Patent Grant
11899097
This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2020-159572 filed in Japan on Sep. 24, 2020; the entire contents of which are incorporated herein by reference.
Embodiments described herein relate generally to a distance measurement device and a distance measurement method.
Recently, a system with which doors of an automobile can be locked and unlocked by pressing a button of a key-fob without inserting a key into a keyhole has been employed on a large number of automobiles. In the system, the doors are locked and unlocked by using wireless communication between the key-fob and the automobile.
In addition, recently, a system with which doors can be locked and unlocked and an engine can be started without touching a key-fob has been employed.
However, incidents in which an automobile is stolen by performing an attack called a “relay attack” on wireless communication between a key-fob and the automobile have been occurring. In a proposed countermeasure against the attack, a distance between the key-fob and the automobile is measured, and control of the automobile through wireless communication is prohibited when it is determined that the measured distance is equal to or longer than a predetermined distance.
The distance between the key-fob and the automobile is measured by, for example, a method in which a predetermined radio frequency (RF) signal (distance measurement signal) is transmitted from one of a distance measurement device mounted on the key-fob and a distance measurement device mounted on the automobile, the transmitted distance measurement signal is received by the other distance measurement device, a time difference between a transmission time point and a reception time point, in other words, a flight time of the distance measurement signal is measured or estimated, and the obtained flight time is multiplied by a light speed to obtain the distance.
A distance measurement device of an embodiment includes a first device, a second device, and a calculation unit. The first device includes a first reference signal source configured to generate a first reference signal, and a first transmitter-receiver configured to transmit a modulated first distance measurement signal, receive a modulated second distance measurement signal, obtain a second demodulated signal through demodulation, and acquire second phase information of the second demodulated signal in a first sampling period based on the first reference signal. The second device includes a second reference signal source configured to operate independently from the first reference signal source and generate a second reference signal, and a second transmitter-receiver configured to transmit the second distance measurement signal, receive the first distance measurement signal, obtain a first demodulated signal through demodulation, and acquire first phase information of the first demodulated signal in a second sampling period based on the second reference signal. The calculation unit calculates a distance between the first device and the second device based on the first phase information and the second phase information. One of the first distance measurement signal and the second distance measurement signal is transmitted once or more, and another is transmitted twice or more. The calculation unit calculates the distance based on a total of three or more pieces of the first phase information and the second phase information acquired through transmission of the first distance measurement signal and the second distance measurement signal three times or more in total, the first sampling period, and the second sampling period.
(Configuration)
The distance measurement device includes a device A1 (hereinafter referred to as a device A) and a device B2 (hereinafter referred to as a device B) configured to perform wireless communication through a radio frequency (RF) signal. The device A and the device B are separated from each other by a certain distance, and the distance may time-sequentially change (at least one of the device A and the device B may be movable) but distance change in a time period in which distance measurement is performed once is negligible.
The device A includes a processor 11, a memory 12, a first reference signal source 13, and a first transmitter-receiver 14.
The device B includes a processor 21, a memory 22, a second reference signal source 23, and a second transmitter-receiver 24.
The first reference signal source 13 generates a first reference clock (first reference signal) and supplies the first reference clock to the processor 11, the memory 12, and the first transmitter-receiver 14.
The memory 12 stores a processing program to be executed by the processor 11, and various kinds of data used in processing at the processor 11.
The processor 11 controls transmission and reception operation of the first transmitter-receiver 14 in accordance with the processing program stored in the memory 12.
The first transmitter-receiver 14 generates a first sampling clock based on the first reference clock supplied from the first reference signal source 13. The first transmitter-receiver 14 transmits a modulated first distance measurement signal, receives a modulated second distance measurement signal transmitted from the second transmitter-receiver 24, and obtains a second demodulated signal through demodulation. The first transmitter-receiver 14 samples second phase information of the second demodulated signal at a timing of the first sampling clock.
In addition, the processor 11 calculates, based on a phase of a distance measurement signal sampled by the first transmitter-receiver 14, a flight time of the distance measurement signal in accordance with the processing program stored in the memory 12, and calculates a flight distance (distance between the device A and the device B) by multiplying the flight time by a light speed c.
