WO 2017/134028
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`PCTflEP2017/051986
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`METHOD FOR CALIBRATING AN ACTIVE SENSOR SYSTEM
`
`The invention relates to a method for calibrating an active sensor system which comprises at least
`
`one active sensor A and one active sensor B. The concept “active” indicates that the sensors A
`
`and B actively emit signals.
`
`The sensor A has a transmitter TXA for emitting a signal STXA and a receiver RXA for receiving a
`
`signal SRXA, wherein the receiver RXA and the transmitter TXA operate independently of one
`
`another to the greatest possible extent in a RADAR mode of the sensor A. The sensor B has a
`
`transmitter TXB, a receiver RXB, and a unit D, by way of which the transmitter TXB is connected
`
`in a transponder mode of the sensor B with the receiver RXB, with the result that a signal SRXB
`
`received by the receiver RXB is emitted again by the transmitter TXB as a signal STXB. A gain
`
`Gem}; between the received signal SRXB and the signal STXB which is emitted again is predefined
`
`in this case. In a RADAR mode of the sensor B, the transmitter TXB is not connected to the
`
`receiver RXB, with the result that the transmitter TXB and the receiver RXB operate
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`independently of one another.
`
`The emitted signals may be, for example, RADAR signals, light signals or acoustic signals. In
`
`this respect, the proposed method is suitable for calibrating RADAR systems, LIDAR systems or
`
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`SONAR systems, for example.
`
`For the calibration of active sensor systems (for example satellite-supported RADAR or SAR
`
`systems, airborne radars or ground-based radars), active and passive reference targets with
`
`known backscatter properties are currently deployed.
`
`For the absolute calibration of RADAR systems, for example, primarily comer reflectors (comer
`
`reflectors), metal balls and metal plates are used (passively), as well as transponders (actively).
`
`The backscattering behavior can be calculated for simple passive targets by approximation. For
`
`realistic, complex or active targets, the backscattering behavior must be determined by means of
`
`more elaborate measurement technology. The measurement uncertainties thus generated add up
`
`and transfer directly to the calibrated active sensor systems. The calibration accuracy decreases
`
`as a result.
`
`The backscattering behavior of the reference targets currently used for calibrating such active
`
`sensor systems must be known exactly. For these purposes, the backscattering behavior is either
`
`captured by means of measurement technology, for instance by means of a calibrated measuring
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`PCTflEP2017/051986
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`instrument, which further increases the uncertainty as compared to the measuring instrument (as
`
`the calibrated accuracy decreases), or it is determined theoretically through simulation or other
`
`analytic methods. Both variations are afflicted by errors that affect the achievable total accuracy
`
`of the current calibration methods. The feedback of measurement values to a fundamental SI unit
`
`as is currently obtained through the calibration of such active sensor systems leads to respectively
`
`higher uncertainties. The reference targets currently used are expensive, due to their required
`
`magnitude and/or production accuracy, and as a result of their manufacturing tolerances they
`
`limit the calibration accuracy of the entire sensor system.
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`The task of the invention is to provide an improved calibration method that at least reduces the
`
`aforementioned disadvantages.
`
`The invention follows from the characteristics of the independent claims. Advantageous further
`
`developments and embodiments are subject of the dependent claims. Additional characteristics,
`
`application options, and advantages of the invention follow from the description and from the
`
`explanation of exemplary embodiments of the invention shown in the figures.
