WO2017077597A1 - Positioning device and positioning method - Google Patents

Positioning device and positioning method Download PDF

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Publication number
WO2017077597A1
WO2017077597A1 PCT/JP2015/081018 JP2015081018W WO2017077597A1 WO 2017077597 A1 WO2017077597 A1 WO 2017077597A1 JP 2015081018 W JP2015081018 W JP 2015081018W WO 2017077597 A1 WO2017077597 A1 WO 2017077597A1
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Prior art keywords
sensor
residual sum
residual
outlier
measured
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PCT/JP2015/081018
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French (fr)
Japanese (ja)
Inventor
網嶋　武
正資 大島
若山　俊夫
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三菱電機株式会社
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Priority to PCT/JP2015/081018 priority Critical patent/WO2017077597A1/en
Priority to JP2017547188A priority patent/JP6261836B2/en
Publication of WO2017077597A1 publication Critical patent/WO2017077597A1/en

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements

Definitions

  • the present invention excludes outliers from a plurality of measured values measured by a plurality of receiving sensors that receive signals from a transmitter, and measures the position of the transmitter using the measured values after the exclusion, and the positioning It is about the method.
  • a displacement measurement system that monitors a slope of a highway or a slope of a forest and detects a sign of a slope collapse (see, for example, Patent Document 1). .
  • a plurality of transmitters are arranged on a slope or the like, and a minute movement caused by a sign of a slope collapse is always measured three-dimensionally with milli-order accuracy.
  • radio waves from a transmitter are synchronously received by a plurality of receiving sensors installed around a slope, and a plurality of phases are measured as a plurality of measured values from the received signals. From these phases, the three-dimensional position of each transmitter is measured.
  • the measured phase accuracy may be significantly degraded due to multipath or the like. Such a phase whose accuracy has deteriorated significantly corresponds to an outlier, and if the positioning calculation of each transmitter is performed with the phases corresponding to the outlier being included in multiple phases, the positioning accuracy will deteriorate. Resulting in.
  • JP 2006-349515 A Japanese Patent No. 4397732 Japanese Patent No. 4129547 JP 2005-227167 A JP 2005-326184 A
  • the phase corresponding to the received signal with low power is specified as the outlier.
  • the phase error may not increase even when the power of the received signal is low. Even when the power of the received signal is high, the phase error may increase. That is, the correlation between the magnitude of the received signal power and the magnitude of the phase error is not necessarily high, and the conventional techniques described in Patent Documents 2 to 5 cannot accurately identify outliers. there is a possibility.
  • the present invention has been made to solve the above problems, and a positioning device capable of excluding outliers from a plurality of measured values without using power information of received signals received by a receiving sensor, and The purpose is to obtain a positioning method.
  • a positioning device is a positioning device that measures the position of a transmitter from a plurality of measurement values measured by a plurality of reception sensors that receive signals from the transmitter, and deviates from the plurality of measurement values.
  • An outlier exclusion processing unit that includes an outlier exclusion processing unit that excludes a value and a positioning calculation unit that measures the position of the transmitter from a plurality of measurement values after the outlier is excluded by the outlier exclusion processing unit.
  • the unit is a difference between a measured value measured by one receiving sensor constituting the sensor combination and a measured value measured by the other receiving sensor for each sensor combination that selects two different ones from a plurality of receiving sensors.
  • the measured value difference calculation unit that calculates the measured value difference and the measured value difference for each sensor combination calculated by the measured value difference calculation unit calculate the measured value difference residual for each sensor combination, and the calculated sensor combination
  • the residual sum calculation unit that calculates the residual sum for each receiving sensor from the measured value difference residual and the maximum residual sum of the residual sums for each receiving sensor calculated by the residual sum calculating unit.
  • Maximum residual sum selection unit to be selected threshold determination unit that determines whether or not the maximum residual sum selected by the maximum residual sum selection unit is greater than a threshold, and a threshold determination unit that determines that the maximum residual sum is greater than the threshold
  • an outlier exclusion unit that excludes outliers from a plurality of measured values, with the measured values corresponding to the excluded reception sensors being excluded as outliers. It is.
  • the positioning method includes an outlier exclusion processing step for excluding outliers from a plurality of measurement values measured by a plurality of reception sensors that receive signals from a transmitter, and an outlier exclusion processing step.
  • a positioning calculation step of measuring the position of the transmitter from a plurality of measured values after the outlier is excluded, and the outlier exclusion processing step is performed for each sensor combination that selects two different ones from the plurality of receiving sensors.
  • a residual sum calculation step for calculating a residual sum for each sensor, a maximum residual sum selection step for selecting a maximum residual sum among residual sums for each reception sensor calculated in the residual sum calculation step, A threshold determination step for determining whether or not the maximum residual sum selected in the maximum residual sum selection step is larger than a threshold, and a reception sensor that takes the maximum residual sum determined to be larger than the threshold in the threshold determination step And an outlier exclusion step of excluding outliers from a plurality of measurement values with the measured values corresponding to the excluded reception sensors as outliers.
  • the measured value measured by one receiving sensor constituting the sensor combination, and the other receiving sensor are excluded from the plurality of measurement values by using the measurement value difference that is the difference from the measurement value measured by the above.
  • FIG. 1 is a configuration diagram showing a positioning system including a positioning device 5 according to Embodiment 1 of the present invention.
  • the positioning system in FIG. 1 includes a plurality of transmitters 3 installed in a measurement area 2 such as a landslide area on a slope, a plurality of reception sensors 4 installed in a stationary area 1 on a slope, and a positioning device 5.
  • transmitter T 1 denoted ⁇ ⁇ ⁇ , T l, ⁇ ⁇ ⁇ , and T L (1 ⁇ L).
  • the receiving sensor R denoted ⁇ ⁇ ⁇ , R m, ⁇ ⁇ ⁇ , and R M (1 ⁇ M).
  • the transmitters 3 installed at a plurality of observation points in the measurement area 2 transmit radio waves having slightly different specific frequencies assigned to the respective transmitters 3.
  • Radio waves from each transmitter 3 are received by a plurality of reception sensors 4 installed in the stationary area 1 and guided to the positioning device 5 by an RF cable or the like.
  • a reception antenna may be used as the reception sensor 4.
  • the waveform of the transmission signal from the transmitter 3 is a sine wave.
  • the position coordinates are expressed as (X m , Y m , Z m ).
  • the positioning device 5 includes a plurality of receivers 6, a plurality of A / D converters 7, a plurality of discrete Fourier transform units 8, a plurality of phase calculation units 9, and a positioning processing unit 10.
  • the reception sensors 4 and the receivers 6 correspond one-to-one, and the numbers of the reception sensors 4, the receivers 6, the AD / converters 7, and the discrete Fourier transform units 8 are the same.
  • the receiver 6 converts the frequency of the reception signal from each reception sensor 4 and outputs the frequency-converted signal to the A / D converter 7.
  • the A / D converter 7 converts the signal input from the receiver 6 into a digital signal. This digital signal is converted into the frequency domain by the discrete Fourier transform unit 8. Since slightly different frequencies are assigned to the transmitters 3 at the respective observation points, the signals of the respective transmitters 3 can be discriminated by Fourier transformation. In this way, the reception signal of each reception sensor 4 is separated for each transmitter 3 by FFT processing.
  • the reception signal of each reception sensor 4 separated for each transmitter 3 is input to the phase calculation unit 9, and the phase calculation unit 9 calculates the observation phase.
  • the observation phase ⁇ l, m corresponding to the reception sensor R m that receives the radio wave transmitted from the transmitter T l is expressed by the following equation (1).
  • Equation (1) (x 1 , y 1 , z 1 ) represents the position coordinates of the transmitter T 1 , and (X m , Y m , Z m ) represents the position coordinates of the reception sensor R m.
  • ⁇ l indicates a transmission signal phase of the transmitter T l
  • ⁇ m indicates a cable delay in a path from the reception sensor R m to the A / D converter 7 or a reception system delay phase amount caused by the receiver 6 and the like.
  • N l, m is a phase integer bias.
  • the position coordinates of the reception sensor R m (X m, Y m , Z m) are known quantities, the position coordinates of the transmitters T l (x l, y l , z l) and the transmission signal phase transmitters T l ⁇ l and the reception system delay phase amount ⁇ m are unknown variables.
  • the transmission signal phase ⁇ l takes a random value every time. Therefore, the observation phase ⁇ l, m is also a random value every time.
  • the L ⁇ M observation phases include outliers whose accuracy is greatly deteriorated due to multipath or the like. If the positioning calculation is performed in a state where the observation phase corresponding to such an outlier is included, the positioning accuracy of each transmitter 3 is deteriorated.
  • phase difference is not random. Specifically, since the initial phase value of a random transmitter is canceled by taking the difference between the phases, the phase difference of signals from the same transmitter is not random. Therefore, it is possible to specify an outlier from the temporal transition of the phase difference.
  • the positioning processing unit 10 is used to specify outliers included in the L ⁇ M observation phases by using the above-described properties and perform the positioning calculation by excluding the outliers. Is configured.
  • FIG. 2 is a configuration diagram showing the configuration of the positioning processing unit 10 according to the first embodiment of the present invention.
  • the positioning processing unit 10 includes an outlier exclusion processing unit 11, a predicted value calculation unit 12, a memory track determination unit 13, and a positioning calculation unit 14.
  • the positioning processing unit 10 is realized by, for example, a CPU that executes a program stored in a memory and a processing circuit such as a system LSI.
  • the outlier exclusion processing unit 11 performs the outlier exclusion processing for each transmitter 3 on the L ⁇ M observation phases ⁇ 1,1 to ⁇ L, M input from the plurality of phase calculation units 9. in, excluding the outliers included in the observation phase ⁇ 1,1 ⁇ ⁇ L, M, and outputs the observation phase outliers are excluded.
  • FIG. 3 is a configuration diagram showing the configuration of the outlier exclusion processing unit 11 according to Embodiment 1 of the present invention.
  • the outlier exclusion processing unit 11 includes a measured value difference calculation unit 111, a residual sum calculation unit 112, a maximum residual sum selection unit 113, a threshold determination unit 114, and an outlier exclusion unit. 115, a process end determination unit 116, a transmitter number designation unit 117, and a storage unit 118.
  • FIG. 4 is an explanatory diagram illustrating a specific example in which an outlier exists in the observation phase input to the positioning processing unit 10 according to the first embodiment of the present invention.
  • the outlier exclusion process is performed for each transmitter 3, and thus the index l attached to the transmitter T is omitted.
  • the measurement value difference calculation unit 111 measures, for each sensor combination that selects two different ones from the plurality of reception sensors 4, the measurement value measured by one reception sensor 4 that constitutes the sensor combination, and the measurement by the other reception sensor 4. A measurement value difference that is a difference from the measured value is calculated.
  • the residual sum calculation unit 112 calculates a measured value difference residual that is a residual between the predicted value of the measured value difference and the measured value difference for each sensor combination. The predicted value of the measured value difference is calculated by a predicted value calculation unit 12 described later.
  • the measurement value difference calculation unit 111 calculates the phase difference as the measurement value difference according to the following equation (2) for each sensor combination.
  • the residual sum calculation unit 112 calculates a phase difference residual as a measurement value difference residual according to the following equation (3) for each sensor combination.
  • ⁇ m1 indicates an observation phase corresponding to the reception sensor R m1
  • ⁇ m2 indicates an observation phase corresponding to the reception sensor R m2
  • ⁇ m1 and m2 are phase differences that are differences between ⁇ m1 and ⁇ m2 Indicates.
  • ⁇ (bar) m1, m2 indicates a predicted value of ⁇ m1, m2
  • z m1, m2 indicates a phase difference residual between ⁇ (bar) m1, m2 and ⁇ m1, m2 . Note that the predicted value of the phase difference is calculated by the predicted value calculation unit 12 described later.
  • FIG. 5 is an explanatory diagram showing the concept of sensor combination in the first embodiment of the present invention.
  • the total number of sensor combinations is “6” as shown in the following formula (4).
  • Each sensor combination is (R 1 , R 2 ) as shown in FIG. , the (R 1, R 3), (R 1, R 4), (R 2, R 3), (R 2, R 4), (R 3, R 4).
  • phase differences ⁇ 1,2 , ⁇ 1,3 , ⁇ 1,4 , ⁇ 2,3 , ⁇ 2,4 , ⁇ 3,4 corresponding to the sensor combination are calculated and corresponding to the sensor combination
  • the phase difference residuals z 1,2 , z 1,3 , z 1,4 , z 2,3 , z 2,4 , z 3,4 are calculated.
  • the residual sum calculation unit 112 performs processing for adding the phase difference residual to each of the two receiving sensors 4 constituting the sensor combination corresponding to the phase difference residual, and calculates all the phase difference residuals calculated.
  • the residual sum calculation processing performed for is performed.
  • the residual sum calculation unit 112 calculates the residual sum for each reception sensor 4 by performing such residual sum calculation processing.
  • the residual sum calculation unit 112 calculates the residual sum for each reception sensor 4 according to the following equation (5).
  • the corresponding residual sum is averaged by dividing by the total number of added phase difference residuals.
  • Equation (5) z m represents the residual sum corresponding to the reception sensor R m , N m represents the total number of phase difference residuals added in the reception sensor R m , and C comb is All sensor combinations are shown.
  • FIG. 6 is an explanatory diagram showing the concept of the residual sum calculation process according to Embodiment 1 of the present invention.
  • the phase difference residual z 1,2 when the phase difference residual z 1,2 is focused as shown in FIG. 6, the two receptions constituting the sensor combination corresponding to the phase difference residual z 1,2 are shown.
  • the phase difference residual z 1,2 is added to each of the sensors R 1 and R 2 .
  • the phase difference residuals z 2 single receiver of the sensor combination corresponding to 1,4 sensor R 1, the phase difference residuals z to each of the R 4 1 and 4 are added.
  • the residual sum calculation process according to the equation (5) is performed, so that the residual sums z 1 , z 2 , z 3 , corresponding to the reception sensors R 1 , R 2 , R 3 , R 4 , z 4 is calculated.
  • threshold determination is performed according to the following equation (6), and the observation phase corresponding to the reception sensor 4 whose residual sum is larger than the threshold ⁇ is set as an outlier. Think about the case. In this case, it is difficult to set the threshold value ⁇ .
  • FIG. 7 is an explanatory diagram showing the concept of the threshold determination processing method according to Embodiment 1 of the present invention.
  • the observation phase corresponding to the reception sensor R 3 is an outlier.
  • the reception sensor R 1 , R 2 , R 4 whose observation phase is not an outlier, and the large phase difference residual due to the observation phase corresponding to the reception sensor R 3 being an outlier.
  • z 1,3 , z 2,3 and z 3,4 are respectively added.
  • the reception sensor R 1 which may regarded as R 2, outlier observations phase corresponding to R 4.
  • the residual sums corresponding to the receiving sensors R 1 , R 2 and R 4 other than the receiving sensor R 3 are larger than the threshold value ⁇ .
  • the threshold ⁇ may be made larger.
  • such a situation becomes more remarkable as the number of outliers increases.
  • a residual sum corresponding to each reception sensor 4 is calculated, and the maximum residual sum is obtained among the residual sums larger than the threshold value ⁇ among the calculated residual sums.