The second reference signal source 23 operates independently from the first reference signal source 13, generates a second reference clock (second reference signal), and supplies the second reference clock to the processor 21, the memory 22, and the second transmitter-receiver 24.
The memory 22 stores a processing program to be executed by the processor 21, and various kinds of data used in processing at the processor 21.
The processor 21 controls transmission and reception operation of the second transmitter-receiver 24 in accordance with the processing program stored in the memory 22.
The second transmitter-receiver 24 generates a second sampling clock based on the second reference clock supplied from the second reference signal source 23. The second transmitter-receiver 24 transmits the second distance measurement signal, receives the first distance measurement signal, and obtains a first demodulated signal through demodulation. The second transmitter-receiver 24 samples first phase information of the first demodulated signal at a timing of the second sampling clock.
In addition, the processor 21 calculates, based on a phase of a distance measurement signal sampled by the second transmitter-receiver 24, the flight time of the distance measurement signal in accordance with the processing program stored in the memory 22, and calculates a flight distance (distance between the device A and the device B) by multiplying the flight time by the light speed c.
Note that the processor 11 and the processor 21 are a calculation unit configured to calculate the distance between the first device and the second device based on the first phase information and the second phase information. However, only one of the processor 11 and the processor 21 may be the calculation unit.
In the embodiment, a relatively narrow band signal using known modulation wave is used as each distance measurement signal. Specifically, a modulated signal is a gaussian filtered minimum-shift keying (GMSK) signal that repeats 0 and 1.
The first transmitter-receiver 14 and the second transmitter-receiver 24 each demodulate a received GMSK signal by separating the GMSK signal into an in-phase component (I signal) and an orthogonal component (Q signal). The phase of the GMSK signal can be calculated based on the I and Q signals.
As illustrated in
The phase θGMSK of the GMSK signal can be approximated by Expression (1).
θGMSK≈A01 sin(2πf01t)+θOFF (1)
In the expression, A01 represents an amplitude of the phase of the GMSK signal, which repeats 0 and 1 (0 for a case in which the phase decreases, and 1 for a case in which the phase increases), f01 represents a basic frequency (reciprocal of a basic period T01) of the phase of the GMSK signal, which repeats 0 and 1, in other words, half of a transmission frequency of the GMSK signal, and θOFF represents an offset phase of the phase of the GMSK signal, which repeats 0 and 1, in other words, π/4. When a time is to be measured, for example, a time in which θGMSK indicated in Expression (1) becomes θOFF may be detected.
When frequencies (sampling frequencies) of the sampling clocks of the device A and the device B are set to be high, time resolution is high, and thus the time in which the phase θGMSK becomes θOFF is accurate. However, with taken into consideration low electric power consumption, it is desired that each sampling frequency is, for example, 16 times approximately higher than the basic frequency of the phase signal θGMSK. To clearly determine in which of four quadrants a phase of the sine wave exists, each sampling clock needs a frequency four times or more higher than the basic frequency of the phase signal θGMSK.
Under such a condition, accuracy of measurement of the flight time can be prevented from significantly decreasing by sampling the phase θGMSK based on the sampling clock of each of Devices A and B and applying a signal that can be approximated to the sine wave indicated in Expression (1). Note that, in the following description, a “signal that can be approximated to a sine wave” is simply referred to as a sinusoidal signal as long as no interpretation problem occurs. In addition, it is assumed that a sinusoidal signal such as the GMSK signal indicated in Expression (1) is used as a distance measurement signal.
A sinusoidal signal (distance measurement signal) starting at the phase θOFF is transmitted at the sampling timing of the device A, and the distance measurement signal is received by the device B after a flight time tx in accordance with the distance between Devices A and B has elapsed. In the time chart of
A time point at which the phase θGMSK,b at the device B is sampled is a time point at which a time period to has elapsed since the distance measurement signal starting at the phase θOFF arrives at the device B. After a predetermined process time period Tpres in which various kinds of calculation and the like are performed has elapsed since reception of the distance measurement signal is detected, the device B transmits a distance measurement signal at the sampling timing of the device B.
