intersections of the TDOA hyperbolic surface and the first AOA straight line.

The regression model result equation moved so that the estimation error becomes the smallest may be obtained by moving the regression model result equation obtained for the plurality of time slots by a constant multiple of the standard deviation.

The resulting equation of the regression model moved so that the estimation error is the smallest may be a lower envelope of the TDOA-AOA-based projectile position estimation value.

The lower envelope may be a 2σ lower envelope of the TDOA-AOA based projectile position estimate.

Kalman filtering may be applied to the estimation result of the lower envelope.

The computer-readable recording medium according to the present invention for solving the above technical problem may record a program for executing the above-described method in a computer.

The projectile positioning system according to the present invention for solving the above technical problem includes a TDOA hyperbolic equation obtained by measuring a difference in radio wave arrival time between a first ground station and a second ground station of a signal transmitted from the projectile, and the first from the projectile. 1 TDOA-AOA position to obtain a TDOA-AOA-based projectile position estimate using the first AOA linear equation corresponding to the radio wave arrival angle to the ground station and the second AOA linear equation corresponding to the radio wave arrival angle from the launch vehicle to the second ground station The estimation unit and the TDOA-AOA-based projectile position estimate are divided into a plurality of time slots having a predetermined time interval, and a regression coefficient and a standard deviation are calculated for the plurality of time slots to obtain a regression model result equation, wherein the And a lower envelope detector for obtaining a regression model result equation obtained by shifting the regression model result equation obtained for each of the plurality of time slots so that the estimation error becomes the smallest.

According to the present invention, it is possible to provide a method and system for positioning a projectile to improve the estimation accuracy of TDOA-AOA by minimizing the variation of the estimation error and removing the bias.

1 is a view showing the configuration of a projectile positioning system according to an embodiment of the present invention.
2 is a diagram for explaining TDOA-AOA based projectile position estimation.
3 shows the results of regression analysis of the second-order polynomial for the observed data and the 3σ lower envelope.
FIG. 4 shows distance information of a target calculated by the TDOA-AOA technique and 1σ, 2σ, and 3σ lower envelopes of an 80-point quadratic polynomial regression analysis compared with GPS distance information.
FIG. 5 shows the comparison of the distance information of the TDOA-AOA technique, the 2σ lower envelope of the second order regression analysis, and the onboard GPS in the entire synchronization period.
6 shows the comparison of the estimated trajectory extracted by the 2σ lower envelope of the second-order regression analysis and the GPS trajectory in three dimensions.
7 and 8 compare the distance estimates of the 2σ lower envelope with the measured values of the onboard GPS when the TDOA-AOA technique is used independently and when the 10 and 20 point regression analysis is performed.
9 shows the comparison of the 2σ lower envelope distance estimation error of 10, 20, 40 and 80 point regression analysis.
FIG. 10 shows the estimation error of the 2σ lower envelope of the 10-point regression analysis and the distance estimation error when the Kalman filtering is applied when the TDOA-AOA technique is used alone.
11 shows the distance estimation error when Kalman filtering is applied to the estimation result of the 2σ lower envelope of 10, 20, 40, and 80 point regression analysis.
12 is a flowchart of a method of positioning a projectile according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those of ordinary skill in the art may easily implement the present invention.

1 is a view showing the configuration of a projectile position positioning system according to an embodiment of the present invention, Figure 2 is a view for explaining the TDOA-AOA based projectile position estimation.

1, the projectile position positioning system 100 according to an embodiment of the present invention includes a frame synchronization unit 105, a TDOA-AOA position estimation unit 110, a lower envelope detection unit 130, and a Kalman filter unit ( 150) may be included.

The frame synchronization unit 105 receives the frames transmitted from the first ground station 10 (Station 1) and the second ground station 20 (Station 0), synchronizes them, and delivers them to the TDOA-AOA position estimation unit 110. Functions. To this end, the first ground station 10 and the second ground station 20 receive signals from the projectile 30, which is a target signal source, and attach a time stamp to each of the received frames.

The TDOA-AOA position estimation unit 110 uses the radio wave arrival time (Rx time) and the radio wave arrival angle (AOA) provided from the first ground station 10 and the second ground station 20 to estimate the location of a projectile based on TDOA-AOA. Can be obtained.