  • the process of excluding the reception sensor 4 and recalculating the residual sum corresponding to each reception sensor 4 after the exclusion is repeated until there is no residual sum larger than the threshold ⁇ .
  • the maximum residual sum selection unit 113 selects the maximum residual sum among the residual sums corresponding to the respective reception sensors 4 calculated by the residual sum calculation unit 112 as the maximum residual sum.
  • the threshold determination unit 114 determines whether or not the maximum residual sum selected by the maximum residual sum selection unit 113 satisfies Expression (6).
  • the outlier exclusion unit 115 excludes the reception sensor 4 having the maximum residual sum that is determined by the threshold determination unit 114 not to satisfy Expression (6), that is, greater than the threshold ⁇ . Further, the outlier exclusion unit 115 excludes outliers from the observation phase by using the observation phase corresponding to the excluded reception sensor 4 as an outlier.
  • the residual sum calculation unit 112 calculates again the residual sum corresponding to each of the remaining reception sensors 4 other than the reception sensor 4 excluded by the outlier exclusion unit 115.
  • the residual sum calculation unit 112 calculates the residual sum for each reception sensor 4 from the measured value difference residual for each sensor combination.
  • the maximum residual sum selection unit 113 selects the maximum residual sum among the residual sums for each reception sensor 4 calculated by the residual sum calculation unit 112.
  • the threshold determination unit 114 determines whether the maximum residual sum selected by the maximum residual sum selection unit 113 is greater than the threshold ⁇ .
  • the outlier exclusion unit 115 excludes the reception sensor 4 having the maximum residual sum determined to be larger than the threshold value ⁇ by the threshold determination unit 114, and sets the measurement value corresponding to the excluded reception sensor 4 as an outlier. As above, outliers are excluded from a plurality of measured values.
  • the threshold determination unit 114 performs a process consisting of an operation by the residual sum calculation unit 112, an operation by the maximum residual sum selection unit 113, an operation by the threshold determination unit 114, and an operation by the outlier exclusion unit 115 by the threshold determination unit 114. It is configured to be repeatedly executed until it is determined that the residual sum is less than the threshold value.
  • FIG. 8 is an explanatory diagram showing the concept of the reception sensor exclusion processing method according to Embodiment 1 of the present invention.
  • the maximum residual sum selection unit 113 sets the residual sum corresponding to the reception sensor R 3 among the residual sums corresponding to each reception sensor 4 as the maximum residual sum.
  • the threshold determination unit 114 determines that the maximum residual sum selected by the maximum residual sum selection unit 113 is larger than the threshold ⁇ . To do.
  • the outlier exclusion unit 115 excludes the reception sensor R 3 as the reception sensor 4 that takes the maximum residual sum determined to be larger than the threshold ⁇ by the threshold determination unit 114.
  • the residual sum calculation unit 112 calculates again the residual sum corresponding to the remaining reception sensors R 1 , R 2 , R 4 other than the reception sensor R 3 excluded by the outlier exclusion unit 115. That is, the residual sum calculation unit 112 performs the residual sum calculation process based on the remaining sensor combinations excluding the sensor combination including the reception sensor R 3, and thereby the remaining reception sensors R 1 , R 2 , R again calculates the residual sum corresponding to 4. Since the residual sums corresponding to the remaining reception sensors R 1 , R 2 , and R 4 obtained by calculating in this way are below the threshold value ⁇ , the processing is terminated.
  • the outlier exclusion processing unit 11 performs the above outlier exclusion processing on the transmitter 3 for the L ⁇ M observation phases ⁇ 1,1 to ⁇ L, M input from the plurality of phase calculation units 9. that is performed to identify outlier included in the observation phase ⁇ 1,1 ⁇ ⁇ L, M, exclude outliers identified from the observed phase ⁇ 1,1 ⁇ ⁇ L, M. Further, the outlier exclusion processing unit 11 outputs the observation phase from which the outlier has been excluded.
  • the residual sum calculation unit 112 adds a corresponding measurement value difference residual for each reception sensor 4 from the calculated measurement value difference residual for each sensor combination.
  • the case of being configured to calculate the residual sum is illustrated. That is, as can be seen from the equations (3) and (5), each reception sensor 4 is simply used by using the average of the absolute values of the difference between the predicted value and the actual measurement value without using the residual quadratic form. The case where it comprises so that the residual sum corresponding to may be calculated is illustrated.
  • the quadratic residual form may be used.
  • an outlier exclusion process is performed using the following formulas (7) to (9) instead of the formulas (3), (5), and (6).
  • ⁇ is a threshold parameter called a gate size parameter.
  • the residual sum calculation unit 112 adds the square value of the corresponding measurement value difference residual for each reception sensor 4 from the calculated measurement value difference residual for each sensor combination. It may be configured to calculate a difference sum.
  • the predicted value calculation unit 12 calculates a predicted value of the phase difference by performing a tracking process using the phase difference input from the outlier removal unit 11.
  • a tracking filter can be used.
  • the following formulas (10) and (11) are followed.
  • an ⁇ - ⁇ filter, a Kalman filter, or the like may be used instead of the ⁇ filter.
  • FIG. 9 is a configuration diagram illustrating another example of the configuration of the positioning processing unit 10 according to the first embodiment of the present invention.
  • the predicted value calculation unit 12 may be configured so that the positioning processing unit 10 calculates the predicted value of the phase difference from the positioning result instead of the tracking process.
  • the predicted value calculation unit 12 calculates the predicted value of the phase difference according to the following formulas (12) and (13).
  • the index l attached to the transmitter T is omitted and the integer value bias is correctly solved.
  • the simultaneous equations for measuring the position of each transmitter 3 if the outlier is excluded from the observation phase, the total number of observation phases is reduced, so the number of equations in the simultaneous equations is also reduced. In this case, the accuracy of the simultaneous equations may be degraded.
  • DOP Degree of Precision
  • the position of each transmitter 3 is determined according to the evaluation result. Is configured to measure.
  • the memory track determination unit 13 calculates the DOP when solving the simultaneous equations that are set up using the observation phase after the outliers are excluded, and compares the DOP with DOP all , so that the DOP is sufficiently Judge whether it is small.
  • DOP all is a DOP for solving simultaneous equations that are set up using the observation phase before outliers are excluded.
  • the memory track determination unit 13 solves the simultaneous equations established using the observation phase after the outlier is excluded, and if the DOP is larger than ⁇ DOP all : It is determined that the DOP is not sufficiently small.
  • the setting parameter ⁇ satisfies ⁇ ⁇ 1.
  • the memory track determination unit 13 performs memory track processing, outputs the processing result as a positioning result, and the positioning calculation unit 14 does not operate.
  • the memory track determination unit 13 determines that the DOP is sufficiently small if the DOP in solving the simultaneous equations established using the observation phase after the outlier is excluded is less than ⁇ DOP all .
  • the positioning calculation unit 14 measures the position of each transmitter 3 by solving simultaneous equations established using the observation phase after outliers are excluded, and outputs the positioning result.
  • FIG. 10 is a flowchart showing a series of operations of the positioning processing unit 10 according to the first embodiment of the present invention.
  • step S101 the outlier removal processing unit 11 receives the observation phase at time k, and the process proceeds to step S102.
  • step S102 the predicted value calculation unit 12 calculates a predicted value of the phase difference at time k by performing a tracking process using the phase difference at time k-1 input from the outlier removal processing unit 11. The process proceeds to step S103.
  • step S103 the outlier exclusion processing unit 11 performs an outlier exclusion process, and the process proceeds to step S104.
  • FIG. 11 is a flowchart showing a series of operations of the outlier exclusion processing unit 11 according to Embodiment 1 of the present invention.
  • step S201 the observation phase at time k is input to the measurement value difference calculation unit 111, and the process proceeds to step S202.
  • the storage unit 118 also stores the input observation phase at time k.
  • step S203 the measured value difference calculation unit 111 calculates the phase difference at time k for each sensor combination with respect to the transmitter Tj . Furthermore, the residual sum calculation unit 112 calculates the phase difference residual at time k for each sensor combination from the phase difference at time k and the predicted value of the phase difference at time k calculated in step S102. The process proceeds to step S204.
  • step S204 the residual sum calculation unit 112 calculates the residual sum for each reception sensor 4 using the phase difference residual at time k calculated for each sensor combination in step S203, and the process proceeds to step S205. Proceed with
  • step S205 the maximum residual sum selection unit 113 selects the maximum residual sum from the residual sums calculated for each reception sensor 4 in step S204, and the process proceeds to step S206.
  • step S206 the threshold determination unit 114 determines whether or not the maximum residual sum selected in step S205 is larger than the threshold ⁇ . If it is determined that the maximum residual sum is larger than the threshold ⁇ (that is, Yes), the process proceeds to step S207. On the other hand, if it is determined that the maximum residual sum is less than the threshold value ⁇ (ie, No), the process proceeds to step S208.
  • step S207 the outlier exclusion unit 115 excludes the reception sensor 4 that takes the maximum residual sum selected in step S205, the process returns to step S204, and the processes after step S204 are performed again.
  • the storage unit 118 stores the observation phase after the outlier is excluded by the outlier exclusion unit 115.
  • step S204 the processing from step S204 to step S207 is repeated until the maximum residual sum becomes less than the threshold value ⁇ .
  • step S208 the process end determination unit 116 determines whether or not the processes have been completed for all the transmitters 3. If it is determined that the process is finished (that is, Yes), the series of processes is finished. On the other hand, if it is determined that the process is not finished (that is, No), the process proceeds to step S209.
  • step S203 to step S209 is repeated until the outlier exclusion processing is performed for all the transmitters 3.
  • step S104 the memory track determination unit 13 calculates DOP for the simultaneous equations that are established using the observation phase after excluding the outlier specified in step S103, and the processing is performed in step S104. Proceed to S105.
  • step S105 the memory track determination unit 13 determines whether or not the DOP calculated in step S104 is sufficiently small. If it is determined that the DOP is sufficiently small (that is, Yes), the process proceeds to step S106. On the other hand, if it is determined that the DOP is not sufficiently small (that is, No), the process proceeds to step S107.
  • step S106 the positioning calculation unit 14 measures the position of each transmitter 3 by solving simultaneous equations established using the observation phase after excluding the outlier specified in step S103, and calculates the positioning.
  • the positioning result obtained by is output, and the process proceeds to step S108.
  • step S107 the memory track determination unit 13 performs memory track processing, outputs the processing result as a positioning result, and the process proceeds to step S108.
  • step S108 the positioning processing unit 10 displays the positioning result obtained in step S106 or step S107 via, for example, a display device, and the process proceeds to step S109.
  • step S109 the positioning processing unit 10 determines whether or not to end the process. If it is determined that the process is to be terminated (that is, Yes), the series of processes is terminated. On the other hand, if it is determined not to end the process, the process proceeds to step S110.
  • step S101 to step S110 is repeated until the time k reaches the set value and the processing is terminated.
  • FIG. 12 is a coordinate diagram showing the position coordinates of each transmitter 3 and each receiving sensor 4 when performing computer simulation in the first embodiment of the present invention.
  • transmitters T 1 to T 6 and reception sensors R 1 to R 8 are used, and transmitter T 1 is a calibration transmitter.
  • the standard deviation of the observation phase error is 3 / ⁇ 2 deg, and the standard deviation of the phase difference error is 3 deg.
  • an observation phase [Phi 3,3 corresponding to the received sensor R 3 for receiving radio waves from a transmitter T 3, from a transmitter T 3 It is assumed that the observation phase ⁇ 3,5 corresponding to the reception sensor R 5 that receives the radio wave is an outlier.
  • 13 to 15 are graphs showing the residual sum corresponding to each reception sensor 4 calculated by the outlier removal processing unit 11 in the state shown in FIG.
  • step S207 sequentially receiving sensor R 5 is excluded for a maximum residual sum greater than a threshold zeta. That is, the outlier exclusion processing unit 11 specifies that the observation phases ⁇ 3,5 are outliers. Thereafter, when step S204 is executed, residual sums corresponding to the remaining reception sensors R 1 to R 4 and R 6 to R 8 other than the excluded reception sensor R 5 are calculated as shown in FIG. . Further, as can be seen from FIG. 14, the reception sensor R 3 takes the maximum residual sum, and the maximum residual sum is larger than the threshold value ⁇ .
  • step S207 sequentially receiving sensor R 3 is excluded to take maximum residual sum greater than a threshold zeta. That is, the outlier exclusion processing unit 11 specifies that the observation phases ⁇ 3,3 are outliers. Thereafter, when step S204 is executed, residual sums corresponding to the remaining reception sensors R 1 , R 2 , R 4 , R 6 to R 8 other than the excluded reception sensor R 3 are obtained as shown in FIG. Calculated. Further, as can be seen from FIG. 15, the reception sensor R 2 takes the maximum residual sum, and the maximum residual sum is less than the threshold value ⁇ .
  • step S205, step S206, step S208 and step S209 are sequentially executed, the transmitter T 4, the processes in and after step S203 are executed.
  • the outlier exclusion processing unit 11 executes the outlier exclusion processing to accurately specify that the observation phase ⁇ 3,3 and the observation phase ⁇ 3,5 are outliers. You can see that you can.
  • FIG. 16 and 17 are graphs showing the positioning results of a specific transmitter T 3 calculated by the positioning processing unit 10 in the state shown in FIG.
  • FIG. 18 is a graph after the moving average processing of the graph of FIG.
  • FIG. 19 is a graph after the moving average processing of the graph of FIG.
  • FIGS. 20 to 23 show the positioning results of the transmitter T 3 obtained when the outlier exclusion process is not performed.
  • FIG. 20 is a graph showing a comparative example of the graph of FIG.
  • FIG. 21 is a graph showing a comparative example of the graph of FIG.
  • FIG. 22 is a graph after the moving average processing of the graph of FIG.
  • FIG. 23 is a graph after the moving average processing of the graph of FIG.
  • the measured value measured by one receiving sensor constituting the sensor combination is configured to be excluded from the plurality of measurement values by using a measurement value difference that is a difference from the measurement value measured by the other receiving sensor.
  • the case where the measurement value is the observation phase is illustrated.
  • it is configured to monitor the temporal transition of the phase difference between different receivers by using the difference in observation phase between the receivers, that is, the phase difference and changing the combination of the receivers. It is possible to specify an observation phase that is significantly different from the observation phase, that is, an outlier.
  • Embodiment 2 the case where the measurement value measured by the reception sensor 4 is the observation phase is exemplified. However, even if the measurement value measured by the reception sensor 4 is a time measurement value, the present invention is applied. Is applicable. In this case, the time measurement value TOA is given by the following equation (15).
  • c represents the speed of light
  • ⁇ l and ⁇ m represent some time delay that occurs in the receiver corresponding to the transmitter T l and the receiving sensor R m , respectively.
  • the outlier exclusion processing unit 11 performs the outlier exclusion processing similar to that of the first embodiment on the time measurement value TOA instead of the observation phase.
  • Embodiment 3 In the first embodiment, the case where the measurement value measured by the reception sensor 4 is the observation phase is exemplified. However, even if the measurement value measured by the reception sensor 4 is a Doppler measurement value, the present invention is applied. Is applicable. In this case, the Doppler measurement value FOA is given by the following equation (16).