The distance measurement signal transmitted from the device B is received by the device A after elapse of the flight time tx. A time point at which the phase θGMSK,a is sampled at the device A is a time point at which a time period ta has elapsed since the sinusoidal signal (distance measurement signal) starting at the phase θOFF arrives at the device A.
The elapsed time ta is calculated by Expression (2) from the phase θGMSK,a sampled by the device A, and the elapsed time to is calculated by Expression (3) from the phase θGMSK,b sampled by the device B.
ta≈{1/(2πf01}sin−1{(θGMSK,a−θOFF)/A01} (2)
tb≈{1/(2πf01)}sin−1{(θGMSK,b−θOFF)/A01)} (3)
Note that, in
A round trip time RTT elapses until the device A receives a signal from the device B after the device A transmits a signal. As understood from
RTT=2tx+ta+tb+Tpres (4)
In the expression, a difference between the round trip time RTT and the process time period Tpres is equal to the sampling period TS, and thus Expression (5) is obtained.
TS=2tx+ta+tb (5)
Expression (5) can be rewritten as Expression (6).
tx=(TS−ta−tb)/2 (6)
Thus, the flight time tx can be accurately obtained through Expression (6) by calculating the elapsed time ta through Expression (2), calculating the elapsed time tb through Expression (3), and using the known sampling period TS.
However, when there is error between the period (reciprocal of the frequency) of the first reference clock of the device A and the period of the second reference clock of the device B, error occurs to the flight time tx calculated through Expression (6). The error occurs by a reason described below.
For example, assume that the reference clock period TA of the device A is accurate and has no error and the reference clock period TB of the device B has error. A ratio TB/TA of the reference clock period TB of the device B relative to the reference clock period TA of the device A is defined by Expression (7).
TB/TA=1−rerr (7)
In the expression, rerr represents an error ratio of the reference clock period TB. A sample signal is generated by dividing or multiplying a reference clock signal, and each sampling frequency is proportional to the reference clock frequency. Thus, a ratio TSB/TS of the sampling period TSB of the device B relative to the sampling period TS of the device A is expressed by Expression (8) similar to Expression (7).
TSB/TS=1−rerr (8)
Note that the sampling period of the device A is not written as TSA because no error is assumed.
When a time period TpresB taken for a process at the device B is N times longer than the sampling period of the device B, Expression (9) is obtained.
TpresB=NTSB (9)
A numerator and a denominator on a left-hand side of Expression (8) are each multiplied by N to obtain Expression (10).
NTSB/NTS=1−rerr (10)
Both sides of Expression (10) are multiplied by NTS to obtain Expression (11).
NTSB=NTS−rerrNTS (11)
Since NTS is the process time period Tpres when the clock period has no error, Expression (12) is obtained by substituting Expression (9) into a left-hand side of Expression (11).
TpresB=Tpres−rerrTpres (12)
Expression (12) indicates that the process time period TpresB of the device B is shorter than the process time period Tpres when there is no error by rerrTpres.
In
Thus, an elapsed time t′a since signal arrival at the device A, which is detected at the sampling timing of the device A, when the clock period of the device B has error is longer by rerrTpres than the elapsed time ta since signal arrival at the device A, which is detected at the sampling timing of the device A, when the clock period of the device B has no error, and accordingly, Expression (13) holds.
t′a=ta+rerrTpres (13)
When t′a to which error occurs is substituted into ta in Expression (6) to calculate a flight time t′x, Expression (14) is obtained.
t′x=(TS−ta−tb−rerrTpres)/2 (14)
As understood from comparison of Expression (14) with Expression (6), error due to rerrTpres occurs to the flight time t′x. For example, when the process time period Tpres is 100 [μs] and rerr is 40 [ppm], rerrTpres/2 is 2 [ns]. Conversion into distance by multiplying 2 [ns] by the light speed indicates that a distance error of 0.6 [m] occurs. The distance error further increases as the process time period and the clock period error further increase.
Subsequently, discussion is made on error that occurs to the flight time when a distance measurement signal makes one round trip starting at the device B with the setting of Expression (7).