`
`A first aspect of the invention relates to a method for the (absolute) calibration of a sensor system
`
`comprising at least one sensor A and one sensor B, the sensor A having a transmitter TXA for
`
`emitting a signal STXA, and a receiver RXA for receiving a signal SRXA, wherein the receiver RXA
`
`and the transmitter TXA operate independently of one another in a RADAR mode of the sensor
`
`A, the sensor B having a transmitter TXB, a receiver RXB, and a unit D, by way of which the
`
`transmitter TXB is connected in a transponder mode of the sensor B with the receiver RXB, with
`
`the result that a signal SRXB received by the receiver RXB is emitted again by the transmitter TXB
`
`as signal STXB, a gain Gum; being predefined between the received signal SRXB and the signal
`
`STXB, which is emitted again, and the transmitter TXB not being connected to the receiver RXB in
`
`a RADAR mode of the sensor B, with the result that the transmitter TXB and the receiver RXB
`
`operate independently of one another, an object C being available for sending back an impinging
`
`signal either actively or passively, and the distance RAB between the sensor A and the sensor B,
`
`the distance RAC between the sensor A and the object C, and the distance RBC between the sensor
`
`B and the object C being known.
`
`The proposed method comprises the following steps.
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`WO 2017/134028
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`PCTflEP2017/051986
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`In a first step, a signal STX! ,C is emitted by the transmitter TX, with a transmitting output
`
`P7X1 ,C to object C, and the reception by the receiver RXi of the signal 512x, ,C subsequently
`
`emitted or reflected by object C with the reception output PRX‘ ,C for i e {A, B}, for determining
`
`the following ratios:
`
`
`
`O
`PVAC = PRXAac and PVBC = PRXB,
`PTXA ,c
`P1X3 ,C
`
`wherein:
`
`
`x1
`
`4
`
`PVAC = [4”]?ch ‘(GRX’A -G7X,A)‘[
`
`
`4
`750-
`
`P
`i
`
`12 Cj=1010
`
`
`x1
`
`PVBC: [4751330]
`
`4
`
`wherein:
`
`‘(GRX,B‘GIX,B)‘[ 12C]: 1010
`
`
`4
`”O-
`
`P
`i
`
`(GRXJ . Gm) :=
`
`the hardware gain of the sensor i for i e {A, B} that is to be determined,
`
`xi :=
`
`wave length,
`
`
`47:0}
`12
`
`_
`.=
`
`.
`.
`.
`equivalent gain of ob] ect C,
`
`0C :=
`
`radar backscatter cross-section of object C.
`
`In a second step, a signal SBA ,3 is emitted by the transmitter TXA with a transmitting output PMA ,3
`
`to sensor B, which is operated in transponder mode with the gain GeomB, and the reception by the
`
`receiver RXA of the signal subsequently emitted by Sensor B as SRXA , B with the reception output
`
`PRXA ,3 for determining the following ratio:
`
`
`P
`RXA’B = PVAB
`IXA,B
`
`wherein:
`
`4
`
`
`A
`471R“;
`
`PVAB =
`
`‘Gconfi
`
`PAB
`‘(GRXJB ‘GIX,B)‘(GRX,A ‘GIX,A) :10?-
`
`In a third step, calibration factors F501,,- are determined based on or traceable to the following
`
`ratio:
`
`1
`1
`Fm],A
`Foal,B :5 1
`GC
`— 1
`
`1
`_1
`1
`
`_1
`1
`1
`
`PAB _ CAB
`PAC _CAC
`PEG — CBC
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`WO 2017/134028
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`wherein:
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`Fcal,i=10 ' 10g (GRX,i ' GTX,i' Fscalej) fOI'l E {A, B},
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`PCTflEP2017/051986
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`
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`GC =10-log[4flO-Cj
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`Fscalai 1=
`
`scaling factor
`
`CAB, CAC, CBC := constants depending on /i and on the distances RAB, RAC, RBC.
`
`In a fourth step, sensors A and/or B are calibrated With the calibration factors FWu.
`
`The first and the second step may be performed simultaneously or in opposite order.
`
`Typically, the transmitters TXA, TXB and the receivers RXA, RXB operate on a predetermined
`
`wave length or frequency band and not exactly on a single wave length /i. The specified method
`
`may be modified for this purpose in such a manner that the wave length /i specified in the
`
`aforementioned forms respectively corresponds to an integral of all frequencies of a band-limited
`
`signal emitted by the respective transmitter TXi, With i E {A, B}.