  • the outlier exclusion processing unit 11 performs the outlier exclusion processing similar to that of the first embodiment on the Doppler measurement value FOA instead of the observation phase.
  • the present invention is applicable not only to slope monitoring but also to monitoring of all structures such as bridges, dams, and tunnels.
  • a positioning system such as GPS uses a phase, and the present invention can be applied to such a positioning system.
  • the present invention can be applied to a wide range of fields.

Abstract

In the present invention, measurement value differences that are the differences, for each combination of two different sensors selected from among a plurality of reception sensors for receiving a signal from a transmitter, between a measurement value measured by one of the reception sensors in the sensor combination and the measurement value measured by the other reception sensor are used to exclude outliers from among the plurality of measurement values measured by the plurality of reception sensors, and the position of the transmitter is measured from the plurality of measurement values having the outliers excluded.

Description

測位装置および測位方法Positioning device and positioning method
　本発明は、発信機からの信号を受信する複数の受信センサによって計測される複数の計測値から外れ値を除外し、除外後の計測値を用いて発信機の位置を計測する測位装置および測位方法に関するものである。 The present invention excludes outliers from a plurality of measured values measured by a plurality of receiving sensors that receive signals from a transmitter, and measures the position of the transmitter using the measured values after the exclusion, and the positioning It is about the method.
　計測値として位相を用いた測位方式の例として、高速道路脇の斜面または山林の斜面をモニタリングし、斜面の崩落の予兆を検知する変位計測システムが知られている（例えば、特許文献１参照）。特許文献１に記載の従来技術では、斜面等に複数の発信機を配置し、斜面の崩落の前兆で生じる微小な動きをミリオーダーの精度で常時３次元計測するように構成されている。 As an example of a positioning method using a phase as a measurement value, a displacement measurement system is known that monitors a slope of a highway or a slope of a forest and detects a sign of a slope collapse (see, for example, Patent Document 1). . In the prior art described in Patent Document 1, a plurality of transmitters are arranged on a slope or the like, and a minute movement caused by a sign of a slope collapse is always measured three-dimensionally with milli-order accuracy.
　特許文献１に記載の従来技術では、発信機からの電波を、斜面周辺に設置された複数の受信センサで同期受信し、その受信信号から複数の計測値として複数の位相を計測し、その複数の位相から、各発信機の３次元位置を計測する。しかしながら、マルチパス等によって、計測された位相精度が大幅に劣化する場合がある。このような精度が大幅に劣化した位相は外れ値に該当し、外れ値に該当する位相が複数の位相に含まれた状態で、各発信機の測位計算が行われると、その測位精度が劣化してしまう。 In the prior art described in Patent Document 1, radio waves from a transmitter are synchronously received by a plurality of receiving sensors installed around a slope, and a plurality of phases are measured as a plurality of measured values from the received signals. From these phases, the three-dimensional position of each transmitter is measured. However, the measured phase accuracy may be significantly degraded due to multipath or the like. Such a phase whose accuracy has deteriorated significantly corresponds to an outlier, and if the positioning calculation of each transmitter is performed with the phases corresponding to the outlier being included in multiple phases, the positioning accuracy will deteriorate. Resulting in.
　そこで、上記の問題を解決するために、複数の位相の中から、このような外れ値を除外する手法が提案されている（例えば、特許文献２～５参照）。特許文献２～５に記載の従来技術では、共通事項として、受信センサで受信した受信信号の電力情報を用いて、外れ値を特定している。例えば、電力の低い受信信号は、マルチパスの影響を受けているものとし、その受信信号から計測された位相は、計測精度が低いとみなし、その位相を外れ値と特定して複数の位相の中から除外している。 Therefore, in order to solve the above problem, a method of excluding such outliers from a plurality of phases has been proposed (see, for example, Patent Documents 2 to 5). In the prior arts described in Patent Documents 2 to 5, as a common matter, outliers are specified using power information of received signals received by a receiving sensor. For example, a received signal with low power is assumed to be affected by multipath, and the phase measured from the received signal is considered to be low in measurement accuracy. Excluded from the inside.
特開２００６－３４９５１５号公報JP 2006-349515 A 特許第４３９７７３２号公報Japanese Patent No. 4397732 特許第４１２９５４７号公報Japanese Patent No. 4129547 特開２００５－２２７１６７号公報JP 2005-227167 A 特開２００５－３２６１８４号公報JP 2005-326184 A
　特許文献２～５に記載の従来技術では、上述したとおり、電力の低い受信信号に対応した位相を外れ値として特定している。しかしながら、電波環境によっては、受信信号の電力が低い場合であっても、位相誤差が増大しないことがある。また、受信信号の電力が高い場合であっても、位相誤差が増大することがある。つまり、受信信号の電力の大きさと、位相誤差の大きさとの間で、必ずしも相関が高いとはいえず、特許文献２～５に記載の従来技術では、外れ値を精度良く特定することができない可能性がある。 In the conventional techniques described in Patent Documents 2 to 5, as described above, the phase corresponding to the received signal with low power is specified as the outlier. However, depending on the radio wave environment, the phase error may not increase even when the power of the received signal is low. Even when the power of the received signal is high, the phase error may increase. That is, the correlation between the magnitude of the received signal power and the magnitude of the phase error is not necessarily high, and the conventional techniques described in Patent Documents 2 to 5 cannot accurately identify outliers. there is a possibility.
　本発明は、上記のような課題を解決するためになされたものであり、受信センサで受信した受信信号の電力情報を用いなくても、複数の計測値から外れ値を除外可能な測位装置および測位方法を得ることを目的とする。 The present invention has been made to solve the above problems, and a positioning device capable of excluding outliers from a plurality of measured values without using power information of received signals received by a receiving sensor, and The purpose is to obtain a positioning method.
　本発明における測位装置は、発信機からの信号を受信する複数の受信センサによって計測される複数の計測値から、発信機の位置を計測する測位装置であって、複数の計測値の中から外れ値を除外する外れ値除外処理部と、外れ値除外処理部によって外れ値が除外された後の複数の計測値から、発信機の位置を計測する測位計算部と、を備え、外れ値除外処理部は、複数の受信センサから異なる２個を選ぶセンサ組合せごとに、センサ組合せを構成する一方の受信センサによって計測された計測値と、他方の受信センサによって計測された計測値との差である計測値差を計算する計測値差計算部と、計測値差計算部によって計算されたセンサ組合せごとの計測値差から、センサ組合せごとに計測値差残差を計算し、計算されたセンサ組合せごとの計測値差残差から、受信センサごとに残差和を計算する残差和計算部と、残差和計算部によって計算された受信センサごとの残差和のうちの最大残差和を選択する最大残差和選択部と、最大残差和選択部によって選択された最大残差和が閾値よりも大きいか否かを判定する閾値判定部と、閾値判定部によって閾値よりも大きいと判定された最大残差和をとる受信センサを除外し、除外された受信センサに対応する計測値を外れ値として、複数の計測値の中から外れ値を除外する外れ値除外部と、を有するものである。 A positioning device according to the present invention is a positioning device that measures the position of a transmitter from a plurality of measurement values measured by a plurality of reception sensors that receive signals from the transmitter, and deviates from the plurality of measurement values. An outlier exclusion processing unit that includes an outlier exclusion processing unit that excludes a value and a positioning calculation unit that measures the position of the transmitter from a plurality of measurement values after the outlier is excluded by the outlier exclusion processing unit. The unit is a difference between a measured value measured by one receiving sensor constituting the sensor combination and a measured value measured by the other receiving sensor for each sensor combination that selects two different ones from a plurality of receiving sensors. The measured value difference calculation unit that calculates the measured value difference and the measured value difference for each sensor combination calculated by the measured value difference calculation unit calculate the measured value difference residual for each sensor combination, and the calculated sensor combination The residual sum calculation unit that calculates the residual sum for each receiving sensor from the measured value difference residual and the maximum residual sum of the residual sums for each receiving sensor calculated by the residual sum calculating unit. Maximum residual sum selection unit to be selected, threshold determination unit that determines whether or not the maximum residual sum selected by the maximum residual sum selection unit is greater than a threshold, and a threshold determination unit that determines that the maximum residual sum is greater than the threshold And an outlier exclusion unit that excludes outliers from a plurality of measured values, with the measured values corresponding to the excluded reception sensors being excluded as outliers. It is.
　また、本発明における測位方法は、発信機からの信号を受信する複数の受信センサによって計測される複数の計測値の中から外れ値を除外する外れ値除外処理ステップと、外れ値除外処理ステップで外れ値が除外された後の複数の計測値から、発信機の位置を計測する測位計算ステップと、を備え、外れ値除外処理ステップは、複数の受信センサから異なる２個を選ぶセンサ組合せごとに、センサ組合せを構成する一方の受信センサによって計測された計測値と、他方の受信センサによって計測された計測値との差である計測値差を計算する計測値差計算ステップと、計測値差計算ステップで計算されたセンサ組合せごとの計測値差から、センサ組合せごとに計測値差残差を計算し、計算されたセンサ組合せごとの計測値差残差から、受信センサごとに残差和を計算する残差和計算ステップと、残差和計算ステップで計算された受信センサごとの残差和のうちの最大残差和を選択する最大残差和選択ステップと、最大残差和選択ステップで選択された最大残差和が閾値よりも大きいか否かを判定する閾値判定ステップと、閾値判定ステップで閾値よりも大きいと判定された最大残差和をとる受信センサを除外し、除外された受信センサに対応する計測値を外れ値として、複数の計測値の中から外れ値を除外する外れ値除外ステップと、を有するものである。 The positioning method according to the present invention includes an outlier exclusion processing step for excluding outliers from a plurality of measurement values measured by a plurality of reception sensors that receive signals from a transmitter, and an outlier exclusion processing step. A positioning calculation step of measuring the position of the transmitter from a plurality of measured values after the outlier is excluded, and the outlier exclusion processing step is performed for each sensor combination that selects two different ones from the plurality of receiving sensors. A measured value difference calculating step for calculating a measured value difference that is a difference between a measured value measured by one receiving sensor and a measured value measured by the other receiving sensor, and a measured value difference calculating From the measured value difference for each sensor combination calculated in the step, the measured value difference residual is calculated for each sensor combination and received from the calculated measured value difference residual for each sensor combination. A residual sum calculation step for calculating a residual sum for each sensor, a maximum residual sum selection step for selecting a maximum residual sum among residual sums for each reception sensor calculated in the residual sum calculation step, A threshold determination step for determining whether or not the maximum residual sum selected in the maximum residual sum selection step is larger than a threshold, and a reception sensor that takes the maximum residual sum determined to be larger than the threshold in the threshold determination step And an outlier exclusion step of excluding outliers from a plurality of measurement values with the measured values corresponding to the excluded reception sensors as outliers.
　本発明によれば、発信機からの信号を受信する複数の受信センサから異なる２個を選ぶセンサ組合せごとに、センサ組合せを構成する一方の受信センサによって計測された計測値と、他方の受信センサによって計測された計測値との差である計測値差を用いて、複数の計測値の中から外れ値を除外するように構成されている。これにより、受信センサで受信した受信信号の電力情報を用いなくても、複数の計測値から外れ値を除外可能な測位装置および測位方法を得ることができる。 According to the present invention, for each sensor combination that selects two different ones from a plurality of receiving sensors that receive signals from a transmitter, the measured value measured by one receiving sensor constituting the sensor combination, and the other receiving sensor The outliers are excluded from the plurality of measurement values by using the measurement value difference that is the difference from the measurement value measured by the above. Thereby, it is possible to obtain a positioning device and a positioning method that can exclude outliers from a plurality of measured values without using power information of received signals received by the receiving sensor.
本発明の実施の形態１における測位装置を含む測位システムを示す構成図である。It is a block diagram which shows the positioning system containing the positioning apparatus in Embodiment 1 of this invention. 本発明の実施の形態１における測位処理部の構成を示す構成図である。It is a block diagram which shows the structure of the positioning process part in Embodiment 1 of this invention. 本発明の実施の形態１における外れ値除外処理部の構成を示す構成図である。It is a block diagram which shows the structure of the outlier exclusion process part in Embodiment 1 of this invention. 本発明の実施の形態１における測位処理部に入力される観測位相の中に外れ値が存在する具体例を示す説明図である。It is explanatory drawing which shows the specific example in which the outlier exists in the observation phase input into the positioning process part in Embodiment 1 of this invention. 本発明の実施の形態１におけるセンサ組合せの概念を示す説明図である。It is explanatory drawing which shows the concept of the sensor combination in Embodiment 1 of this invention. 本発明の実施の形態１における残差和計算処理の手法の概念を示す説明図である。It is explanatory drawing which shows the concept of the method of the residual sum calculation process in Embodiment 1 of this invention. 本発明の実施の形態１における閾値判定処理の手法の概念を示す説明図である。It is explanatory drawing which shows the concept of the method of the threshold determination process in Embodiment 1 of this invention. 本発明の実施の形態１における受信センサ除外処理の手法の概念を示す説明図である。It is explanatory drawing which shows the concept of the method of the reception sensor exclusion process in Embodiment 1 of this invention. 本発明の実施の形態１における測位処理部の構成の別例を示す構成図である。It is a block diagram which shows another example of a structure of the positioning process part in Embodiment 1 of this invention. 本発明の実施の形態１における測位処理部の一連の動作を示すフローチャートである。It is a flowchart which shows a series of operation | movement of the positioning process part in Embodiment 1 of this invention. 本発明の実施の形態１における外れ値除外処理部の一連の動作を示すフローチャートである。It is a flowchart which shows a series of operation | movement of the outlier exclusion process part in Embodiment 1 of this invention. 本発明の実施の形態１における計算機シミュレーションを行う際の各発信機および各受信センサの位置座標を示す座標図である。It is a coordinate diagram which shows the position coordinate of each transmitter and each receiving sensor at the time of performing the computer simulation in Embodiment 1 of this invention. 図１２に示す状態において、外れ値除外処理部によって計算される各受信センサに対応する残差和を示すグラフである。It is a graph which shows the residual sum corresponding to each receiving sensor calculated by the outlier exclusion process part in the state shown in FIG. 図１２に示す状態において、外れ値除外処理部によって計算される各受信センサに対応する残差和を示すグラフである。It is a graph which shows the residual sum corresponding to each receiving sensor calculated by the outlier exclusion process part in the state shown in FIG. 図１２に示す状態において、外れ値除外処理部によって計算される各受信センサに対応する残差和を示すグラフである。It is a graph which shows the residual sum corresponding to each receiving sensor calculated by the outlier exclusion process part in the state shown in FIG. 図１２に示す状態において、測位処理部によって計算される特定の発信機の測位結果を示すグラフである。It is a graph which shows the positioning result of the specific transmitter calculated by the positioning process part in the state shown in FIG. 図１２に示す状態において、測位処理部によって計算される特定の発信機の測位結果を示すグラフである。It is a graph which shows the positioning result of the specific transmitter calculated by the positioning process part in the state shown in FIG. 図１６のグラフを移動平均処理した後のグラフである。It is a graph after carrying out the moving average process of the graph of FIG. 図１７のグラフを移動平均処理した後のグラフである。It is a graph after carrying out the moving average process of the graph of FIG. 図１６のグラフの比較例を示すグラフである。It is a graph which shows the comparative example of the graph of FIG. 図１７のグラフの比較例を示すグラフである。It is a graph which shows the comparative example of the graph of FIG. 図２０のグラフを移動平均処理した後のグラフである。It is a graph after carrying out the moving average process of the graph of FIG. 図２１のグラフを移動平均処理した後のグラフである。It is a graph after carrying out the moving average process of the graph of FIG.