In
When the distance measurement signal makes one round trip in a reverse order, as well, the round trip time RTT is expressed by Expression (4) and the flight time tx is expressed by Expression (6) as long as the reference clock periods of Devices A and B are both accurate.
However, when the distance measurement signal makes one round trip between the device B illustrated at the lower part and the device A illustrated at the upper part in
RTTB represents the round trip time RTT detected based on an internal clock of the device B and is expressed by Expression (15).
RTTB=2tx+ta+t′b+Tpres (15)
In the expression, t′b is an elapsed time calculated by Expression (3) based on a detection phase θ′GMSK,b of a GMSK signal received by the device B. Since RTTB=(N+1)TSB, Expression (16) is obtained by using Expression (8) and Tpres=NTS.
RTTB=(N+1)TS−rerr(N+1)TS=Tpres+TS−rerr(N+1)TS (16)
Comparison of right hand sides of Expressions (15) and (16) obtains Expression (17).
TS=2tx+ta+t′b+rerr(N+1)TS (17)
Comparison of Expressions (5) and (17) obtains Expression (18).
t′b=tb−rerr(N+1)TS (18)
Expression (18) means that a timing at which the distance measurement signal received from the device A is sampled by the device B at the lower part when the round trip time RTTB has elapsed is earlier by rerr(N+1)TS than a timing at which the distance measurement signal received from the device A is sampled by the device B at the middle part.
When t′b to which error has occurred is substituted into Expression (6) to calculate a flight time t″x and Tpres=NTS is used, Expression (19) is obtained.
t″x=(TS−ta−tb+rerrTpres+rerrTS)/2 (19)
Comparison between Expression (14), which is obtained as the distance measurement signal makes one round trip starting at the device A, and Expression (19), which is obtained as the distance measurement signal makes one round trip starting at the device B indicates that the error time period rerrTpres has opposite signs between the expressions. In addition, the other error time period rerrTS in Expression (19) is clearly small as compared to rerrTpres. Thus, the terms rerrTpres are eliminated by averaging the flight time t′x estimated by Expression (14) and the flight time t″x estimated by Expression (19), and the accuracy of the estimated time clearly improves.
For example, rerrTpres/4=1.25 [μs] is obtained for rerr=40 [ppm] and TS=125 [ns]. Conversion into distance by multiplying 1.25 [ps] by the light speed obtains a distance error of 0.4 [mm], which indicates significant improvement of measurement accuracy as compared to the distance error of 0.6 [m] when the distance measurement signal makes one round trip starting at the device A.
Thus, significant accuracy improvement of an estimated distance is achieved when the distance measurement signal is transmitted in the following order of the device A to the device B and distance measurement is performed, the distance measurement signal is transmitted in the following order of the device B to the device A and distance measurement is performed again, and results of the two distance measurements are averaged.
However, in
The elapsed time ta illustrated in
Thus, the elapsed time ta illustrated in
Specifically, it is described that, even when the distance measurement signal is transmitted by the device B with delay of a predetermined number of clocks, for example, L clocks, the flight time expressed by Expression (19) when the distance measurement signal is transmitted without delay holds, and the estimated flight distance is same irrespective of a time point at which the distance measurement signal is transmitted.
A distance measurement result obtained by the first-time distance measurement is same as Expression (19).
In the second-time distance measurement, the distance measurement signal is transmitted from the device B after the time period LTSB has elapsed since the first-time distance measurement signal is transmitted by the device B. A time at which the transmitted distance measurement signal is received by the device A is represented by taL. The time taL is a time calculated by substituting a phase θGMSK,aL observed (sampled) by the device A into Expression (2).
When the process time period Tpres=NTS has elapsed since the phase θGMSK,aL of the distance measurement signal is detected, the distance measurement signal is transmitted by the device A. The device B observes (samples) a phase θ′GMSK,bL of the distance measurement signal from the device A and substitutes the phase into Expression (3) to calculate an elapsed time t′bL.
The time period LTSB that has elapsed until the distance measurement signal is transmitted by the device B in the second-time distance measurement since the distance measurement signal is transmitted by the device B in the first-time distance measurement is expressed by Expression (20) by using Expression (8).