Specifically, the TDOA-AOA position estimating unit 110 is a TDOA hyperbolic equation obtained by measuring the difference in arrival time of the radio waves between the first ground station 10 and the second ground station 20 of the signal transmitted from the projectile 30 as the target signal source. , Using the first AOA linear equation corresponding to the propagation arrival angle from the launch vehicle 30 to the first ground station 10 and the second AOA linear equation corresponding to the propagation arrival angle from the launch vehicle 30 to the second ground station 20 Thus, the TDOA-AOA-based projectile position estimate can be obtained.

The algorithm applied to the TDOA-AOA-based projectile position estimation will be described in detail.

Two ground stations are required to combine TDOA and AOA information. Thus, one hyperbolic equation and two straight line equations are created. The TDOA hyperbolic equation is shown in Equation 3 below, and the AOA linear equation is shown in Equation 4 below.

[Equation 1]

Distance from ground station to target signal source (projectile):

[Equation 2]

Distance difference between i and j ground stations:

[Equation 3]

TDOA hyperboloid equation using i and j ground stations:

[Equation 4]

j AOA linear equation from ground station (reference ground station):

Where i, j: ground station index

(x, y, z): coordinates of the target signal source

P _j (x _j , y _j , z _j ): j ground station coordinates

d _j : Distance between target signal source and j ground station

c: Propagation speed 299792458 (m/s).

In order to obtain the coordinates of the target signal source, the AOA straight line of Equation 4 is substituted into Equation 3 with a variable t as a parameter, and is summarized as Equation 5 below.

[Equation 5]

Where P _j (x _j , y _j , z _j ): j ground station coordinates,

i, j 지상국간 직선 벡터

i, j linear vector between ground stations

i, j 지상국간 직선 거리

i, j linear distance between ground stations

Equation 5 is summarized as an equation of the parameter t, and rearranged into a quadratic equation up to Equations 6 and 7 in order to obtain the value of the parameter t.

[Equation 6]

[Equation 7]

Eventually, the parameter t has two solutions based on the root formula as shown in Equation 8.

[Equation 8]

Therefore, as in Equation 9, the first cross point 1 and the second cross point 2 at the reference ground station 10 can be obtained.

[Equation 9]

Where k=1, 2: cross point index

Finally, among the two intersection points, the intersection point having a small angle may be estimated as the position of the target signal source by comparing the angle between the AOA unit vector of the counterpart ground station 20 and the angle as shown in Equation 10.

[Equation 10]

The TDOA-AOA position estimating unit 110 may estimate the position of the projectile based on the TDOA-AOA algorithm described above.

However, if the antenna elevation angle of either of the reference ground station 10 and the counter ground station 20 is less than 5 degrees, the estimation accuracy of the position estimation result of the TDOA-AOA algorithm is greatly degraded due to propagation delay due to multipath. In order to remove the variability in the position estimation accuracy due to the multipath delay, a quadratic polynomial regression model can be used for the estimation result of TDOA-AOA.

The lower envelope detection unit 130 divides the TDOA-AOA-based projectile position estimate into a plurality of time slots by applying a window having a predetermined time interval, and calculates a regression coefficient and a standard deviation for the plurality of time slots, respectively, resulting in a regression model. You can find the equation.

The lower envelope detection unit 130 may move the regression model result equation obtained for each of the plurality of time slots to a place where the estimation error is the smallest. That is, the regression model result equation obtained for a plurality of time slots is moved by a certain multiple of the standard deviation (y-axis movement) to obtain a regression model result equation with the smallest estimation error. This is the lower envelope of the TDOA-AOA estimate.

[Equation 11]

는 TDOA-AOA 추정에 의한 목표 신호원과 지상국간 거리 정보, β₀, β₁, β₂는 회귀 계수, t는 전파 도달 시간(Rx time)(Rx time stamp), ε은 오차, n은 관측치 개수임.here,

Is the distance information between the target signal source and the ground station by TDOA-AOA estimation, β ₀ , β ₁ , β ₂ is the regression coefficient, t is the radio wave arrival time (Rx time) (Rx time stamp), ε is the error, and n is the observed value. It is a number.