　以下、本発明による測位装置および測位方法を、好適な実施の形態にしたがって図面を用いて説明する。なお、図面の説明においては、同一部分または相当部分には同一符号を付し、重複する説明を省略する。また、以下の実施の形態では、斜面の変位を計測する特許文献１に記載の測位システムに本願発明を適用する場合を例示する。 Hereinafter, a positioning device and a positioning method according to the present invention will be described with reference to the drawings according to a preferred embodiment. In the description of the drawings, the same portions or corresponding portions are denoted by the same reference numerals, and redundant description is omitted. Moreover, in the following embodiment, the case where this invention is applied to the positioning system of patent document 1 which measures the displacement of a slope is illustrated.
　実施の形態１．
　図１は、本発明の実施の形態１における測位装置５を含む測位システムを示す構成図である。図１における測位システムは、斜面内の地滑りエリア等の計測エリア２に設置された複数の発信機３と、斜面の静止エリア１に設置された複数の受信センサ４と、測位装置５とを備える。なお、説明を分かりやすくするために、各発信機３を区別する必要がある場合、発信機Ｔ1、・・・、Ｔl、・・・、ＴL（１≦Ｌ）と表記する。同様に、各受信センサ４を区別する必要がある場合、受信センサＲ1、・・・、Ｒm、・・・、ＲM（１＜Ｍ）と表記する。 Embodiment 1 FIG.
FIG. 1 is a configuration diagram showing a positioning system including a positioning device 5 according to Embodiment 1 of the present invention. The positioning system in FIG. 1 includes a plurality of transmitters 3 installed in a measurement area 2 such as a landslide area on a slope, a plurality of reception sensors 4 installed in a stationary area 1 on a slope, and a positioning device 5. . Incidentally, for ease of description, when it is necessary to distinguish each transmitter 3, transmitter T 1, denoted · · ·, T l, · · ·, and T L (1 ≦ L). Similarly, when it is necessary to distinguish each receiving sensors 4, the receiving sensor R 1, denoted · · ·, R m, · · ·, and R M (1 <M).
　計測エリア２内の複数の観測点に設置された発信機３は、各発信機３に割り当てられたわずかに異なる固有の周波数の電波を発信する。各発信機３からの電波は、静止エリア１に設置された複数の受信センサ４によって受信され、ＲＦケーブル等で測位装置５に導かれる。なお、ここでは、発信機３によって発信される信号が電波である場合を例示しているので、受信センサ４としては、受信アンテナを用いればよい。 The transmitters 3 installed at a plurality of observation points in the measurement area 2 transmit radio waves having slightly different specific frequencies assigned to the respective transmitters 3. Radio waves from each transmitter 3 are received by a plurality of reception sensors 4 installed in the stationary area 1 and guided to the positioning device 5 by an RF cable or the like. In addition, since the case where the signal transmitted by the transmitter 3 is a radio wave is illustrated here, a reception antenna may be used as the reception sensor 4.
　なお、ここでは、説明を分かりやすくするために、発信機３からの送信信号の波形が正弦波であるものとして説明する。また、発信機Ｔlにおいて、位置座標を（ｘl，ｙl，ｚl）、発信周波数をｆl、送信信号位相をψlと表記する。さらに、受信センサＲmにおいて、位置座標を（Ｘm，Ｙm，Ｚm）と表記する。 Here, in order to make the explanation easy to understand, it is assumed that the waveform of the transmission signal from the transmitter 3 is a sine wave. Further, the transmitter T l, the position coordinates (x l, y l, z l), the oscillation frequency f l, denoted the transmitted signal phase as [psi l. Further, in the receiving sensor R m , the position coordinates are expressed as (X m , Y m , Z m ).
　測位装置５は、複数の受信機６と、複数のＡ／Ｄ変換器７と、複数の離散フーリエ変換部８と、複数の位相算出部９と、測位処理部１０とを有する。受信センサ４と受信機６は１対１で対応しており、受信センサ４、受信機６、ＡＤ／変換器７および離散フーリエ変換部８のそれぞれの個数は同数である。 The positioning device 5 includes a plurality of receivers 6, a plurality of A / D converters 7, a plurality of discrete Fourier transform units 8, a plurality of phase calculation units 9, and a positioning processing unit 10. The reception sensors 4 and the receivers 6 correspond one-to-one, and the numbers of the reception sensors 4, the receivers 6, the AD / converters 7, and the discrete Fourier transform units 8 are the same.
　受信機６は、各受信センサ４からの受信信号を周波数変換し、周波数変換後の信号をＡ／Ｄ変換器７に出力する。Ａ／Ｄ変換器７は、受信機６から入力された信号をディジタル信号に変換する。このディジタル信号は、離散フーリエ変換部８によって周波数領域に変換される。各観測点の発信機３は、わずかに異なる周波数が割り当てられているので、フーリエ変換によって各発信機３の信号を弁別することができる。このように、各受信センサ４の受信信号は、ＦＦＴ処理によって発信機３ごとに分離される。 The receiver 6 converts the frequency of the reception signal from each reception sensor 4 and outputs the frequency-converted signal to the A / D converter 7. The A / D converter 7 converts the signal input from the receiver 6 into a digital signal. This digital signal is converted into the frequency domain by the discrete Fourier transform unit 8. Since slightly different frequencies are assigned to the transmitters 3 at the respective observation points, the signals of the respective transmitters 3 can be discriminated by Fourier transformation. In this way, the reception signal of each reception sensor 4 is separated for each transmitter 3 by FFT processing.
　発信機３ごとに分離された各受信センサ４の受信信号は、位相算出部９に入力され、位相算出部９は、観測位相を算出する。 The reception signal of each reception sensor 4 separated for each transmitter 3 is input to the phase calculation unit 9, and the phase calculation unit 9 calculates the observation phase.
　このとき、発信機Ｔlから発信される電波を受信する受信センサＲmに対応する観測位相Φl,mは、以下の式（１）のようになる。 At this time, the observation phase Φ l, m corresponding to the reception sensor R m that receives the radio wave transmitted from the transmitter T l is expressed by the following equation (1).
Figure JPOXMLDOC01-appb-M000001
Figure JPOXMLDOC01-appb-M000001
　ただし、式（１）において、（ｘl，ｙl，ｚl）は、発信機Ｔlの位置座標を示し、（Ｘm，Ｙm，Ｚm）は、受信センサＲmの位置座標を示す。ψlは、発信機Ｔlの送信信号位相を示し、ξmは、受信センサＲmからＡ／Ｄ変換器７に至る経路のケーブル遅延、または受信機６等に起因した受信系遅延位相量を示し、Ｎl,mは、位相整数値バイアスである。 In Equation (1), (x 1 , y 1 , z 1 ) represents the position coordinates of the transmitter T 1 , and (X m , Y m , Z m ) represents the position coordinates of the reception sensor R m. Show. ψ l indicates a transmission signal phase of the transmitter T l , and ξ m indicates a cable delay in a path from the reception sensor R m to the A / D converter 7 or a reception system delay phase amount caused by the receiver 6 and the like. N l, m is a phase integer bias.
　受信センサＲmの位置座標（Ｘm，Ｙm，Ｚm）は既知数であり、発信機Ｔlの位置座標（ｘl，ｙl，ｚl）と、発信機Ｔlの送信信号位相ψlと、受信系遅延位相量ξmは、未知変数である。なお、送信信号位相ψlは毎回ランダムな値をとる。よって、観測位相Φl,mも毎回ランダムな値となる。 The position coordinates of the reception sensor R m (X m, Y m , Z m) are known quantities, the position coordinates of the transmitters T l (x l, y l , z l) and the transmission signal phase transmitters T l ψ l and the reception system delay phase amount ξ m are unknown variables. The transmission signal phase ψ l takes a random value every time. Therefore, the observation phase Φ l, m is also a random value every time.
　ここで、図１に示すとおり、測位システムにおいて、Ｌ個の発信機３と、Ｍ個の受信センサ４が存在する場合を考える。この場合、観測位相の総数はＬ×Ｍ個であるので、式（１）の方程式の数がＬ×Ｍ個の連立方程式を立てることができる。なお、連立方程式の式の数が未知変数以上であれば、その連立方程式を解くことができ、さらに、Ｌ個の発信機３のうちの一部を校正局として用いることで、未知数を減らすことが可能である。 Here, as shown in FIG. 1, a case where there are L transmitters 3 and M reception sensors 4 in the positioning system is considered. In this case, since the total number of observation phases is L × M, it is possible to establish a simultaneous equation with the number of equations of Expression (1) being L × M. If the number of simultaneous equations is greater than or equal to an unknown variable, the simultaneous equations can be solved, and the unknowns can be reduced by using a part of the L transmitters 3 as a calibration station. Is possible.
　特許文献１に記載の従来技術では、Ｌ×Ｍ個の観測位相のすべてを用いて上記の連立方程式を立て、その連立方程式を解く測位演算を行うことで、各発信機３の位置を計測する。したがって、受信系遅延位相量ξmに経時変化がある場合であっても、各発信機３の測位精度の向上を図ることが可能となる。なお、上記の連立方程式の具体的な解法の詳細については、特許文献１に開示されているので、ここでは説明を省略する。 In the prior art described in Patent Document 1, the above simultaneous equations are set up using all the L × M observation phases, and the position of each transmitter 3 is measured by performing a positioning operation to solve the simultaneous equations. . Therefore, even when the reception system delay phase amount ξ m changes with time, it is possible to improve the positioning accuracy of each transmitter 3. Note that details of a specific method for solving the above simultaneous equations are disclosed in Patent Document 1, and thus description thereof is omitted here.
　しかしながら、Ｌ×Ｍ個の観測位相の中には、マルチパス等に起因して精度が大幅に劣化している外れ値が含まれると考えられる。このような外れ値に該当する観測位相が含まれた状態で、測位演算を行うと、各発信機３の測位精度が劣化してしまう。 However, it is considered that the L × M observation phases include outliers whose accuracy is greatly deteriorated due to multipath or the like. If the positioning calculation is performed in a state where the observation phase corresponding to such an outlier is included, the positioning accuracy of each transmitter 3 is deteriorated.
　ここで、位相はランダムでも、位相差はランダムでないという性質に着目する。具体的には、ランダムな発信機の初期位相値は位相間の差分をとることでキャンセルされるので、同一発信機からの信号の位相差はランダムでない。したがって、位相差の時間的な推移から外れ値の特定が可能である。 Note here that the phase is random, but the phase difference is not random. Specifically, since the initial phase value of a random transmitter is canceled by taking the difference between the phases, the phase difference of signals from the same transmitter is not random. Therefore, it is possible to specify an outlier from the temporal transition of the phase difference.
　そこで、本願発明では、上記の性質を利用して、Ｌ×Ｍ個の観測位相の中に含まれる外れ値を特定し、その外れ値を除外して測位演算を行うように、測位処理部１０を構成している。 Therefore, in the present invention, the positioning processing unit 10 is used to specify outliers included in the L × M observation phases by using the above-described properties and perform the positioning calculation by excluding the outliers. Is configured.
　以下、測位処理部１０の構成について、図２を参照しながら説明する。図２は、本発明の実施の形態１における測位処理部１０の構成を示す構成図である。 Hereinafter, the configuration of the positioning processing unit 10 will be described with reference to FIG. FIG. 2 is a configuration diagram showing the configuration of the positioning processing unit 10 according to the first embodiment of the present invention.
　図２に示すように、測位処理部１０は、外れ値除外処理部１１と、予測値計算部１２と、メモリトラック判定部１３と、測位計算部１４とを有する。測位処理部１０は、例えば、メモリに記憶されたプログラムを実行するＣＰＵと、システムＬＳＩ等の処理回路によって実現される。 2, the positioning processing unit 10 includes an outlier exclusion processing unit 11, a predicted value calculation unit 12, a memory track determination unit 13, and a positioning calculation unit 14. The positioning processing unit 10 is realized by, for example, a CPU that executes a program stored in a memory and a processing circuit such as a system LSI.
　外れ値除外処理部１１は、複数の位相算出部９から入力されたＬ×Ｍ個の観測位相Φ1,1～ΦL,Mに対して、発信機３ごとに外れ値除外処理を行うことで、観測位相Φ1,1～ΦL,Mに含まれる外れ値を除外し、外れ値が除外された観測位相を出力する。 The outlier exclusion processing unit 11 performs the outlier exclusion processing for each transmitter 3 on the L × M observation phases Φ 1,1 to Φ L, M input from the plurality of phase calculation units 9. in, excluding the outliers included in the observation phase Φ 1,1 ~ Φ L, M, and outputs the observation phase outliers are excluded.
　ここで、外れ値除外処理について、図３～図８を参照しながら説明する。図３は、本発明の実施の形態１における外れ値除外処理部１１の構成を示す構成図である。 Here, the outlier exclusion process will be described with reference to FIGS. FIG. 3 is a configuration diagram showing the configuration of the outlier exclusion processing unit 11 according to Embodiment 1 of the present invention.
　図３に示すように、外れ値除外処理部１１は、計測値差計算部１１１と、残差和計算部１１２と、最大残差和選択部１１３と、閾値判定部１１４と、外れ値除外部１１５と、処理終了判定部１１６と、発信機番号指定部１１７と、記憶部１１８とを有する。 As shown in FIG. 3, the outlier exclusion processing unit 11 includes a measured value difference calculation unit 111, a residual sum calculation unit 112, a maximum residual sum selection unit 113, a threshold determination unit 114, and an outlier exclusion unit. 115, a process end determination unit 116, a transmitter number designation unit 117, and a storage unit 118.
　図４は、本発明の実施の形態１における測位処理部１０に入力される観測位相の中に外れ値が存在する具体例を示す説明図である。 FIG. 4 is an explanatory diagram illustrating a specific example in which an outlier exists in the observation phase input to the positioning processing unit 10 according to the first embodiment of the present invention.
　ここで、発信機３ごとに行われる外れ値除外処理を説明するにあたって、外れ値除外処理は、発信機３ごとに行われるので、発信機Ｔに付したインデックスｌを省略する。また、図４に示すように、具体例として、受信センサ４の個数についてＭ＝４とし、発信機Ｔからの電波の受信センサＲ1、Ｒ2、Ｒ3、Ｒ4に対応する観測位相のうちの受信センサＲ3に対応する観測位相が外れ値であるものとする。 Here, in describing the outlier exclusion process performed for each transmitter 3, the outlier exclusion process is performed for each transmitter 3, and thus the index l attached to the transmitter T is omitted. Further, as shown in FIG. 4, as a specific example, the number of reception sensors 4 is M = 4, and the observation phases corresponding to the reception sensors R 1 , R 2 , R 3 , R 4 of the radio waves from the transmitter T are set. It is assumed that the observation phase corresponding to the reception sensor R 3 is an outlier.