LTSB=LTS−rerrLTS (20)
A transmission time point of the distance measurement signal of the device B is earlier by rerrLTS with respect to the device A. Thus, a time at which the distance measurement signal is received by the device A is earlier by the same amount, and accordingly, taL is given by Expression (21).
taL=ta+rerrLTS (21)
However, since the round trip time RTTB=(N+1)TSB is constant, the round trip time in the first-time distance measurement and the round trip time in the second-time distance measurement are same. The round trip time RTTB in the second-time distance measurement is given by Expression (22).
RTTB=2tx+taL+t′bL+Tpres (22)
Since Expression (22) is same as Expression (15), t′bL is given by Expression (23).
t′bL=tb−rerr(N+1)TS−rerrLTS (23)
The flight time tx is calculated by substituting taL into ta and substituting t′bL into tb in Expression (6) while assuming that the device A and the device B operate at accurate clocks. Accordingly. Expression (24) is obtained.
tx=(TS−taL−t′bL=(TS−ta−tb+rerrTpres+rerrTS)/2 (24)
Since Expressions (19) and (24) are same, a distance measurement result when the distance measurement signal is transmitted in the following order of the device B to the device A is same irrespective of a distance measurement start time. Thus, after the distance measurement signal is transmitted in the following order of the device A to the device B and the first-time distance measurement is performed, the distance measurement signal is transmitted in the following order of the device B to the device A and the second-time distance measurement is performed, and results of the two distance measurements are averaged to obtain the flight time and hence the flight distance at improved accuracy.
In
When a flight time estimated from tb1 and ta1 is represented by tx1 and a flight time estimated from tb2 and ta2 is represented by tx2, Expressions (25) and (26) are obtained from Expressions (14) and (24), respectively.
tx1=(TS−ta1−tb1)/2=(TS−ta−tb−rerrTpres)/2 (25)
tx2=(TS−ta2−tb2)/2=(TS−ta−tb+rerrTpres+rerrTS)/2 (26)
Thus, the flight time tx obtained by averaging tx1 and tx2 is given by Expression (27).
tx=(tx1+tx2)/2={TS−ta−tb+(rerrTS)/2}/2 (27)
According to the first embodiment, round trip sequences with different starting points, namely, a distance measurement sequence in which the distance measurement signal makes a round trip starting at the device A and a distance measurement sequence in which the distance measurement signal makes a round trip starting at the device B are performed, and flight times obtained by the respective distance measurement sequences are averaged. Accordingly, when the reference clock periods of the device A and the device B have error, error of an estimated flight time can be significantly reduced, and thus, error of the flight distance obtained by multiplying the flight time by the light speed can be significantly reduced.
Specifically, in the present embodiment, a time offset (TOFF illustrated in
Note that although flight times are averaged in the above description, flight distances may be calculated from the flight times and then averaging may be performed, or sampled phases may be averaged and then a flight time and a flight distance may be calculated (refer to Expression (72) in a seventh embodiment, for example).
In a second embodiment, any part same as a part in the first embodiment is denoted by the same reference sign, description of the part is omitted, and difference will be mainly described.
In the above description, elapsed times until phase signals are sampled since crossing the phase offset θOFF corresponding to a zero cross point are measured by Devices A and B. In description of the first embodiment, the phase θGMSK,a or θGMSK,b at a sample point right after reception is started is measured, and one phase data is targeted.
However, when one reception duration of the distance measurement signal is long as compared to a period 1/f01 of the distance measurement signal, and for example, the distance measurement signal of K periods (K is a natural number) can be received, an elapsed time until sampling since crossing of a plurality of phase offsets θOFF can be measured in one reception duration of the distance measurement signal. In this case, measurement variance of phase detection due to noise and the like can be prevented by detecting the phase a plurality of times and averaging the phases, and thus the flight time tx can be accurately estimated.
However, it is needed to prove that, when there is a frequency offset between the reference clocks of Devices A and B, the flight time tx calculated by one phase detection is equal to the flight time tx calculated by detecting the phase a plurality of times and performing averaging. The following proves that these flight times are equal.