The regression model for the distance information between the target signal source and the ground station by TDOA-AOA estimation can be expressed as Equation 11. The error term ε is the same as Equation 12, and the regression coefficients β ₀ , β ₁ , and β ₂ can be estimated through the least squares method of Equations 13 to 15 so that the error term ε is minimized.

[Equation 12]

를 구한다.Estimation of the regression coefficient by the least-squares method is the estimated value by partially differentiating the sum of squares E of the error term for each β _j and solving the system of equations in Equation 13 which is 0

Find

[Equation 13]

[Equation 14]

If Equation 13 is developed as in Equation 14 and then expressed as a matrix operation, it is shown in Equation 15.

[Equation 15]

[Equation 16]

[Equation 17]

는 회귀모델

에 대한 추정 결과식,

는 회귀 계수 추정 결과, k는 표준편차에 대한 승수 인자, σ는 표준 편차,

는 TDOA-AOA 추정 거리정보의 하위 포락선이다.here

Is the regression model

The result of estimation for

Is the regression coefficient estimation result, k is the multiplier for the standard deviation, σ is the standard deviation,

Is the lower envelope of the TDOA-AOA estimated distance information.

3 shows the results of regression analysis of the second-order polynomial for the observed data and the 3σ lower envelope.

In statistics, if the data fits very closely to the normal distribution, about 68.23% of the data is within 1 times the standard deviation (1σ) of the mean, about 95.45% is within 2 times the standard deviation (2σ), and about 99.7% is the standard deviation. It is distributed within 3 times (3σ). By comparing the location information estimated through TDOA-AOA with the location information measured by the on-board GPS, the lower envelope with the minimum error and a multiplier for the standard deviation at this time can be obtained.

The performance evaluation test of the system according to the present invention illustrated in FIG. 1 was set and performed as follows.

end. Test setup

In order to extract TDOA information, the first ground station 10 was set as the reference ground station and the second ground station 20 was set as the counterpart ground station. Both ground stations 10 and 20 simultaneously received signals from the target signal source and attached a time stamp to each frame received by each ground station.

The input parameter of the TDOA-AOA algorithm is the equation of the received frame time stamp of each ground station and a straight line in the AOA direction. Table 1 is a description of the test conditions. In order to evaluate the performance of the proposed technique, the Naro telemetry data acquired in the third flight test of the Naro in January 2013 and the operation data of each ground station were used. The telemetry data received from the on-board GPS was used as a reference for calculating the error of the TDOA-AOA positioning technique as the location data of the target projectile.

[Table 1]

I. 1σ, 2σ and 3σ sub-envelope detection

FIG. 4 shows distance information of a target calculated by the TDOA-AOA technique and 1σ, 2σ, and 3σ lower envelopes of an 80-point quadratic polynomial regression analysis compared with GPS distance information. Among them, it can be seen that the 2σ lower envelope is the closest to the GPS distance information. Therefore, the 2σ lower envelope of the quadratic polynomial regression analysis can improve the estimation accuracy by reducing the error of the TDOA-AOA positioning technique. In statistics, the 2σ sub-envelope centered on the mean of the observations that are normally distributed corresponds to 97.7% lower of the observation.

For the test evaluation of the present invention, the received frames of the ground stations 0 and 1 were synchronized through frame ID comparison in the interval of 295 to 521 seconds, and TDOA information was extracted. 5 shows the comparison of the distance information of the TDOA-AOA technique, the 2σ lower envelope of the second-order regression analysis, and the onboard GPS in the entire synchronization period. Here, it was confirmed that the bias error of the TDOA-AOA technique was removed when the 2σ lower envelope of the second order regression analysis was applied. On the other hand, the 1σ and 3σ lower envelopes did not eliminate the bias error. In the end, it was confirmed that the 2σ lower envelope eliminates the error caused by the multi-path delay of the TDOA-AOA technique and can approximate GPS performance.

6 is a three-dimensional comparison of the estimated trajectory extracted from the 2σ lower envelope of the second-order regression analysis and the GPS trajectory.