`
`Advantageously, the transmitter TXB comprises a digital-to-analog converter (DAC) and a
`
`transmitting antenna, the receiver RXB comprises an analog-to-digital converter (ADC) and a
`
`receiving antenna, and the unit D comprises a unit for digital signal processing, connecting the
`
`transmitter TXB With the receiver RXB for the purpose of data communication in the transponder
`
`mode.
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`The unit D may comprise, for example, a signal amplifier, a time delay component, a signal
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`shaping component, etc., the modification of the signal in the unit D being known and
`
`deterministic. Advantageously, the signals received by receiver RXB in the transponder mode are
`
`amplified and/or filtered and/or time-delayed by the unit D before being conveyed to the
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`
`transmitter TXB.
`
`Advantageously, sensor A and sensor B are RADAR sensors (RADAR = Edio detection and
`
`ranging), SONAR sensors (SONAR = “gund Evigation and ranging), 0r LIDAR sensors
`
`(LIDAR = “_ight detection and ranging).
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`Advantageously, the distances RAB, RAC, RBC meet the following requirement:
`
`RAB, RAC, RBC > (2*D2) D»
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`WO 2017/134028
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`wherein
`
`D:
`
`9»:
`
`diameter of the respective transmitting antenna
`
`wave length of signal S.
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`PCTflEP2017/051986
`
`In an advantageous further development of the proposed method, steps 1 through 3 are repeated q
`
`times, wherein q = l, 2, 3, ..., such that the calibration factors F501,,- are determined as mean
`
`values < F501,,- >q (i E {A, B }). Naturally, other averaging methods are covered by the inventive
`
`concept as well. The averaging leads to an improvement of the calibration accuracy.
`
`In a typical application example of the proposed calibration method, the sensor A is a satellite-
`
`based RADAR system, the sensor B is a RADAR transponder, and the object C is a corner
`
`reflector. The sensor B may be a satellite-based RADAR system as well.
`
`An additional aspect of the invention pertains to a system comprising a sensor A, a sensor B, and
`
`a control and evaluation system connected with the two sensors A, B, wherein the control and
`
`evaluation system is adapted and designed for the implementation of a method as explained
`
`above.
`
`An additional aspect of the invention pertains to a computer system with a data processing
`
`device, wherein the data processing device is designed such that a method as explained above is
`
`executed on the data processing device.
`
`An additional aspect of the invention pertains to a digital storage medium with electronically
`
`readable control signals, wherein the control signals can interact with a programmable computer
`
`system, such that a method as described above is executed.
`
`An additional aspect of the invention pertains to a computer program product with a program
`
`code, stored on a machine-readable medium, for the implementation of the method as explained
`
`above, when the program code is executed on a data processing device.
`
`An additional aspect of the invention pertains to a computer program with program codes for the
`
`implementation of the method, as explained above, when the program runs on a data processing
`
`device. For these purposes, the data processing device may be embodied as an arbitrary computer
`
`system known from prior art.
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`PCTflEP2017/051986
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`Additional advantages, characteristics and details follow from the following description, in which
`
`at least one exemplary embodiment is described in detail, possibly with reference to the
`
`drawings. Identical, similar, and/or analog parts are marked with the same reference numbers.
`
`The figures show as follows:
`
`Fig. l
`
`Fig. 2
`
`Fig. 3
`
`a schematic block diagram of sensor A,
`
`a schematic block diagram of sensor B, and
`
`a schematic process flow of the proposed calibration method.
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`The invention describes a method for calibrating a radar system that is operated either in a
`
`stationary manner on the ground or in motion in the atmosphere or in space. Radar systems
`
`operated in motion often take the form of so-called “synthetic aperture radars” (SARs) and are
`
`often used for ground exploration purposes. The calibration of such complex radar systems,
`
`which are often based on so-called “active phased array” antennas and consequently features a
`
`plurality of different operating modes, is very complex and costly.