Assume that, when there is no frequency error, the period 1/f01 of the distance measurement signal is m times longer than the sampling period TS, and a duration in which the distance measurement signal is received is K/f01.
First, when the distance measurement signal is transmitted from the device A to the device B, a sum tsumB of detection elapsed times sampled K times (elapsed times until sampling since crossing of θOFF) is calculated with reference to
A time at which the distance measurement signal is sampled by the device B for the first time is referred to as a time tb1 based on a detection phase θGMSK,b1. An elapsed time until next phase detection since phase detection for the first time is represented by mTSB.
A detection time for the second time is earlier than a correct time by rerrmTS by using Expression (8) because mTSB has elapsed since a detection time for the first time, and thus an observed time is tb1−rerrmTS.
Similarly, by analogy, a k-th detection time is tb1−(k−1)rerrmTS. Thus, the sum tsumB of the first to K-th detection times is given by Expression (28).
tsumB=Σ1K{tb1−(k−1)rerrmTS}=K(tb1+rerrmTS)−{K(K+1)/2}rerrmTS (28)
Thus, an average of tsumB when detection is performed K times is given by Expression (29).
tsumB/K=tb1−{(K−1)/2}rerrmTS (29)
When the distance measurement signal is transmitted from the device A to the device B, an average of elapsed times detected K times at intervals of m sampling periods is shorter than an elapsed time detected only once on the first time by an elapsed time {(K−1)/2}rerrmTS.
Subsequently, an elapsed time based on phases detected K times by the device A when the distance measurement signal is transmitted from the device B to the device A after the time period NTSB has elapsed is calculated with reference to
An elapsed time calculated based on initial phase detection is represented by ta1. A time difference between first phase detection and second phase detection is mTS, time advances by rerrmTS at the device B in mTS, and the distance measurement signal is transmitted earlier accordingly. Thus, an elapsed time calculated based on the second phase detection is ta1+rerrmTS.
Similarly, by analogy, a k-th detection elapsed time is ta1+(k−1)rerrmTS. Thus, a sum tsumA of the first to K detection elapsed times is given by Expression (30).
tsumA=Σ1K{ta1+(k−1)rerrmTS}=K(ta1−rerrmTS)+{K(K+1)/2}rerrmTS (30)
Thus, an average of tsumA when detection is performed K times is given by Expression (31).
tsumA/K=ta1+{(K−1)/2}rerrmTS (31)
When the distance measurement signal is transmitted from the device B to the device A, an average of elapsed times detected K times at intervals of m sampling periods is longer than an elapsed time detected only once on the first time by the elapsed time {(K−1)/2}rerrmTS.
However, when tsumA/K and tsumB/K are used in place of ta and tb in Expression (6), a flight time tx1_avg of an initial round trip is estimated as in Expression (32).
tx1_avg={TS−(tsumA/K)−(tsumB/K)}/2=(TS−ta1−tb1)/2=(TS−ta−tb−rerrTpres)/2=tx1 (32)
This is same as a flight time without averaging.
In the first embodiment, when a flight time is calculated through one phase detection, error due to a frequency difference included in the estimated flight time tx1 is reduced by averaging elapsed times calculated by using a sequence in which the distance measurement signal is transmitted from the device A to the device B, from the device B to the device A, from the device B to the device A, and from the device A to the device B as illustrated in
Similarly, in the present embodiment, error of flight time estimation is reduced by using the sequence illustrated in
A sequence on first and second rows in
As illustrated on the third and fourth rows in
Thereafter, when phases are detected K times, a sum tsumA2 of elapsed times calculated from the detected phases is equal to an expression obtained by replacing ta1 with ta2 in Expression (30). Thus, an average tsumA2/K of tsumA2 is given by Expression (33).
tsumA2/K=ta2+{(K−1)/2}rerrmTS (33)
Subsequently, when the distance measurement signal is transmitted from the device A to the device B and the distance measurement signal is received by the device B, a first detection phase is θGMSK,b2, and an elapsed time corresponding to the detection phase is tb2.