In the synchronous section of the two ground stations, the tracking information (distance, antenna elevation) in the initial section was (576km, 24°) at ground station 0 and (1176km, 7.4°) at ground station 1. In the last section, the two ground stations were (1862km, 1°) and (410km, 45.6°) respectively. When the TDOA-AOA technique is used independently without applying the 2σ lower envelope of the 2nd regression analysis, the multipath delay due to the low antenna elevation at ground station 0 in the last synchronization section of the two ground stations increases, resulting in a sharp position estimation error. Increased. It was confirmed that the estimation error was eliminated when the present invention was applied.

All. 2σ lower envelope according to regression size

It has been shown that GPS performance can be approximated by applying the 2σ lower envelope of the quadratic regression analysis. Here, we analyze the difference in estimation accuracy according to the size of the regression section, that is, the number of observations in the same 2σ lower envelope. The estimated error was analyzed for the number of observations in regression analysis of 10, 20, 40, 80, and 160 points. In addition, an optimized value for the multiplier factor k for the standard deviation of Equation 17 was calculated.

7 and 8 compare the estimated range of the 2σ lower envelope with the measured values of the on-board GPS when the TDOA-AOA technique was independently used and when the 10 and 20 point regression analysis was performed. It was confirmed that the distance estimate in the 20-point regression analysis was closer to the GPS distance trajectory than the 10-point regression analysis. Therefore, as the size of the regression analysis section increases, it can be inferred that the distance estimation accuracy approaches GPS performance.

9 shows the comparison of the 2σ lower envelope distance estimation error of 10, 20, 40, and 80 point regression analysis, and Table 2 shows the average and standard deviation of the TDOA-AOA and 2σ lower envelope distance estimation error for each section.

[Table 2]

In Fig. 9 and Table 2, when the 20-point regression analysis was performed in the entire section, that is, the CT 295-521 second period, the estimation error was significantly reduced from 135m to 40m compared to the 10-point regression analysis. In the TDOA-AOA technique without sub-envelope detection, the average of the estimated error was about 2.9 km. Through this, it was verified that the accuracy of the TDOA-AOA technique can be significantly improved by applying the lower envelope detection technique proposed in the present invention. On the other hand, even if the regression analysis points were increased to 40 points and 80 points, the reduction in distance estimation error was not large.

Table 3 shows the distance error according to the regression section size and standard deviation multiplier. In 10-point regression analysis, when 2.1 was applied to the standard deviation multiplier k, the mean estimation error was -1.9m. In the 20 and 40 point regression analysis, when 2.03 was applied to k, the mean estimation errors were -2.5m and -2.7m, respectively. In 80 and 160 point regression analysis, it was confirmed that the optimal standard deviation multipliers k were 2.02 and 2.01, respectively.

[Table 3]

The Kalman filter unit 150 may apply Kalman filtering to the estimation result of the lower envelope derived from the lower envelope detection unit 130. 1 illustrates that the Kalman filter unit 150 performs Kalman filtering on the result output from the TDOA-AOA position estimator 110, but the result output from the TDOA-AOA position estimator 110 is a lower envelope In the embodiment used in the detection unit 130, it is unnecessary.

la. KALMAN filtering

FIG. 10 shows the estimation error of the 2σ lower envelope of the 10-point regression analysis and the distance estimation error when the Kalman filtering is applied to the above result, when the TDOA-AOA technique is used alone. If Kalman filtering is applied to the result of using the TDOA-AOA technique alone, it can be confirmed that there is an average distance estimation error of 1 to 3 km, that is, a bias error, in the CT 300 to 470 second interval. In the section after CT 470 seconds, it was confirmed that the antenna elevation angle at ground station 0 decreased to 5° or less, and the bias error rapidly increased due to the multipath delay. On the other hand, the estimation result of the 2σ lower envelope of the 10-point regression analysis eliminated the bias error generated above. Here, Kalman filtering is applied to greatly reduce the fluctuation range of the estimation error to obtain a smoothing effect.

11 shows distance estimation errors when Kalman filtering is applied to the estimation results of the 2σ lower envelope of 10, 20, 40, and 80 point regression analysis, respectively. This shows that even if the regression size increases, the effect of Kalman filtering is not large. Therefore, it is confirmed that the bias error can be removed through the detection of the 2σ lower envelope of the regression analysis, and the variation width of the distance estimation error can be smoothed through Kalman filtering. I did.