`
`The calibration of a measurement instrument or of a sensor involves generating a connection
`
`between measurement values of one or multiple fundamental physical units to the other. There
`
`are only seven such fundamental physical units in what is known as the SI System of Units. All
`
`other physical units are derived from them.
`
`The proposed method for calibrating a radar system allows for the direct calibration of the
`
`absolute system gain of the entire radar system without using a specially assigned radiometric
`
`calibration standard. The calibration factors (the connection between measured values and
`
`physical units) of the radar system are determined directly by way of comparing at least three
`
`units (of which two are sensors) with specific properties.
`
`At least one of the sensors (sensor A) has a transmitter TXA for emitting a signal STXA and a
`
`receiver RXA for receiving a signal SRXA, wherein the receiver RXA and the transmitter TXA
`
`operate independently of one another in a RADAR mode of the sensor A. Sensor A therefore
`
`represents a typical sensor, which operates according to the radar principle. Fig. 1 shows a
`
`respective block diagram. The receiver RXA features an analog-to-digital converter (ADC). The
`
`transmitter TXA features a digital-to-analog converter (DAC). In the RADAR mode, the
`
`transmitted signal STXA is independent of a received signal SRXA.
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`WO 2017/134028
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`PCTflEP2017/051986
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`Fig. 2 shows a block diagram of sensor B. The second sensor (sensor B) has a transmitter TXB, a
`
`receiver RXB, and a unit D, by way of which the transmitter TXB is connected in a transponder
`
`mode of the sensor B with the receiver RXB, with the result that a signal SRXB received by the
`
`receiver RXB is emitted again by the transmitter TXB as signal STXB, a gain Gem}; being
`
`predefined between the received signal SRXB and the signal STXB, which is emitted again, and
`
`with which the transmitter TXB is not connected with the receiver RXB in a RADAR mode of the
`
`sensor B, such that the transmitter TXB and the receiver RXB operate independently of one
`
`another. Switching between transponder mode and RADAR mode is done by way of switch S. In
`
`the illustrated form, the sensor B is switched to RADAR mode. The sensor B can therefore
`
`operate either according to the transponder principle or according to the radar principle. In the
`
`transponder mode (switch S is closed), a signal SRXB received by the receiver RXB is converted
`
`by the analog-to-digital converter into digital signals and conveyed to unit D. The unit D allows
`
`for the modification of the digital signal in a predetermined manner (for example by way of a
`
`predetermined time delay, by way of a predetermined gain, a predetermined deformation, etc.).
`
`From unit D, the possibly modified digital signal is transmitted to the transmitter TXB, where it is
`
`converted by a digital-to-analog converter (DAC) into an analog signal, which is then emitted via
`
`the transmitting antenna.
`
`In the RADAR mode of the sensor B, a signal STXB is generated and emitted via the antennas of
`
`the transmitter TXB. The signal is reflected or sent back and captured by the antenna of the
`
`receiver RXB. The switch S is open in this case, such that the unit D is not involved in this case.
`
`Advantageously, the unit D is a digital unit of which the exact behavior and properties are
`
`known.
`
`For the proposed calibration method, the following conditions are necessary:
`
`1.
`
`the sensor A is adapted and designed for capturing the backscatter properties of at least
`
`two additional objects Tr1 (n = l, 2, ..., N and N > 2,
`
`2. one of these additional objects is the sensor B, capable at least of capturing the
`
`backscatter properties of one of the other objects Tn. The sensor B must be able to operate
`
`both in a transponder mode and a RADAR mode.
`
`The proposed calibration method is explained by way of the example of a RADAR sensor
`
`system. A different active sensor system (for example: a SONAR system or a LIDAR system)
`
`may be used, as long as it meets the aforementioned conditions.
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`In the following, a fundamental equation system is described, from which a set of linear
`
`equations can be derived and solved. Depending on the properties of the calibrated objects, small
`
`differences show up in the equations.