　計測値差計算部１１１は、複数の受信センサ４から異なる２個を選ぶセンサ組合せごとに、そのセンサ組合せを構成する一方の受信センサ４によって計測された計測値と、他方の受信センサ４によって計測された計測値との差である計測値差を計算する。残差和計算部１１２は、センサ組合せごとに、計測値差の予測値と計測値差との残差である計測値差残差を計算する。なお、計測値差の予測値は、後述する予測値計算部１２によって計算される。 The measurement value difference calculation unit 111 measures, for each sensor combination that selects two different ones from the plurality of reception sensors 4, the measurement value measured by one reception sensor 4 that constitutes the sensor combination, and the measurement by the other reception sensor 4. A measurement value difference that is a difference from the measured value is calculated. The residual sum calculation unit 112 calculates a measured value difference residual that is a residual between the predicted value of the measured value difference and the measured value difference for each sensor combination. The predicted value of the measured value difference is calculated by a predicted value calculation unit 12 described later.
　ここでは、受信センサ４によって計測された計測値は、観測位相であるので、計測値差計算部１１１は、センサ組合せごとに、以下の式（２）に従って、位相差を計測値差として計算する。また、残差和計算部１１２は、センサ組合せごとに、以下の式（３）に従って、位相差残差を計測値差残差として計算する。 Here, since the measurement value measured by the reception sensor 4 is the observation phase, the measurement value difference calculation unit 111 calculates the phase difference as the measurement value difference according to the following equation (2) for each sensor combination. . Further, the residual sum calculation unit 112 calculates a phase difference residual as a measurement value difference residual according to the following equation (3) for each sensor combination.
Figure JPOXMLDOC01-appb-M000002
Figure JPOXMLDOC01-appb-M000002
　ただし、上式において、ｍ１およびｍ２は、センサ組合せを構成する一方の受信センサＲm1および他方の受信センサＲm2に対応する。Φm1は、受信センサＲm1に対応する観測位相を示し、Φm2は、受信センサＲm2に対応する観測位相を示し、φm1,m2は、Φm1とΦm2との差である位相差を示す。また、φ（バー）m1,m2はφm1,m2の予測値を示し、ｚm1,m2は、φ（バー）m1,m2とφm1,m2との位相差残差を示す。なお、位相差の予測値は、後述する予測値計算部１２によって計算される。 However, in the above formula, m1 and m2 correspond to the received sensor R m1 and the other receiving sensors R m2 on one of the sensor combination. Φ m1 indicates an observation phase corresponding to the reception sensor R m1 , Φ m2 indicates an observation phase corresponding to the reception sensor R m2 , and φ m1 and m2 are phase differences that are differences between Φ m1 and Φ m2 Indicates. Φ (bar) m1, m2 indicates a predicted value of φ m1, m2 , and z m1, m2 indicates a phase difference residual between φ (bar) m1, m2 and φ m1, m2 . Note that the predicted value of the phase difference is calculated by the predicted value calculation unit 12 described later.
　図５は、本発明の実施の形態１におけるセンサ組合せの概念を示す説明図である。例えば、上記の図４に示す状況のとき、センサ組合せの総数は、以下の式（４）のとおり、「６」となり、各センサ組合せは、図５に示すとおり、（Ｒ1，Ｒ2）、（Ｒ1，Ｒ3）、（Ｒ1，Ｒ4）、（Ｒ2，Ｒ3）、（Ｒ2，Ｒ4）、（Ｒ3，Ｒ4）となる。この場合、センサ組合せに対応する位相差φ1,2、φ1,3、φ1,4、φ2,3、φ2,4、φ3,4が計算されるとともに、センサ組合せに対応する位相差残差ｚ1,2、ｚ1,3、ｚ1,4、ｚ2,3、ｚ2,4、ｚ3,4が計算される。 FIG. 5 is an explanatory diagram showing the concept of sensor combination in the first embodiment of the present invention. For example, in the situation shown in FIG. 4, the total number of sensor combinations is “6” as shown in the following formula (4). Each sensor combination is (R 1 , R 2 ) as shown in FIG. , the (R 1, R 3), (R 1, R 4), (R 2, R 3), (R 2, R 4), (R 3, R 4). In this case, phase differences φ 1,2 , φ 1,3 , φ 1,4 , φ 2,3 , φ 2,4 , φ 3,4 corresponding to the sensor combination are calculated and corresponding to the sensor combination The phase difference residuals z 1,2 , z 1,3 , z 1,4 , z 2,3 , z 2,4 , z 3,4 are calculated.
Figure JPOXMLDOC01-appb-M000003
Figure JPOXMLDOC01-appb-M000003
　ここで、仮に、式（３）で計算された位相差残差が大きい場合、位相差を計算する際に用いた２つの観測位相のうちのどちらが、位相差残差が大きくなる原因となっているか判別することができない。 Here, if the phase difference residual calculated by Equation (3) is large, which of the two observation phases used to calculate the phase difference causes the phase difference residual to increase. It cannot be determined.
　そこで、残差和計算部１１２は、位相差残差に対応するセンサ組合せを構成する２つの受信センサ４のそれぞれにその位相差残差を加算する処理を、計算されたすべての位相差残差について行う残差和計算処理を行う。残差和計算部１１２は、このような残差和計算処理を行うことで、受信センサ４ごとに残差和を計算する。 Therefore, the residual sum calculation unit 112 performs processing for adding the phase difference residual to each of the two receiving sensors 4 constituting the sensor combination corresponding to the phase difference residual, and calculates all the phase difference residuals calculated. The residual sum calculation processing performed for is performed. The residual sum calculation unit 112 calculates the residual sum for each reception sensor 4 by performing such residual sum calculation processing.
　具体的には、残差和計算部１１２は、以下の式（５）に従って、受信センサ４ごとに残差和を計算する。なお、各受信センサ４において、対応する残差和は、加算される位相差残差の総数で割ることで、平均化されている。 Specifically, the residual sum calculation unit 112 calculates the residual sum for each reception sensor 4 according to the following equation (5). In each reception sensor 4, the corresponding residual sum is averaged by dividing by the total number of added phase difference residuals.
Figure JPOXMLDOC01-appb-M000004
Figure JPOXMLDOC01-appb-M000004
　ただし、式（５）において、ｚmは、受信センサＲmに対応する残差和を示し、Ｎmは、受信センサＲmにおいて加算される位相差残差の総数を示し、Ｃcombは、すべてのセンサ組合せを示す。 In Equation (5), z m represents the residual sum corresponding to the reception sensor R m , N m represents the total number of phase difference residuals added in the reception sensor R m , and C comb is All sensor combinations are shown.
　図６は、本発明の実施の形態１における残差和計算処理の手法の概念を示す説明図である。例えば、上記の図４に示す状況のとき、図６に示すとおり、位相差残差ｚ1,2に着目すると、その位相差残差ｚ1,2に対応するセンサ組合せを構成する２つの受信センサＲ1、Ｒ2のそれぞれにその位相差残差ｚ1,2が加算される。同様に、位相差残差ｚ1,4に着目すると、その位相差残差ｚ1,4に対応するセンサ組合せを構成する２つの受信センサＲ1、Ｒ4のそれぞれにその位相差残差ｚ1,4が加算される。このように、式（５）に従った残差和計算処理が行われることで、受信センサＲ1、Ｒ2、Ｒ3、Ｒ4に対応する残差和ｚ1、ｚ2、ｚ3、ｚ4が計算される。 FIG. 6 is an explanatory diagram showing the concept of the residual sum calculation process according to Embodiment 1 of the present invention. For example, in the situation shown in FIG. 4, when the phase difference residual z 1,2 is focused as shown in FIG. 6, the two receptions constituting the sensor combination corresponding to the phase difference residual z 1,2 are shown. The phase difference residual z 1,2 is added to each of the sensors R 1 and R 2 . Similarly, when focusing on the phase difference residuals z 1,4, the phase difference residuals z 2 single receiver of the sensor combination corresponding to 1,4 sensor R 1, the phase difference residuals z to each of the R 4 1 and 4 are added. Thus, the residual sum calculation process according to the equation (5) is performed, so that the residual sums z 1 , z 2 , z 3 , corresponding to the reception sensors R 1 , R 2 , R 3 , R 4 , z 4 is calculated.
　ここで、仮に、各受信センサ４に対応する残差和について、以下の式（６）に従って閾値判定を行い、残差和が閾値ζよりも大きい受信センサ４に対応する観測位相を外れ値とみなす場合を考える。この場合、閾値ζの値を設定することが難しい。 Here, for the residual sum corresponding to each reception sensor 4, threshold determination is performed according to the following equation (6), and the observation phase corresponding to the reception sensor 4 whose residual sum is larger than the threshold ζ is set as an outlier. Think about the case. In this case, it is difficult to set the threshold value ζ.
Figure JPOXMLDOC01-appb-M000005
Figure JPOXMLDOC01-appb-M000005
　図７は、本発明の実施の形態１における閾値判定処理の手法の概念を示す説明図である。例えば、上記の図４に示す状況のとき、受信センサＲ3に対応する観測位相が外れ値である。また、残差和計算処理では、観測位相が外れ値でない受信センサＲ1、Ｒ2、Ｒ4に、受信センサＲ3に対応する観測位相が外れ値であることに起因した大きな位相差残差ｚ1,3、ｚ2,3、ｚ3,4がそれぞれ加算されることとなる。 FIG. 7 is an explanatory diagram showing the concept of the threshold determination processing method according to Embodiment 1 of the present invention. For example, in the situation shown in FIG. 4, the observation phase corresponding to the reception sensor R 3 is an outlier. Also, in the residual sum calculation process, the reception sensor R 1 , R 2 , R 4 whose observation phase is not an outlier, and the large phase difference residual due to the observation phase corresponding to the reception sensor R 3 being an outlier. z 1,3 , z 2,3 and z 3,4 are respectively added.
　したがって、図７に示すとおり、閾値ζの設定によっては、観測位相が外れ値でない受信センサＲ1、Ｒ2、Ｒ4についても、残差和が閾値ζよりも大きくなり、その結果、受信センサＲ1、Ｒ2、Ｒ4に対応する観測位相を外れ値であるとみなす可能性がある。 Therefore, as shown in FIG. 7, depending on the setting of the threshold ζ, the residual sum of the reception sensors R 1 , R 2 , and R 4 whose observation phases are not outliers becomes larger than the threshold ζ, and as a result, the reception sensor R 1, which may regarded as R 2, outlier observations phase corresponding to R 4.
　例えば、観測位相の計測精度σΦを用いて、位相差の計測精度σ（＝√２×σΦ）を求め、３σの値を閾値ζとして設定した場合であっても、観測位相が外れ値である受信センサＲ3以外の受信センサＲ1、Ｒ2、Ｒ4に対応する残差和が閾値ζよりも大きくなってしまう。ここで、閾値ζをより大きくすればよいという考え方もある。しかしながら、外れ値が真値に対してどの程度外れているかの先験情報がなければ、閾値ζをどの程度大きくすればよいか判断することができない。また、外れ値の数が多いほど、このような状況がさらに顕著になる。 For example, the measurement accuracy σ (= √2 × σ Φ ) of the phase difference is obtained using the measurement accuracy σ Φ of the observation phase, and even if the value of 3σ is set as the threshold value ζ, the observation phase is outlier. The residual sums corresponding to the receiving sensors R 1 , R 2 and R 4 other than the receiving sensor R 3 are larger than the threshold value ζ. Here, there is also an idea that the threshold ζ may be made larger. However, if there is no a priori information indicating how much the outlier is deviated from the true value, it cannot be determined how much the threshold ζ should be increased. Moreover, such a situation becomes more remarkable as the number of outliers increases.
　そこで、本実施の形態１では、各受信センサ４に対応する残差和を計算し、計算された残差和のうちの閾値ζよりも大きい残差和の中で最大の残差和をとる受信センサ４を除外し、除外後の各受信センサ４に対応する残差和を再度計算する処理を、閾値ζよりも大きい残差和が存在しなくなるまで繰り返すように構成している。 Therefore, in the first embodiment, a residual sum corresponding to each reception sensor 4 is calculated, and the maximum residual sum is obtained among the residual sums larger than the threshold value ζ among the calculated residual sums. The process of excluding the reception sensor 4 and recalculating the residual sum corresponding to each reception sensor 4 after the exclusion is repeated until there is no residual sum larger than the threshold ζ.
　最大残差和選択部１１３は、残差和計算部１１２によって計算された各受信センサ４に対応する残差和のうちの最大の残差和を最大残差和として選択する。閾値判定部１１４は、最大残差和選択部１１３によって選択された最大残差和が式（６）を満たすか否かを判定する。 The maximum residual sum selection unit 113 selects the maximum residual sum among the residual sums corresponding to the respective reception sensors 4 calculated by the residual sum calculation unit 112 as the maximum residual sum. The threshold determination unit 114 determines whether or not the maximum residual sum selected by the maximum residual sum selection unit 113 satisfies Expression (6).
　外れ値除外部１１５は、閾値判定部１１４によって、式（６）を満たさない、すなわち、閾値ζよりも大きいと判定された最大残差和をとる受信センサ４を除外する。また、外れ値除外部１１５は、除外された受信センサ４に対応する観測位相を外れ値として、観測位相の中から外れ値を除外する。残差和計算部１１２は、外れ値除外部１１５によって除外された受信センサ４以外の残りの各受信センサ４に対応する残差和を再度計算する。 The outlier exclusion unit 115 excludes the reception sensor 4 having the maximum residual sum that is determined by the threshold determination unit 114 not to satisfy Expression (6), that is, greater than the threshold ζ. Further, the outlier exclusion unit 115 excludes outliers from the observation phase by using the observation phase corresponding to the excluded reception sensor 4 as an outlier. The residual sum calculation unit 112 calculates again the residual sum corresponding to each of the remaining reception sensors 4 other than the reception sensor 4 excluded by the outlier exclusion unit 115.
　このように、残差和計算部１１２は計算されたセンサ組合せごとの計測値差残差から、受信センサ４ごとに残差和を計算する。また、最大残差和選択部１１３は、残差和計算部１１２によって計算された受信センサ４ごとの残差和のうちの最大残差和を選択する。閾値判定部１１４は、最大残差和選択部１１３によって選択された最大残差和が閾値ζよりも大きいか否かを判定する。また、外れ値除外部１１５は、閾値判定部１１４によって閾値ζよりも大きいと判定された最大残差和をとる受信センサ４を除外し、除外された受信センサ４に対応する計測値を外れ値として、複数の計測値の中から外れ値を除外する。 In this way, the residual sum calculation unit 112 calculates the residual sum for each reception sensor 4 from the measured value difference residual for each sensor combination. The maximum residual sum selection unit 113 selects the maximum residual sum among the residual sums for each reception sensor 4 calculated by the residual sum calculation unit 112. The threshold determination unit 114 determines whether the maximum residual sum selected by the maximum residual sum selection unit 113 is greater than the threshold ζ. Further, the outlier exclusion unit 115 excludes the reception sensor 4 having the maximum residual sum determined to be larger than the threshold value ζ by the threshold determination unit 114, and sets the measurement value corresponding to the excluded reception sensor 4 as an outlier. As above, outliers are excluded from a plurality of measured values.