12 is a flowchart of a method of positioning a projectile according to an embodiment of the present invention.

12, the TDOA-AOA position estimation unit 110 uses radio wave arrival time (Rx time) and radio wave arrival angle (AOA) information provided from the first and second ground stations 10 and 20. A TDOA-AOA based projectile position estimate can be obtained (S1210).

Next, the lower envelope detection unit 130 divides the TDOA-AOA-based projectile position estimate into a plurality of time slots having a predetermined time interval in step S1210 (S1220), and calculates a regression coefficient and a standard deviation for the plurality of time slots. By calculating, each regression model result equation can be obtained (S1230).

Thereafter, the lower envelope detection unit 130 may obtain a regression model result equation obtained by moving the regression model result equation obtained for each of the plurality of time slots in step S1230 so that the estimation error is the smallest (S1240).

Finally, the Kalman filter unit 150 may apply Kalman filtering to the estimation result of the lower envelope corresponding to the regression model result equation obtained in step S1240 (S1250).

The embodiments described above may be implemented as a hardware component, a software component, and/or a combination of a hardware component and a software component. For example, the devices, methods, and components described in the embodiments include, for example, a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable gate (FPGA). array), programmable logic unit (PLU), microprocessor, or any other device capable of executing and responding to instructions, such as one or more general purpose computers or special purpose computers. The processing device may execute an operating system (OS) and one or more software applications executed on the operating system. In addition, the processing device may access, store, manipulate, process, and generate data in response to the execution of software. For the convenience of understanding, although it is sometimes described that one processing device is used, one of ordinary skill in the art, the processing device is a plurality of processing elements and/or a plurality of types of processing elements. It can be seen that it may include. For example, the processing device may include a plurality of processors or one processor and one controller. In addition, other processing configurations are possible, such as a parallel processor.

The software may include a computer program, code, instructions, or a combination of one or more of these, configuring the processing unit to behave as desired or processed independently or collectively. You can command the device. Software and/or data may be interpreted by a processing device or to provide instructions or data to a processing device, of any type of machine, component, physical device, virtual equipment, computer storage medium or device. , Or may be permanently or temporarily embodyed in a transmitted signal wave. The software may be distributed over networked computer systems and stored or executed in a distributed manner. Software and data may be stored on one or more computer-readable recording media.

The method according to the embodiment may be implemented in the form of program instructions that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, etc. alone or in combination. The program instructions recorded on the medium may be specially designed and configured for the embodiment, or may be known and usable to those skilled in computer software. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tapes, optical media such as CD-ROMs and DVDs, and magnetic media such as floptical disks. -A hardware device specially configured to store and execute program instructions such as magneto-optical media, and ROM, RAM, flash memory, and the like. Examples of the program instructions include not only machine language codes such as those produced by a compiler, but also high-level language codes that can be executed by a computer using an interpreter or the like. The hardware device described above may be configured to operate as one or more software modules to perform the operation of the embodiment, and vice versa.

As described above, although the embodiments have been described by the limited drawings, a person of ordinary skill in the art can apply various technical modifications and variations based on the above. For example, the described techniques are performed in a different order from the described method, and/or components such as a system, structure, device, circuit, etc. described are combined or combined in a form different from the described method, or other components Alternatively, even if substituted or substituted by an equivalent, an appropriate result can be achieved.

Claims (13)