`
`The backscatter properties of an object can be described by way of the so-called radar backscatter
`
`cross-section (or “radar cross section”, RCS). The radar backscatter cross-section am of a
`
`transponder m featuring a receiver with a reception gain GRX,m, a transmitter with a transmission
`
`gain GTX,m, and a gain of the unit Dm Gwnam, may be defined as follows:
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`10
`
`£2
`12
`(1) 0' =—-G =—-G
`m
`47?:
`m
`47?:
`
`-G
`
`TX,m
`
`RX,m
`
`-G
`
`can ,m
`
`in which /i stands for the wave length on which the system is operated.
`
`The capturing of targets with a radar system
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`
`Active targets (case 1 !
`
`Using the basic radar equation for point targets, the following is the result for the ratio of
`
`received to transmitted output of a sensor n, which captures the target Tm:
`
`(2)
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`20
`
` PR
`PM Tm
`
`,12
`=G ”Emu—'0».
`RX’
`T’
`(47:)3R4
`
`PR)“, defines the received output, and PT)“, defines the emitted output of the radar sensor n, GR)”,
`
`defines the gain of the receiver, GT”, defines the gain of the transmitter, and R defines the one-
`
`way distance from the sensor n to the target Tm. The notation Tm indicates the measurement of the
`
`target Tm. The measuring system is represented by n.
`
`If equation (1) is inserted into equation (2), the result is:
`
`4 G
`
`(G
`
`G
`
`) (G
`
` (3) PR”
`’1
`G )
`PTx’n T _
`472,-R
`comm
`RX,m
`Tx,m
`RX,n
`Tx,n
`The firstterm on the right side [ER] -Gm,m] (case 1) is known, whereas the product
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`fl,
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`4
`
`(GRXM - GT”) - (GRXJ, - GT”) is to be determined.
`
`Logarithmically, equation (3) leads to
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`(4)
`
`P” Tm = C
`
`nm,1
`
`+Gn,S +Gm,S
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`WO 2017/134028
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`PCTflEP2017/051986
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`wherein for CW 1:
`
`4
`
`
`
`(5) CW1 = lOlog[ A—] +lOlog(G
`
`47rR
`
`can,m )
`
`the system gain having to be determined as follows:
`
`(6)
`
`Gn,S = 1010?; (GRXJL ' GTx,n)
`
`(7)
`
`Gm,S = 1010?; (GRx,m ' GTx,m)
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`
`Passive targets (case 21
`
`For this purpose, the RADAR equation (2) must be expanded as follows:
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`15
`
`(8)
`
`P
`Rx,”
`PTX,”
`
` Tm at
`
`GRX,n . GTx,n) .[
`
`Logarithmically, equation (8) leads to
`
`(9)
`
`P”
`
` Tm
`
`= C
`
`nm,2
`
`+ Gms + GM
`
`
`
`
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`47mm ]12
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`in which Cm,“ is
`
`known:
`
`(10) CW = 10
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`4
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`log[—]
`
`471R
`
`the system gain haVing to be determined as follows:
`
`(11) Gn,S = 1010g(GRxn ' GTx,n)
`
`(12) Gm,P=10log£ 22m]
`
` 47m
`
`In this case, Gm]: is a gain that is proportional to the RADAR backscatter cross section of target
`In.
`
`Capturing targets with an image radar (case 3!
`
`The radar backscatter cross-section of a target, captured by an image radar can be described
`
`within an image that may have been generated through the processing of the recorded
`
`measurement data by way of the integrated pixel intensity with the aid of a calibration factor (a
`
`linear time-invariant system is presumed).
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`The output ratio
`
`
`PRx,n
`
`P
`Tx,n Tm
`
`of equation (3) may be replaced by an image intensity In and a
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`WO 2017/134028
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`scaling factor Fscale,n- If this approach is followed, a combined calibration factor can be
`
`determined, which converts the image intensity directly into backscatter cross sections.
`
`Active targets (case 3!