　また、残差和計算部１１２による動作と、最大残差和選択部１１３による動作と、閾値判定部１１４による動作と、外れ値除外部１１５による動作とからなる処理が、閾値判定部１１４によって最大残差和が閾値未満であると判定されるまで、繰り返し実行されるように構成されている。 Further, the threshold determination unit 114 performs a process consisting of an operation by the residual sum calculation unit 112, an operation by the maximum residual sum selection unit 113, an operation by the threshold determination unit 114, and an operation by the outlier exclusion unit 115 by the threshold determination unit 114. It is configured to be repeatedly executed until it is determined that the residual sum is less than the threshold value.
　図８は、本発明の実施の形態１における受信センサ除外処理の手法の概念を示す説明図である。例えば、上記の図４に示す状況のとき、図８に示すとおり、各受信センサ４に対応する残差和がすべて閾値ζよりも大きい。この場合、最大残差和選択部１１３は、各受信センサ４に対応する残差和のうち、受信センサＲ3に対応する残差和を最大残差和とする。 FIG. 8 is an explanatory diagram showing the concept of the reception sensor exclusion processing method according to Embodiment 1 of the present invention. For example, in the situation shown in FIG. 4, the residual sums corresponding to the reception sensors 4 are all larger than the threshold value ζ, as shown in FIG. In this case, the maximum residual sum selection unit 113 sets the residual sum corresponding to the reception sensor R 3 among the residual sums corresponding to each reception sensor 4 as the maximum residual sum.
　続いて、受信センサＲ3に対応する残差和が閾値ζよりも大きいので、閾値判定部１１４は、最大残差和選択部１１３によって選択された最大残差和が閾値ζよりも大きいと判定する。外れ値除外部１１５は、閾値判定部１１４によって閾値ζよりも大きいと判定された最大残差和をとる受信センサ４として、受信センサＲ3を除外する。 Subsequently, since the residual sum corresponding to the reception sensor R 3 is larger than the threshold ζ, the threshold determination unit 114 determines that the maximum residual sum selected by the maximum residual sum selection unit 113 is larger than the threshold ζ. To do. The outlier exclusion unit 115 excludes the reception sensor R 3 as the reception sensor 4 that takes the maximum residual sum determined to be larger than the threshold ζ by the threshold determination unit 114.
　残差和計算部１１２は、外れ値除外部１１５によって除外された受信センサＲ3以外の残りの受信センサＲ1、Ｒ2、Ｒ4に対応する残差和を再度計算する。すなわち、残差和計算部１１２は、受信センサＲ3を含むセンサ組合せを除外した残りのセンサ組合せを基に、残差和計算処理を行うことで、残りの受信センサＲ1、Ｒ2、Ｒ4に対応する残差和を再度計算する。このように計算することで得られた残りの受信センサＲ1、Ｒ2、Ｒ4に対応する残差和は、閾値ζを下回るので、処理が終了となる。 The residual sum calculation unit 112 calculates again the residual sum corresponding to the remaining reception sensors R 1 , R 2 , R 4 other than the reception sensor R 3 excluded by the outlier exclusion unit 115. That is, the residual sum calculation unit 112 performs the residual sum calculation process based on the remaining sensor combinations excluding the sensor combination including the reception sensor R 3, and thereby the remaining reception sensors R 1 , R 2 , R again calculates the residual sum corresponding to 4. Since the residual sums corresponding to the remaining reception sensors R 1 , R 2 , and R 4 obtained by calculating in this way are below the threshold value ζ, the processing is terminated.
　このように、１回の処理を行うことで、閾値ζよりも大きい最大残差和をとる受信センサ４を特定することができ、その受信センサ４に対応する観測位相を外れ値とすることができる。したがって、本処理を外れ値の数だけ行えば、すべての外れ値を特定することができる。 In this way, by performing the process once, it is possible to specify the reception sensor 4 that has the maximum residual sum larger than the threshold value ζ, and to set the observation phase corresponding to the reception sensor 4 as an outlier. it can. Therefore, if this process is performed for the number of outliers, all outliers can be identified.
　外れ値除外処理部１１は、複数の位相算出部９から入力されたＬ×Ｍ個の観測位相Φ1,1～ΦL,Mに対して、以上に示す外れ値除外処理を発信機３ごとに行うことで、観測位相Φ1,1～ΦL,Mに含まれる外れ値を特定し、観測位相Φ1,1～ΦL,Mの中から特定した外れ値を除外する。また、外れ値除外処理部１１は、外れ値が除外された観測位相を出力する。 The outlier exclusion processing unit 11 performs the above outlier exclusion processing on the transmitter 3 for the L × M observation phases Φ 1,1 to Φ L, M input from the plurality of phase calculation units 9. that is performed to identify outlier included in the observation phase Φ 1,1 ~ Φ L, M, exclude outliers identified from the observed phase Φ 1,1 ~ Φ L, M. Further, the outlier exclusion processing unit 11 outputs the observation phase from which the outlier has been excluded.
　なお、ここでは、説明を分かりやすくするため、残差和計算部１１２は、計算されたセンサ組合せごとの計測値差残差から、受信センサ４ごとに、対応する計測値差残差を加算することで、残差和を計算するように構成される場合を例示している。すなわち、式（３）および式（５）から分かるように、残差二次形式を用いずに、単純に予測値と実測値との差の絶対値の加算平均を用いて、各受信センサ４に対応する残差和を計算するように構成する場合を例示している。 Here, for easy understanding, the residual sum calculation unit 112 adds a corresponding measurement value difference residual for each reception sensor 4 from the calculated measurement value difference residual for each sensor combination. Thus, the case of being configured to calculate the residual sum is illustrated. That is, as can be seen from the equations (3) and (5), each reception sensor 4 is simply used by using the average of the absolute values of the difference between the predicted value and the actual measurement value without using the residual quadratic form. The case where it comprises so that the residual sum corresponding to may be calculated is illustrated.
　しかしながら、各受信センサ４に対応する残差和をより厳密に計算したいのであれば、残差二次形式を用いてもよい。この場合、式（３）、式（５）および式（６）の代わりに、以下の式（７）～式（９）を用いて、外れ値除外処理を行うように構成する。 However, if it is desired to calculate the residual sum corresponding to each receiving sensor 4 more strictly, the quadratic residual form may be used. In this case, an outlier exclusion process is performed using the following formulas (7) to (9) instead of the formulas (3), (5), and (6).
Figure JPOXMLDOC01-appb-M000006
Figure JPOXMLDOC01-appb-M000006
　ただし、式（９）において、γは、ゲートサイズパラメータと呼ばれる閾値パラメータである。 However, in Equation (9), γ is a threshold parameter called a gate size parameter.
　このように、残差和計算部１１２は、計算されたセンサ組合せごとの計測値差残差から、受信センサ４ごとに、対応する計測値差残差の２乗値を加算することで、残差和を計算するように構成されてもよい。 In this way, the residual sum calculation unit 112 adds the square value of the corresponding measurement value difference residual for each reception sensor 4 from the calculated measurement value difference residual for each sensor combination. It may be configured to calculate a difference sum.
　図２の説明に戻り、予測値計算部１２は、外れ値除外処理部１１から入力された位相差を用いて、追尾処理を行うことで、位相差の予測値を計算する。なお、予測値計算部１２として、例えば、追尾フィルタを用いることができる。例えば、αフィルタで追尾処理を行う場合には、以下の式（１０）および式（１１）に従う。なお、αフィルタの代わりに、α－βフィルタまたはカルマンフィルタ等を用いてもよい。 2, the predicted value calculation unit 12 calculates a predicted value of the phase difference by performing a tracking process using the phase difference input from the outlier removal unit 11. As the predicted value calculation unit 12, for example, a tracking filter can be used. For example, when the tracking process is performed with the α filter, the following formulas (10) and (11) are followed. Note that an α-β filter, a Kalman filter, or the like may be used instead of the α filter.
Figure JPOXMLDOC01-appb-M000007
Figure JPOXMLDOC01-appb-M000007
　図９は、本発明の実施の形態１における測位処理部１０の構成の別例を示す構成図である。なお、ここでは、追尾処理を行うことで位相差の予測値を計算する場合を例示している。しかしながら、図９に示すとおり、測位処理部１０において、追尾処理の代わりに、測位結果から位相差の予測値を計算するように、予測値計算部１２を構成してもよい。 FIG. 9 is a configuration diagram illustrating another example of the configuration of the positioning processing unit 10 according to the first embodiment of the present invention. Here, the case where the predicted value of the phase difference is calculated by performing the tracking process is illustrated. However, as shown in FIG. 9, the predicted value calculation unit 12 may be configured so that the positioning processing unit 10 calculates the predicted value of the phase difference from the positioning result instead of the tracking process.
　図９において、予測値計算部１２は、以下の式（１２）および式（１３）に従って、位相差の予測値を計算する。なお、ここでは、説明を分かりやすくするために、発信機Ｔに付したインデックスｌを省略し、整数値バイアスが正しく解けていると仮定している。 9, the predicted value calculation unit 12 calculates the predicted value of the phase difference according to the following formulas (12) and (13). Here, in order to make the explanation easy to understand, it is assumed that the index l attached to the transmitter T is omitted and the integer value bias is correctly solved.
Figure JPOXMLDOC01-appb-M000008
Figure JPOXMLDOC01-appb-M000008
　なお、各発信機３の位置を計測するための連立方程式において、観測位相から外れ値が除外されると観測位相の総数が減るので、その連立方程式の式の数も減る。この場合、連立方程式の解の精度が劣化する恐れがある。 In the simultaneous equations for measuring the position of each transmitter 3, if the outlier is excluded from the observation phase, the total number of observation phases is reduced, so the number of equations in the simultaneous equations is also reduced. In this case, the accuracy of the simultaneous equations may be degraded.
　そこで、本実施の形態１では、外れ値が除外された後の観測位相を用いて立てられる連立方程式を解く場合のＤＯＰ（Ｄｉｌｕｔｉｏｎ　ｏｆ　Ｐｒｅｃｉｓｉｏｎ）を評価し、評価結果に従って、各発信機３の位置を計測するように構成されている。 Therefore, in the first embodiment, DOP (Dilution of Precision) when solving simultaneous equations set up using the observation phase after outliers are excluded is evaluated, and the position of each transmitter 3 is determined according to the evaluation result. Is configured to measure.
　メモリトラック判定部１３は、外れ値が除外された後の観測位相を用いて立てられる連立方程式を解く場合のＤＯＰを計算し、そのＤＯＰとＤＯＰallとを比較することで、そのＤＯＰが十分に小さいか判断する。なお、ＤＯＰallは、外れ値が除外される前の観測位相を用いて立てられる連立方程式を解く場合のＤＯＰである。 The memory track determination unit 13 calculates the DOP when solving the simultaneous equations that are set up using the observation phase after the outliers are excluded, and compares the DOP with DOP all , so that the DOP is sufficiently Judge whether it is small. Note that DOP all is a DOP for solving simultaneous equations that are set up using the observation phase before outliers are excluded.
　具体的には、メモリトラック判定部１３は、以下の式（１４）に従って、外れ値が除外された後の観測位相を用いて立てられる連立方程式を解く場合のＤＯＰがκＤＯＰallよりも大きければ、そのＤＯＰが十分に小さくないと判断する。なお、設定パラメータκについて、κ≧１を満たす。 Specifically, according to the following equation (14), the memory track determination unit 13 solves the simultaneous equations established using the observation phase after the outlier is excluded, and if the DOP is larger than κDOP all : It is determined that the DOP is not sufficiently small. The setting parameter κ satisfies κ ≧ 1.
Figure JPOXMLDOC01-appb-M000009
Figure JPOXMLDOC01-appb-M000009
　この場合、メモリトラック判定部１３は、メモリトラック処理を行い、その処理結果を測位結果として出力し、測位計算部１４は、動作しない。 In this case, the memory track determination unit 13 performs memory track processing, outputs the processing result as a positioning result, and the positioning calculation unit 14 does not operate.
　一方、メモリトラック判定部１３は、外れ値が除外された後の観測位相を用いて立てられる連立方程式を解く場合のＤＯＰがκＤＯＰall未満であれば、そのＤＯＰが十分に小さいと判断する。この場合、測位計算部１４は、外れ値が除外された後の観測位相を用いて立てられる連立方程式を解くことで、各発信機３の位置を計測し、その測位結果を出力する。 On the other hand, the memory track determination unit 13 determines that the DOP is sufficiently small if the DOP in solving the simultaneous equations established using the observation phase after the outlier is excluded is less than κDOP all . In this case, the positioning calculation unit 14 measures the position of each transmitter 3 by solving simultaneous equations established using the observation phase after outliers are excluded, and outputs the positioning result.
　次に、本実施の形態１における測位処理部１０の一連の動作について、図１０を参照しながら説明する。図１０は、本発明の実施の形態１における測位処理部１０の一連の動作を示すフローチャートである。 Next, a series of operations of the positioning processing unit 10 according to the first embodiment will be described with reference to FIG. FIG. 10 is a flowchart showing a series of operations of the positioning processing unit 10 according to the first embodiment of the present invention.
　ステップＳ１０１において、外れ値除外処理部１１には、時刻ｋの観測位相が入力され、処理がステップＳ１０２へと進む。 In step S101, the outlier removal processing unit 11 receives the observation phase at time k, and the process proceeds to step S102.
　ステップＳ１０２において、予測値計算部１２は、外れ値除外処理部１１から入力された時刻ｋ－１の位相差を用いて、追尾処理を行うことで、時刻ｋの位相差の予測値を計算し、処理がステップＳ１０３へと進む。 In step S102, the predicted value calculation unit 12 calculates a predicted value of the phase difference at time k by performing a tracking process using the phase difference at time k-1 input from the outlier removal processing unit 11. The process proceeds to step S103.
　ステップＳ１０３において、外れ値除外処理部１１は、外れ値除外処理を行い、処理がステップＳ１０４へと進む。 In step S103, the outlier exclusion processing unit 11 performs an outlier exclusion process, and the process proceeds to step S104.
　ここで、外れ値除外処理部１１による外れ値除外処理について、図１１を参照しながら説明する。図１１は、本発明の実施の形態１における外れ値除外処理部１１の一連の動作を示すフローチャートである。 Here, the outlier exclusion processing by the outlier exclusion processing unit 11 will be described with reference to FIG. FIG. 11 is a flowchart showing a series of operations of the outlier exclusion processing unit 11 according to Embodiment 1 of the present invention.
　ステップＳ２０１において、計測値差計算部１１１には、時刻ｋの観測位相が入力され、処理がステップＳ２０２へと進む。また、記憶部１１８は、入力された時刻ｋの観測位相を記憶する。 In step S201, the observation phase at time k is input to the measurement value difference calculation unit 111, and the process proceeds to step S202. The storage unit 118 also stores the input observation phase at time k.
　ステップＳ２０２において、発信機番号指定部１１７は、発信機番号を示す変数ｊについて、ｊ＝１に指定し、処理がステップＳ２０３へと進む。 In step S202, the transmitter number specifying unit 117 specifies j = 1 for the variable j indicating the transmitter number, and the process proceeds to step S203.
　ステップＳ２０３において、計測値差計算部１１１は、発信機Ｔjについて、センサ組合せごとに時刻ｋの位相差を計算する。さらに、残差和計算部１１２は、その時刻ｋの位相差と、ステップＳ１０２で計算された時刻ｋの位相差の予測値とから、センサ組合せごとに、時刻ｋの位相差残差を計算し、処理がステップＳ２０４へと進む。 In step S203, the measured value difference calculation unit 111 calculates the phase difference at time k for each sensor combination with respect to the transmitter Tj . Furthermore, the residual sum calculation unit 112 calculates the phase difference residual at time k for each sensor combination from the phase difference at time k and the predicted value of the phase difference at time k calculated in step S102. The process proceeds to step S204.