delete TDOA hyperbolic equation obtained by measuring the difference in radio wave arrival time between the first and second ground stations of the signal transmitted from the launch vehicle, the first AOA linear equation corresponding to the radio wave arrival angle from the launch vehicle to the first ground station, and from the launch vehicle Obtaining a TDOA-AOA based projectile position estimate using a second AOA linear equation corresponding to an angle of arrival of a radio wave to the second ground station,
Dividing the TDOA-AOA-based projectile position estimate into a plurality of time slots having a predetermined time interval, calculating a regression coefficient and a standard deviation for the plurality of time slots to obtain a regression model result equation, and
Obtaining a regression model result equation obtained by moving the result equation of the regression model obtained for each of the plurality of time slots so that the estimation error is the smallest
Including,
The TDOA-AOA based projectile position estimate value,
A projectile position positioning method in which an intersection of the second AOA straight line and a small angle between the two intersections of the TDOA hyperbolic surface and the first AOA straight line is obtained as the position of the projectile. TDOA hyperbolic equation obtained by measuring the difference in radio wave arrival time between the first and second ground stations of the signal transmitted from the launch vehicle, the first AOA linear equation corresponding to the radio wave arrival angle from the launch vehicle to the first ground station, and from the launch vehicle Obtaining a TDOA-AOA based projectile position estimate using a second AOA linear equation corresponding to an angle of arrival of a radio wave to the second ground station,
Dividing the TDOA-AOA-based projectile position estimate into a plurality of time slots having a predetermined time interval, calculating a regression coefficient and a standard deviation for the plurality of time slots to obtain a regression model result equation, and
Obtaining a regression model result equation obtained by moving the result equation of the regression model obtained for each of the plurality of time slots so that the estimation error is the smallest
Including,
The result of the regression model shifted so that the estimation error is the smallest,
The projectile position positioning method obtained by moving the result equation of the regression model obtained for the plurality of time slots by a constant multiple of a standard deviation. In claim 3,
The result of the regression model shifted so that the estimation error is the smallest,
The method of positioning a projectile, which is a lower envelope of the TDOA-AOA-based projectile location estimate. In claim 4,
The lower envelope is a 2σ lower envelope of the projectile position estimate based on the TDOA-AOA. In claim 4 or 5,
Applying Kalman filtering to the estimation result of the lower envelope
Projectile position positioning method further comprising a. A computer-readable recording medium in which a program for executing any one of claims 2 to 5 is recorded on a computer. delete TDOA hyperbolic equation obtained by measuring the difference in radio wave arrival time between the first and second ground stations of the signal transmitted from the launch vehicle, the first AOA linear equation corresponding to the radio wave arrival angle from the launch vehicle to the first ground station, and from the launch vehicle A TDOA-AOA position estimation unit for obtaining a TDOA-AOA-based projectile position estimate using a second AOA linear equation corresponding to an angle of arrival of the radio wave to the second ground station, and
Dividing the TDOA-AOA-based projectile position estimate into a plurality of time slots having a predetermined time interval, calculating a regression coefficient and a standard deviation for the plurality of time slots to obtain a regression model result equation, respectively, and the plurality of time slots Lower envelope detection unit that obtains the regression model result equation obtained by shifting the regression model result equation obtained for each to have the smallest estimation error
Including,
The TDOA-AOA based projectile position estimate value,
A projectile position positioning system in which an intersection of the second AOA straight line and a small angle between two intersections of the TDOA hyperbolic surface and the first AOA straight line is obtained as the position of the projectile. TDOA hyperbolic equation obtained by measuring the difference in radio wave arrival time between the first and second ground stations of the signal transmitted from the launch vehicle, the first AOA linear equation corresponding to the radio wave arrival angle from the launch vehicle to the first ground station, and from the launch vehicle A TDOA-AOA position estimation unit for obtaining a TDOA-AOA-based projectile position estimate using a second AOA linear equation corresponding to an angle of arrival of the radio wave to the second ground station, and
Dividing the TDOA-AOA-based projectile position estimate into a plurality of time slots having a predetermined time interval, calculating a regression coefficient and a standard deviation for the plurality of time slots to obtain a regression model result equation, respectively, and the plurality of time slots Lower envelope detection unit that obtains the regression model result equation obtained by shifting the regression model result equation obtained for each to have the smallest estimation error
Including,
The result of the regression model shifted so that the estimation error is the smallest,
A projectile position positioning system obtained by moving a result equation of a regression model obtained for the plurality of time slots by a constant multiple of a standard deviation. In claim 10,
The result of the regression model shifted so that the estimation error is the smallest,
A projectile position positioning system that is a lower envelope of the TDOA-AOA-based projectile position estimate. In claim 11,
The lower envelope is a 2σ lower envelope of the TDOA-AOA-based projectile position estimate. In claim 11 or 12,
A projectile position positioning system further comprising a Kalman filter for applying Kalman filtering to the estimation result of the lower envelope.

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