`
`Equation (3) for the radar capture of an active targets lead to:
`
`
`PRx,”
`
`TmPTX,”
`
`Tm
`
`4
`
`fl,
`47IR
`
`(13)
`
` I
`"
`
`(14)
`
`I”
`
`10
`
`
`Fsmle,n : [[—j .Geomm]. (GRX,n .GTx,n .Fsmle,n) . (GRX,m .GTx,m)
`Tm : [ER] .Goonm]. Foal,” .(GRX,m .GUM)
`
`2,
`
`4
`
`in which (GRXJ, - GT)”, - lem) = F501,, is a new combined calibration factor that is to be
`
`determined for the system. This calibration factor also comprises any gain resulting from the
`
`image generation (for example in case of SAR focusing).
`
`15
`
`Passive targets (case 41
`
`The aforementioned scaling may be applied to equation (8):
`
`PRx,”
`
`(15)
`
`In Tm _
`
`
`
`TX,” Tm
`
`. Fsmle,n : [fl] . (GRX,n . GTx,n . Fsmle,n) . E
`
`x1
`
`4
`
`
`47mm
`
`12
`
`j
`
`The equations (14) and (15), if logarithmically phrased, lead to a linear equation system.
`
`Depending on the calibrated system, the equations (3), (8), (14), and (15) are used in logarithmic
`
`representation in order to form a linear equation system.
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`If, for example, it is assumed that a sensor A operating in the RADAR mode, that a sensor B
`
`operates in the transponder mode and measures a corner reflector C, the ratios captured by the
`
`sensor A of the transmitted and received outputs PA TB and PA TC can be determined. In an
`
`additional step, the sensor B, which now operates in the RADAR mode, measures the corner
`
`reflector C. From this, the output ratio PB TCcan be determined.
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`
`Based on the logarithmic version of equation (3), the following system of linear equation can be
`
`phrased:
`
`(16)
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`35
`
`1
`1
`0
`
`1
`0
`1
`
`0
`1
`1
`
`
`CAB,1
`GA,S
`PA Ts
`
`- GM 2 PA TC — CAC,2
`
`GOP
`PB Tc
`CBC,2
`
`The constant terms CK,y are defined in the equation (5) and (10). The system gains GK, follow
`
`from the equations (6), (7), (11), and (12).
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`The solution of the equation system is done through the inversion of the matrices:
`
`(17)
`
`1
`1
`GAS
`GB“, 25 1
`Gap
`_1
`
`1
`—1
`1
`
`—1
`1
`1
`
`
`PATB
`
`PATC
`
`PBTC
`
`CM,1
`—
`— CA”
`_ CBC,2
`
`The solution of this equation leads to the system gain GA,S of the sensor A, to the system gain
`
`G353 of the sensor B, and to the equivalent gain Gcap of the target C.
`
`It from the equations (5) and (10), for example, that for calibrating an SAR system, only the
`
`measured output ratios, the calibration wave length /i of the measurement frequency and the
`
`distance R have to be known. For large distances, for example in case of satellite-based SAR
`
`systems, the proposed calibration method is less prone to errors as compared to constant offset
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`errors of the measurements.
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`Even though the aforementioned equations depart from a calibration wave length /i, they cannot
`
`be simply transferred to band-limited signals in which an integral of all frequencies is used.
`
`The aforementioned elaborations will be explained again in further detail below by way of an
`
`example. The example relates to the calibration of a satellite-based SAR system (sensor A), using
`
`a corner reflector (target C) and a radar/transponder (sensor B).
`
`Contrary to the customary calibration method of a satellite-based SAR system, in which a known
`
`calibration of a ground-based target is transferred to the satellite, the proposed method makes it
`
`possible to calibrate the SAR system on the satellite and the targets in a single step, in other
`
`words. The need to calibrate a ground targets in advance is removed. The satellite-based SAR
`
`system would be the sensor A operated in the RADAR mode. Furthermore, there would be a
`
`sensor B, which can be operated both in the transponder mode and in the RADAR mode. In
`
`addition, there would be a ground-based target C, which is a corner reflector.