　ステップＳ２０４において、残差和計算部１１２は、ステップＳ２０３でセンサ組合せごとに計算された時刻ｋの位相差残差を用いて、受信センサ４ごとに残差和を計算し、処理がステップＳ２０５へと進む。 In step S204, the residual sum calculation unit 112 calculates the residual sum for each reception sensor 4 using the phase difference residual at time k calculated for each sensor combination in step S203, and the process proceeds to step S205. Proceed with
　ステップＳ２０５において、最大残差和選択部１１３は、ステップＳ２０４で受信センサ４ごとに計算された残差和の中から、最大残差和を選択し、処理がステップＳ２０６へと進む。 In step S205, the maximum residual sum selection unit 113 selects the maximum residual sum from the residual sums calculated for each reception sensor 4 in step S204, and the process proceeds to step S206.
　ステップＳ２０６において、閾値判定部１１４は、ステップＳ２０５で選択された最大残差和が閾値ζよりも大きいか否かを判定する。最大残差和が閾値ζよりも大きい（すなわち、Ｙｅｓ）と判定された場合には、処理がステップＳ２０７へと進む。一方、最大残差和が閾値ζ未満（すなわち、Ｎｏ）と判定された場合には、処理がステップＳ２０８へと進む。 In step S206, the threshold determination unit 114 determines whether or not the maximum residual sum selected in step S205 is larger than the threshold ζ. If it is determined that the maximum residual sum is larger than the threshold ζ (that is, Yes), the process proceeds to step S207. On the other hand, if it is determined that the maximum residual sum is less than the threshold value ζ (ie, No), the process proceeds to step S208.
　ステップＳ２０７において、外れ値除外部１１５は、ステップＳ２０５で選択された最大残差和をとる受信センサ４を除外し、処理がステップＳ２０４へと戻り、ステップＳ２０４以降の処理が再度行われる。また、記憶部１１８は、外れ値除外部１１５によって外れ値が除外された後の観測位相を記憶する。 In step S207, the outlier exclusion unit 115 excludes the reception sensor 4 that takes the maximum residual sum selected in step S205, the process returns to step S204, and the processes after step S204 are performed again. In addition, the storage unit 118 stores the observation phase after the outlier is excluded by the outlier exclusion unit 115.
　このように、最大残差和が閾値ζ未満となるまで、ステップＳ２０４～ステップＳ２０７の処理が繰り返し行われる。 In this way, the processing from step S204 to step S207 is repeated until the maximum residual sum becomes less than the threshold value ζ.
　ステップＳ２０８において、処理終了判定部１１６は、すべての発信機３について処理が終了したか否かを判定する。処理終了である（すなわち、Ｙｅｓ）と判定された場合には、一連の処理が終了となる。一方、処理終了でない（すなわち、Ｎｏ）と判定された場合には、ステップＳ２０９へと進む。 In step S208, the process end determination unit 116 determines whether or not the processes have been completed for all the transmitters 3. If it is determined that the process is finished (that is, Yes), the series of processes is finished. On the other hand, if it is determined that the process is not finished (that is, No), the process proceeds to step S209.
　ステップＳ２０９において、発信機番号指定部１１７は、変数ｊについて、ｊ＝ｊ＋１に指定し、処理がステップＳ２０３へと戻り、次の発信機Ｔj+1について、ステップＳ２０３以降の処理が再度行われる。 In step S209, the transmitter number designation unit 117 designates j = j + 1 for the variable j, the process returns to step S203, and the processes after step S203 are performed again for the next transmitter T j + 1. .
　このように、すべての発信機３について外れ値除外処理が行われるまで、ステップＳ２０３～ステップＳ２０９の処理が繰り返し行われる。 In this way, the processing from step S203 to step S209 is repeated until the outlier exclusion processing is performed for all the transmitters 3.
　図１０の説明に戻り、ステップＳ１０４において、メモリトラック判定部１３は、ステップＳ１０３で特定された外れ値を除外した後の観測位相を用いて立てられる連立方程式について、ＤＯＰを計算し、処理がステップＳ１０５へと進む。 Returning to the description of FIG. 10, in step S104, the memory track determination unit 13 calculates DOP for the simultaneous equations that are established using the observation phase after excluding the outlier specified in step S103, and the processing is performed in step S104. Proceed to S105.
　ステップＳ１０５において、メモリトラック判定部１３は、ステップＳ１０４で計算されたＤＯＰが十分小さいか否かを判定する。ＤＯＰが十分小さい（すなわち、Ｙｅｓ）と判定された場合には、処理がステップＳ１０６へと進む。一方、ＤＯＰが十分小さくない（すなわち、Ｎｏ）と判定された場合には、処理がステップＳ１０７へと進む。 In step S105, the memory track determination unit 13 determines whether or not the DOP calculated in step S104 is sufficiently small. If it is determined that the DOP is sufficiently small (that is, Yes), the process proceeds to step S106. On the other hand, if it is determined that the DOP is not sufficiently small (that is, No), the process proceeds to step S107.
　ステップＳ１０６において、測位計算部１４は、ステップＳ１０３で特定された外れ値を除外した後の観測位相を用いて立てられる連立方程式を解くことで、各発信機３の位置を計測し、その測位計算によって得られる測位結果を出力し、処理がステップＳ１０８へと進む。 In step S106, the positioning calculation unit 14 measures the position of each transmitter 3 by solving simultaneous equations established using the observation phase after excluding the outlier specified in step S103, and calculates the positioning. The positioning result obtained by is output, and the process proceeds to step S108.
　ステップＳ１０７において、メモリトラック判定部１３は、メモリトラック処理を行い、その処理結果を測位結果として出力し、処理がステップＳ１０８へと進む。 In step S107, the memory track determination unit 13 performs memory track processing, outputs the processing result as a positioning result, and the process proceeds to step S108.
　ステップＳ１０８において、測位処理部１０は、ステップＳ１０６またはステップＳ１０７で得られた測位結果を、例えば表示装置を介して表示し、処理がステップＳ１０９へと進む。 In step S108, the positioning processing unit 10 displays the positioning result obtained in step S106 or step S107 via, for example, a display device, and the process proceeds to step S109.
　ステップＳ１０９において、測位処理部１０は、処理を終了させるか否かを判定する。処理を終了させる（すなわち、Ｙｅｓ）と判定された場合には、一連の処理が終了となる。一方、処理を終了させないと判定された場合には、処理がステップＳ１１０へと進む。 In step S109, the positioning processing unit 10 determines whether or not to end the process. If it is determined that the process is to be terminated (that is, Yes), the series of processes is terminated. On the other hand, if it is determined not to end the process, the process proceeds to step S110.
　ステップＳ１１０において、測位処理部１０は、時刻ｋについて、ｋ＝ｋ＋１に設定し、処理がステップＳ１０１へと戻り、時刻ｋ＋１の観測位相について、ステップＳ１０１以降の処理が再度行われる。 In step S110, the positioning processing unit 10 sets k = k + 1 for the time k, the process returns to step S101, and the processes after step S101 are performed again for the observation phase at the time k + 1.
　このように、時刻ｋが設定値に達して処理が終了となるまで、ステップＳ１０１～ステップＳ１１０の処理が繰り返し行われる。 In this way, the processing from step S101 to step S110 is repeated until the time k reaches the set value and the processing is terminated.
　次に、計算機シミュレーションに従って、本実施の形態１における測位装置５を動作させたときに得られる結果について、図１２～図２３を参照しながら説明する。図１２は、本発明の実施の形態１における計算機シミュレーションを行う際の各発信機３および各受信センサ４の位置座標を示す座標図である。 Next, the results obtained when the positioning device 5 according to the first embodiment is operated according to the computer simulation will be described with reference to FIGS. FIG. 12 is a coordinate diagram showing the position coordinates of each transmitter 3 and each receiving sensor 4 when performing computer simulation in the first embodiment of the present invention.
　なお、計算機シミュレーションでは、図１２に示すように、発信機Ｔ1～Ｔ6と、受信センサＲ1～Ｒ8を使用し、さらに、発信機Ｔ1は、校正用発信機であるものとする。また、観測位相の誤差の標準偏差は、３／√２ｄｅｇであり、位相差の誤差の標準偏差は、３ｄｅｇであるものとする。さらに、時刻ｋ＝６０の観測位相が測位処理部１０に入力されるとき、発信機Ｔ3からの電波を受信する受信センサＲ3に対応する観測位相Φ3,3と、発信機Ｔ3からの電波を受信する受信センサＲ5に対応する観測位相Φ3,5とは、外れ値であるものとする。 In the computer simulation, as shown in FIG. 12, transmitters T 1 to T 6 and reception sensors R 1 to R 8 are used, and transmitter T 1 is a calibration transmitter. . The standard deviation of the observation phase error is 3 / √2 deg, and the standard deviation of the phase difference error is 3 deg. Furthermore, when the observation phase of the time k = 60 is input to the positioning processor 10, an observation phase [Phi 3,3 corresponding to the received sensor R 3 for receiving radio waves from a transmitter T 3, from a transmitter T 3 It is assumed that the observation phase Φ 3,5 corresponding to the reception sensor R 5 that receives the radio wave is an outlier.
　図１３～図１５は、図１２に示す状態において、外れ値除外処理部１１によって計算される各受信センサ４に対応する残差和を示すグラフである。 13 to 15 are graphs showing the residual sum corresponding to each reception sensor 4 calculated by the outlier removal processing unit 11 in the state shown in FIG.
　時刻ｋ＝６０の場合において、外れ値除外処理部１１は、図１１のフローチャートの処理を実行する。特に、変数ｊがｊ＝３に達したとき、発信機Ｔ3について、ステップＳ２０３以降の処理が実行される。ステップＳ２０３およびステップＳ２０４が順次実行されれば、図１３に示すとおり、各受信センサＲ1～Ｒ8に対応する残差和が計算される。また、図１３から分かるように、受信センサＲ5が最大残差和をとり、さらに、その最大残差和は閾値ζよりも大きい。 In the case of time k = 60, the outlier exclusion processing unit 11 executes the processing of the flowchart of FIG. In particular, when the variable j reaches j = 3, the transmitter T 3, the processes in and after step S203 are executed. If Step S203 and Step S204 are executed in sequence, as shown in FIG. 13, the residual sum for each receiving sensors R 1 ~ R 8 is calculated. Further, as can be seen from FIG. 13, the reception sensor R 5 takes the maximum residual sum, and the maximum residual sum is larger than the threshold value ζ.
　続いて、図１３に示す状態において、ステップＳ２０５～ステップＳ２０７が順次実行されれば、閾値ζよりも大きい最大残差和をとる受信センサＲ5が除外される。つまり、外れ値除外処理部１１は、観測位相Φ3,5が外れ値であると特定している。その後、ステップＳ２０４が実行されれば、図１４に示すとおり、除外された受信センサＲ5以外の残りの受信センサＲ1～Ｒ4、Ｒ6～Ｒ8に対応する残差和が計算される。また、図１４から分かるように、受信センサＲ3が最大残差和をとり、さらに、その最大残差和は閾値ζよりも大きい。 Subsequently, in the state shown in FIG. 13, if it is executed steps S205 ~ step S207 sequentially receiving sensor R 5 is excluded for a maximum residual sum greater than a threshold zeta. That is, the outlier exclusion processing unit 11 specifies that the observation phases Φ 3,5 are outliers. Thereafter, when step S204 is executed, residual sums corresponding to the remaining reception sensors R 1 to R 4 and R 6 to R 8 other than the excluded reception sensor R 5 are calculated as shown in FIG. . Further, as can be seen from FIG. 14, the reception sensor R 3 takes the maximum residual sum, and the maximum residual sum is larger than the threshold value ζ.
　続いて、図１４に示す状態において、ステップＳ２０５～ステップＳ２０７が順次実行されれば、閾値ζよりも大きい最大残差和をとる受信センサＲ3が除外される。つまり、外れ値除外処理部１１は、観測位相Φ3,3が外れ値であると特定している。その後、ステップＳ２０４が実行されれば、図１５に示すとおり、除外された受信センサＲ3以外の残りの受信センサＲ1、Ｒ2、Ｒ4、Ｒ6～Ｒ8に対応する残差和が計算される。また、図１５から分かるように、受信センサＲ2が最大残差和をとり、さらに、その最大残差和は閾値ζ未満である。 Subsequently, in the state shown in FIG. 14, if it is executed steps S205 ~ step S207 sequentially receiving sensor R 3 is excluded to take maximum residual sum greater than a threshold zeta. That is, the outlier exclusion processing unit 11 specifies that the observation phases Φ 3,3 are outliers. Thereafter, when step S204 is executed, residual sums corresponding to the remaining reception sensors R 1 , R 2 , R 4 , R 6 to R 8 other than the excluded reception sensor R 3 are obtained as shown in FIG. Calculated. Further, as can be seen from FIG. 15, the reception sensor R 2 takes the maximum residual sum, and the maximum residual sum is less than the threshold value ζ.
　続いて、図１５に示す状態において、ステップＳ２０５、ステップＳ２０６、ステップＳ２０８およびステップＳ２０９が順次実行され、発信機Ｔ4について、ステップＳ２０３以降の処理が実行される。 Subsequently, in the state shown in FIG. 15, step S205, step S206, step S208 and step S209 are sequentially executed, the transmitter T 4, the processes in and after step S203 are executed.
　以上、図１３～図１５から、外れ値除外処理部１１は、外れ値除外処理を実行することで、観測位相Φ3,3および観測位相Φ3,5が外れ値であることを正確に特定することができることが分かる。 As described above, from FIG. 13 to FIG. 15, the outlier exclusion processing unit 11 executes the outlier exclusion processing to accurately specify that the observation phase Φ 3,3 and the observation phase Φ 3,5 are outliers. You can see that you can.
　図１６および図１７は、図１２に示す状態において、測位処理部１０によって計算される特定の発信機Ｔ3の測位結果を示すグラフである。図１８は、図１６のグラフを移動平均処理した後のグラフである。図１９は、図１７のグラフを移動平均処理した後のグラフである。 16 and 17 are graphs showing the positioning results of a specific transmitter T 3 calculated by the positioning processing unit 10 in the state shown in FIG. FIG. 18 is a graph after the moving average processing of the graph of FIG. FIG. 19 is a graph after the moving average processing of the graph of FIG.
　なお、図１６では、時刻ｋ＝０の測位結果におけるｘ座標の値を基準として、その基準に対して、各時刻ｋの測位結果におけるｘ座標の値がどの程度変化しているかを変位ｘｈで示している。同様に、図１７では、時刻ｋ＝０の測位結果におけるｙ座標の値を基準として、その基準に対して、各時刻ｋの測位結果におけるｙ座標の値がどの程度変化しているかを変位ｙｈで示している。 In FIG. 16, the x-coordinate value in the positioning result at time k = 0 is used as a reference, and the displacement xh indicates how much the x-coordinate value in the positioning result at each time k changes with respect to the reference. Show. Similarly, in FIG. 17, with reference to the y-coordinate value in the positioning result at time k = 0, the displacement yh indicates how much the y-coordinate value in the positioning result at each time k changes with respect to the reference. Is shown.