`
`The absolute radiometric calibration of the satellite-based SAR system (sensor A) follows from
`
`three relative measurements of output ratios, the familiar distances between the sensors A and B,
`
`between the sensor B and the target C, and the wave length/frequency of the transmitter of the
`
`sensors A and B.
`
`In this example, the sensor B is also a satellite-based sensor. To begin with, the sensor A
`
`determines the output ratio when scanning the target C and the output ratio when scanning the
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`sensor B, the sensor B operating in the transponder mode. Independently thereof, the sensor B
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`determines the output ratio When scanning the passive target C.
`
`Using the logarithmic version of the three equations (8), (14), and (15) leads to the following
`
`
`equation system (in Which the indication of the captured target X T is not specified, for
`
`simplification purposes).
`
`(18)
`
`1
`
`1
`
`0
`
`1
`
`0
`
`1
`
`0
`
`1
`
`1
`
`Eal,A
`
`[AB
`
`CAB,1
`
`‘ G35
`
`2 [AC _ CAC,2
`
`Gas
`
`PBC
`
`CBC,2
`
`IAB and IAC are here the measured image intensities (in case of SAR after focusing) of the sensor
`
`A for the targets of sensor B and comer reflector C. PBC is the output ratio determined by the
`
`transponder B When scanning the corner reflector C. Foam is the calibration factor that is to be
`
`determined, Which converts RCS values directly into image intensities (for this, compare With
`
`equation (14)). Gcap is the backscatter cross section-equivalent gain of the corner reflector, and
`
`G353 is the system gain of the transponder (sensor B). The constant part of the three equations
`
`follows for:
`
`4
`
`’
`
`47rR
`
`’
`
`(19) CAB 1 = 1010g[i] +1010g(Gc0n B)
`A”
`g[475R]
`E”
`g[4m]
`
`(20) C
`
`/’L
`= 1010 —
`
`(21) C
`
`/1
`21010 —
`
`4
`
`4
`
`Inverting the system leads to:
`
`(22)
`
`1
`1
`Eal,A
`FB,S 2; 1
`Gap
`‘1
`
`1
`_1
`1
`
`_1
`1
`1
`
`[AB _ CAB,1
`[AC _CAC,2
`[BC _CBC,2
`
`The backscatter cross section-equivalent gain Gcap of the passive target C is not explicitly
`
`necessary for the calibration of the radar system, but may be of interest in order to convert it back
`
`into a backscatter cross section (RCS) of the corner reflector C (compare With equation (12)).
`
`This also provides an immediate absolute calibration of the target C.
`
`The proposed method for calibrating an active sensor system makes possible an increased
`
`calibration accuracy based on less relevant sources of inaccuracy, on the possibility of
`
`compensating expansion effects, and on dispensing With reference targets calibrated in advance.
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`Fig. 3 shows a schematic flow of the proposed method for calibrating an sensor system
`
`comprising at least a sensor A and a sensor B, the sensor A having a transmitter TXA for emitting
`
`a signal STXA, and a receiver RXA for receiving a signal SRXA, wherein the receiver RXA and the
`
`transmitter TXA operate independently of one another in a RADAR mode of the sensor A, the
`
`sensor B having a transmitter TXB, a receiver RXB, and a unit D, by way of which the transmitter
`
`TXB is connected in a transponder mode of the sensor B with the receiver RXB, with the result
`
`that a signal SRXB received by the receiver RXB is emitted again by the transmitter TXB as signal
`
`STXB, a gain Gem}; being predefined between the received signal SRXB and the signal STXB, which
`
`is emitted again, and with which the transmitter TXB is not connected with the receiver RXBin a
`
`RADAR mode of the sensor B, such that the transmitter TXB and the receiver RXB operate
`
`independently of one another, an object C being available for sending back an impinging signal
`
`either actively or passively, and the distance RAB between the sensor A and the sensor B, the
`
`distance RAC between the sensor A and the object C, and the distance RBC between the sensor B
`
`and the object C being known.
`
`The method comprises the following steps.
`
`In a first step 101, a signal S,X ,C is emitted by the transmitter TXi with a transmitting output
`
`PIX! ,C to the object C, and the capture of the signal SRX! ,0 subsequently emitted or reflected from
`
`object C by the receiver RXi with the reception output PRX‘ ,C for i E {A, B} for determining the
`ratios:
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`15
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`20
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`
`
`P
`P
`PVAC = RXA,C and PVBC = RXB,C
`TXA ,C
`TXB ,C
`
`25
`
`wherein:
`
`
`a
`
`—
`
`4
`
`4
`
`//i,
`
`30
`
`j - 1010
`12
`PVAC— [4”]?ch (GRX’A GUM) E
`PVBC= [E (GRXB~GIX,B)'[ 12C]: 10?
`
`.
`
`
`4
`flO-C
`
`.
`
`P
`— i
`
`
`47Z'O-
`
`PBC
`
`wherein:
`
`(GRXi - Gym) :=
`
`the hardware gain of the sensor i for i E {A, B} that is to be determined,
`
`35
`
`/l :=
`
`wave length,
`
`
`4720}:
`22
`
`:=
`
`.
`.
`.
`equivalent gain of object C,
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`CC :=
`
`radar backscatter cross-section of object C.
`
`In a second step 102, a signal SIXA ,Bis emitted by the transmitter TXA with a transmitting output PIXA ,B
`
`to sensor B, which is operated in transponder mode with the gain Geon,B , and the reception by the
`
`receiver RXA of the signal subsequently emitted by Sensor B as SRXA , B with the reception output PRXA ,B
`
`for determining the following ratio:
`
`
`P
`RXA’B = PVAB
`PIXA,B
`
`wherein:
`
`4
`
`
`l
`471R”
`
`PVAB =
`
`10
`
`‘Gconfi
`
`PAB
`‘(GRXJB ‘GIX,B)‘(GRX,A ‘GIX,A) = 10?:
`
`In a third step 103, calibration factors F501,,- are determined based on or traceable to the following
`
`COHtCXtI
`
`1
`1
`Foam
`FcaLB _ _ 1
`2
`
`1
`_1
`
`_1
`1
`
`PAB _ CAB
`PAC _ CAC
`
`15
`
`GC
`
`—1
`
`1
`
`1
`
`PRC—CBC
`
`wherein:
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`
`Fcal,i=10 ' 10g (GRXJ ' GIXJ ' Fscalej) fOI'l E {A, B}
`
`
`
`GC =lO-logE47/[g-C]
`
`Fscalai 1=
`
`scaling factor
`
`CAB, CAC, CBC := constants depending on /i and on the distances RAB, RAC, RBC.
`
`In a fourth step 104 involves the calibration of the sensors A and B using the calibration factors
`
`F501,,- and of the target C via the backscatter cross section-equivalent gain Gc.
`
`Even though the invention is explained in detail and illustrated by way of preferred exemplary
`
`embodiments, the invention is not limited to the disclosed examples, and other variations may be
`
`derived from them by the person skilled in the art without leaving the protective scope of the
`
`invention. It is therefore clear that there is a plurality of possible variations. It is also clear that
`
`exemplary embodiments are really only examples that should not in any way be understood as a
`
`limitation of the scope of protection, of the application options, or of the configuration of the
`
`invention. In fact, the description above and the description of the figures allow the person
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`skilled in the art to concretely implement the exemplary embodiments While being able, With the
`
`knowledge of the disclosed inventive concept, to make numerous amendments, for example With
`
`respect to the function or the arrangement of individual elements mentioned in the context of an
`
`exemplary embodiment, Without leaving the scope of protection defined by the claims and their
`
`legally corresponding passages such as the extensive explanations in the description.
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`Reference list
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`5
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`101 - 104
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`The steps of the method
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