　ここで、本実施の形態１における測位処理装置の比較例として、外れ値除外処理が行われていない場合に得られる発信機Ｔ3の測位結果について、図２０～図２３に示す。 Here, as a comparative example of the positioning processing apparatus according to the first embodiment, FIGS. 20 to 23 show the positioning results of the transmitter T 3 obtained when the outlier exclusion process is not performed.
　図２０は、図１６のグラフの比較例を示すグラフである。図２１は、図１７のグラフの比較例を示すグラフである。図２２は、図２０のグラフを移動平均処理した後のグラフである。図２３は、図２１のグラフを移動平均処理した後のグラフである。 FIG. 20 is a graph showing a comparative example of the graph of FIG. FIG. 21 is a graph showing a comparative example of the graph of FIG. FIG. 22 is a graph after the moving average processing of the graph of FIG. FIG. 23 is a graph after the moving average processing of the graph of FIG.
　例えば、図１６～図２３の各グラフにおいて、時刻ｋ＝６０に着目する。ここで、時刻ｋ＝６０は、上述したとおり、観測位相に外れ値が含まれる時刻である。 For example, in the graphs of FIGS. 16 to 23, pay attention to time k = 60. Here, time k = 60 is a time at which an outlier is included in the observation phase, as described above.
　図２０～図２３から、外れ値除外処理が行われていない場合、時刻ｋ＝６０において、外れ値が除外されていないことに起因して、変位計測誤差が増大していることが分かる。これに対して、図１６～図１９から、外れ値除外処理が行われている場合、時刻ｋ＝６０において、外れ値が除外されていることから、変位計測誤差が増大しておらず、比較例と比べて、測位精度が良好であることが分かる。 20 to 23, when the outlier exclusion process is not performed, it can be seen that the displacement measurement error increases due to the fact that the outlier is not excluded at time k = 60. On the other hand, from FIG. 16 to FIG. 19, when the outlier exclusion process is performed, since the outlier is excluded at time k = 60, the displacement measurement error does not increase, and the comparison It can be seen that the positioning accuracy is better than the example.
　以上、本実施の形態１によれば、発信機からの信号を受信する複数の受信センサから異なる２個を選ぶセンサ組合せごとに、センサ組合せを構成する一方の受信センサによって計測された計測値と、他方の受信センサによって計測された計測値との差である計測値差を用いて、複数の計測値の中から外れ値を除外するように構成されている。なお、本実施の形態１では、計測値が観測位相である場合を例示している。 As described above, according to the first embodiment, for each sensor combination in which two different sensors are selected from a plurality of receiving sensors that receive a signal from a transmitter, the measured value measured by one receiving sensor constituting the sensor combination The outlier is configured to be excluded from the plurality of measurement values by using a measurement value difference that is a difference from the measurement value measured by the other receiving sensor. In the first embodiment, the case where the measurement value is the observation phase is illustrated.
　これにより、受信センサで受信した受信信号の電力情報を用いなくても、複数の計測値から外れ値を除外可能な測位装置を得ることができる。 This makes it possible to obtain a positioning device that can exclude outliers from a plurality of measured values without using the power information of the received signal received by the receiving sensor.
　また、受信機間での観測位相の差、すなわち、位相差を用い、受信機の組み合わせを変えて異なる受信機間の位相差の時間的な推移をモニタするように構成されているので、他の観測位相と比べて著しく値の異なる観測位相、すなわち、外れ値を特定することができる。 In addition, it is configured to monitor the temporal transition of the phase difference between different receivers by using the difference in observation phase between the receivers, that is, the phase difference and changing the combination of the receivers. It is possible to specify an observation phase that is significantly different from the observation phase, that is, an outlier.
　実施の形態２．
　なお、先の実施の形態１では、受信センサ４によって計測された計測値が観測位相である場合を例示したが、受信センサ４によって計測された計測値が時間計測値であっても、本願発明を適用可能である。この場合、時間計測値ＴＯＡは、以下の式（１５）で与えられる。 Embodiment 2. FIG.
In the first embodiment, the case where the measurement value measured by the reception sensor 4 is the observation phase is exemplified. However, even if the measurement value measured by the reception sensor 4 is a time measurement value, the present invention is applied. Is applicable. In this case, the time measurement value TOA is given by the following equation (15).
Figure JPOXMLDOC01-appb-M000010
Figure JPOXMLDOC01-appb-M000010
　ただし、ｃは光速を示し、μl及びηmはそれぞれ発信機Ｔl、および受信センサＲmに対応する受信機内で生じる何らかの時間遅延を示す。 Where c represents the speed of light, and μ l and η m represent some time delay that occurs in the receiver corresponding to the transmitter T l and the receiving sensor R m , respectively.
　また、外れ値除外処理部１１は、観測位相の代わりに、時間計測値ＴＯＡに対して、先の実施の形態１と同様の外れ値除外処理を行う。 Further, the outlier exclusion processing unit 11 performs the outlier exclusion processing similar to that of the first embodiment on the time measurement value TOA instead of the observation phase.
　実施の形態３．
　なお、先の実施の形態１では、受信センサ４によって計測された計測値が観測位相である場合を例示したが、受信センサ４によって計測された計測値がドップラー計測値であっても、本願発明を適用可能である。この場合、ドップラー計測値ＦＯＡは、以下の式（１６）で与えられる。 Embodiment 3 FIG.
In the first embodiment, the case where the measurement value measured by the reception sensor 4 is the observation phase is exemplified. However, even if the measurement value measured by the reception sensor 4 is a Doppler measurement value, the present invention is applied. Is applicable. In this case, the Doppler measurement value FOA is given by the following equation (16).
Figure JPOXMLDOC01-appb-M000011
Figure JPOXMLDOC01-appb-M000011
　ただし、
Figure JPOXMLDOC01-appb-M000012
 は、発信機Ｔlの３次元速度ベクトルを示し、ｐl＝［ｘl　ｙl　ｚl］Tは発信機Ｔlの３次元位置ベクトル、Ｐm＝［Ｘm　Ｙm　Ｚm］Tは受信センサＲmの３次元位置ベクトルである。また、λは波長を示し、ρlおよびυmはそれぞれ発信機Ｔl、および受信センサＲmに対応する受信機内で生じる何らかの周波数シフト値である。 However,
Figure JPOXMLDOC01-appb-M000012
 Represents the three-dimensional velocity vector of the transmitter T l , p 1 = [x 1 y 1 z 1 ] T is the 3D position vector of the transmitter T 1 , and P m = [X m Y m Z m ] T is it is a three-dimensional position vector of the receiving sensor R m. In addition, λ indicates a wavelength, and ρ l and υ m are some frequency shift values generated in the receiver corresponding to the transmitter T l and the receiving sensor R m , respectively.
　また、外れ値除外処理部１１は、観測位相の代わりに、ドップラー計測値ＦＯＡに対して、先の実施の形態１と同様の外れ値除外処理を行う。 Further, the outlier exclusion processing unit 11 performs the outlier exclusion processing similar to that of the first embodiment on the Doppler measurement value FOA instead of the observation phase.
　なお、本願発明は、斜面のモニタリングだけでなく、橋梁、ダム、トンネルなど、あらゆる構造物のモニタリングにも適用可能である。また、ＧＰＳ等の測位システムにおいても、位相を用いており、このような測位システムにも本願発明を適用可能である。このように、本願発明は、幅広い分野への応用が可能である。 Note that the present invention is applicable not only to slope monitoring but also to monitoring of all structures such as bridges, dams, and tunnels. Also, a positioning system such as GPS uses a phase, and the present invention can be applied to such a positioning system. Thus, the present invention can be applied to a wide range of fields.

Claims (8)

  1. 　発信機からの信号を受信する複数の受信センサによって計測される複数の計測値から、発信機の位置を計測する測位装置であって、
    　前記複数の計測値の中から外れ値を除外する外れ値除外処理部と、
    　前記外れ値除外処理部によって前記外れ値が除外された後の前記複数の計測値から、前記発信機の位置を計測する測位計算部と、
    　を備え、
    　前記外れ値除外処理部は、
    　　前記複数の受信センサから異なる２個を選ぶセンサ組合せごとに、前記センサ組合せを構成する一方の受信センサによって計測された計測値と、他方の受信センサによって計測された計測値との差である計測値差を計算する計測値差計算部と、
    　　前記計測値差計算部によって計算された前記センサ組合せごとの計測値差から、前記センサ組合せごとに計測値差残差を計算し、計算された前記センサ組合せごとの計測値差残差から、受信センサごとに残差和を計算する残差和計算部と、
    　　前記残差和計算部によって計算された前記受信センサごとの残差和のうちの最大残差和を選択する最大残差和選択部と、
    　　前記最大残差和選択部によって選択された前記最大残差和が閾値よりも大きいか否かを判定する閾値判定部と、
    　　前記閾値判定部によって前記閾値よりも大きいと判定された前記最大残差和をとる受信センサを除外し、除外された前記受信センサに対応する計測値を前記外れ値として、前記複数の計測値の中から前記外れ値を除外する外れ値除外部と、
    　を有する測位装置。     A positioning device that measures the position of a transmitter from a plurality of measurement values measured by a plurality of receiving sensors that receive signals from the transmitter,
    An outlier exclusion processing unit for excluding outliers from the plurality of measurement values;
    From the plurality of measured values after the outlier has been excluded by the outlier exclusion processing unit, a positioning calculation unit that measures the position of the transmitter;
    With
    The outlier exclusion processing unit
    For each sensor combination that selects two different ones from the plurality of receiving sensors, the measurement is a difference between a measured value measured by one receiving sensor that constitutes the sensor combination and a measured value measured by the other receiving sensor. A measurement value difference calculation unit for calculating a value difference;
    From the measured value difference for each sensor combination calculated by the measured value difference calculation unit, calculate a measured value difference residual for each sensor combination, and receive from the calculated measured value difference residual for each sensor combination. A residual sum calculator for calculating the residual sum for each sensor;
    A maximum residual sum selection unit that selects a maximum residual sum of residual sums for each of the reception sensors calculated by the residual sum calculation unit;
    A threshold determination unit that determines whether or not the maximum residual sum selected by the maximum residual sum selection unit is greater than a threshold;
    A reception sensor that takes the maximum residual sum determined to be larger than the threshold by the threshold determination unit is excluded, and a measurement value corresponding to the excluded reception sensor is set as the outlier, and the plurality of measurement values An outlier exclusion unit for excluding the outlier from the inside;
    Positioning device having.
  2. 　前記残差和計算部による動作と、前記最大残差和選択部による動作と、前記閾値判定部による動作と、前記外れ値除外部による動作とからなる処理が、前記閾値判定部によって前記最大残差和が閾値未満であると判定されるまで、繰り返し実行されるように構成されている
    　請求項１に記載の測位装置。     A process comprising an operation by the residual sum calculation unit, an operation by the maximum residual sum selection unit, an operation by the threshold determination unit, and an operation by the outlier exclusion unit is performed by the threshold determination unit. The positioning device according to claim 1, wherein the positioning device is configured to be repeatedly executed until it is determined that the difference sum is less than a threshold value.
  3. 　前記残差和計算部は、
    　　計算された前記センサ組合せごとの計測値差残差から、受信センサごとに、対応する計測値差残差を加算することで、前記残差和を計算する
    　請求項１または２に記載の測位装置。     The residual sum calculation unit
    The positioning device according to claim 1, wherein the residual sum is calculated by adding a corresponding measured value difference residual for each reception sensor from the calculated measured value difference residual for each sensor combination. .
  4. 　前記残差和計算部は、
    　　計算された前記センサ組合せごとの計測値差残差から、受信センサごとに、対応する計測値差残差の２乗値を加算することで、前記残差和を計算する
    　請求項１または２に記載の測位装置。     The residual sum calculation unit
    The residual sum is calculated by adding the square value of the corresponding measured value difference residual for each receiving sensor from the calculated measured value difference residual for each sensor combination. The described positioning device.
  5. 　前記計測値は、観測位相である
    　請求項１から４のいずれか１項に記載の測位装置。     The positioning device according to claim 1, wherein the measurement value is an observation phase.
  6. 　前記計測値は、時間計測値である
    　請求項１から４のいずれか１項に記載の測位装置。     The positioning device according to claim 1, wherein the measurement value is a time measurement value.
  7. 　前記計測値は、ドップラー計測値である
    　請求項１から４のいずれか１項に記載の測位装置。     The positioning device according to claim 1, wherein the measurement value is a Doppler measurement value.
  8. 　発信機からの信号を受信する複数の受信センサによって計測される複数の計測値の中から外れ値を除外する外れ値除外処理ステップと、
    　前記外れ値除外処理ステップで前記外れ値が除外された後の前記複数の計測値から、前記発信機の位置を計測する測位計算ステップと、
    　を備え、
    　前記外れ値除外処理ステップは、
    　　前記複数の受信センサから異なる２個を選ぶセンサ組合せごとに、前記センサ組合せを構成する一方の受信センサによって計測された計測値と、他方の受信センサによって計測された計測値との差である計測値差を計算する計測値差計算ステップと、
    　　前記計測値差計算ステップで計算された前記センサ組合せごとの計測値差から、前記センサ組合せごとに計測値差残差を計算し、計算された前記センサ組合せごとの計測値差残差から、受信センサごとに残差和を計算する残差和計算ステップと、
    　　前記残差和計算ステップで計算された前記受信センサごとの残差和のうちの最大残差和を選択する最大残差和選択ステップと、
    　　前記最大残差和選択ステップで選択された前記最大残差和が閾値よりも大きいか否かを判定する閾値判定ステップと、
    　　前記閾値判定ステップで前記閾値よりも大きいと判定された前記最大残差和をとる受信センサを除外し、除外された前記受信センサに対応する計測値を前記外れ値として、前記複数の計測値の中から外れ値を除外する外れ値除外ステップと、
    　を有する測位方法。     Outlier exclusion processing step for excluding outliers from a plurality of measurement values measured by a plurality of receiving sensors that receive signals from a transmitter;
    From the plurality of measured values after the outlier is excluded in the outlier exclusion processing step, a positioning calculation step of measuring the position of the transmitter;
    With
    The outlier exclusion processing step includes:
    For each sensor combination that selects two different ones from the plurality of receiving sensors, the measurement is a difference between a measured value measured by one receiving sensor that constitutes the sensor combination and a measured value measured by the other receiving sensor. A measurement value difference calculating step for calculating a value difference;
    From the measured value difference for each sensor combination calculated in the measured value difference calculation step, the measured value difference residual is calculated for each sensor combination, and received from the calculated measured value difference residual for each sensor combination. A residual sum calculation step for calculating a residual sum for each sensor;
    A maximum residual sum selection step of selecting a maximum residual sum of residual sums for each of the reception sensors calculated in the residual sum calculation step;
    A threshold determination step for determining whether or not the maximum residual sum selected in the maximum residual sum selection step is larger than a threshold;
    The reception sensor that takes the maximum residual sum determined to be larger than the threshold value in the threshold determination step is excluded, and a measurement value corresponding to the excluded reception sensor is set as the outlier, and the plurality of measurement values An outlier exclusion step for excluding outliers from within,
    A positioning method having
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