Thereafter, when phases are detected K times, a sum tsumB2 of elapsed times calculated from the detected phases is equal to an expression obtained by replacing tb1 with tb2 in Expression (29). Thus, an average tsumB2/K of tsumB2 is given by Expression (34).
tsumB2/K=tb2−{(K−1)/2}rerrmTS (34)
When tsumA2/K and tsumB2/K are used in place of ta and tb in Expression (6), a flight time of a second round trip is estimated as in Expression (35), which is same as an estimated flight time without averaging.
tx2_avg={TS−(tsumA2/K)−(tsumB2/K)}/2=(TS−ta−tb2)/2=(TS−ta−tb+rerrTpres+rerrTS)/2=tx2 (35)
A flight time tx_avg is calculated by averaging tx1_avg and tx2_avg as in Expression (36).
tx_avg=(tx1_sum+tx2_sum)/2={TS−ta−tb+(rerrTS/2)}/2=tx (36)
A flight time obtained by performing phase detection K times in a sequence in which the distance measurement signal is transmitted from the device A to the device B, from the device B to the device A, from the device B to the device A, and from the device A to the device B in the stated order and averaging elapsed times obtained from detected phases is same as a flight time obtained by performing phase detection once. However, the same result is obtained by an expectation value, and a result of the averaging has reduced error attributable to measurement variance.
According to the second embodiment, effects substantially same as effects of the first embodiment described above are achieved, and in addition, distance measurement can be performed at higher accuracy by increasing the amount of data sampled through the distance measurement sequence and averaging the obtained data.
In the distance measurement sequence illustrated in
In the sequence in
As indicated by comparison between Expressions (19) and (24), one-round-trip distance measurement sequence of the device B to the device A obtains a unique flight time tx2 irrespective of a starting point of time. Thus, an elapsed time observed in the sequence of the device B to the device A illustrated in
Note that although not illustrated, it is clear that the method of performing phase detection K times for each m samples and averaging elapsed times obtained from detected phases according to the second embodiment is also applicable to the present embodiment.
According to the third embodiment, it is possible to reduce the distance measurement time period by using the 1.5-round-trip distance measurement sequence in effect in place of the two-round-trip distance measurement sequence in the first and second embodiments described above. In a specific example, a time period reduced by the sequence in
In a fourth embodiment, any part same as a part in the first to third embodiments is denoted by the same reference sign, description of the part is omitted, and difference will be mainly described.
Calculation of the flight time tx needs data of the elapsed times ta1 and ta2, tb1, and tb2 until sampling since crossing of the phase offset θOFF, the data being obtained through phase detection by the device A and the device B.
Data of tb1 and tb2 needs to be sent from the device B to the device A to calculate the flight time tx at the device A, and data of ta1 and ta2 needs to be sent from the device A to the device B to calculate the flight time tx at the device B.
This communication of distance measurement data is performed by using typical digital communication after the distance measurement data is detected. A time taken for communication of distance measurement data depends on requested accuracy, transmission rate, and the like of the distance measurement data and is, for example, a time period of several hundreds [μs] approximately in some cases. Thus, when communication of distance measurement data is unnecessary, a time taken for a distance measurement sequence is reduced. The present embodiment relates to a technology of producing the distance measurement signal that reduces or eliminates the time of communication of distance measurement data.
Note that the distance measurement time period is reduced by performing at least one of transmission of the distance measurement signal of the phase θGMSK,b1 by the device B at the timing NTSB and transmission of the distance measurement signal of the phase θGMSK,a2 by the device A at the timing NTS.
The following describes a reason why the distance measurement time period is reduced by transmitting the distance measurement signal of the phase θGMSK,b1 from the device B at the timing NTSB. Assume that distance measurement calculation is performed by the device A.
When the distance measurement signal of the phase θGMSK,b1 is transmitted by the device B at the timing NTSB, a timing of the offset phase θOFF is earlier than the timing NTSB by tb1. When a time point of the offset phase θOFF is a time point of transmission start of the distance measurement signal, the time point of transmission start is NTSB−tb1.
Subsequently, a case in which the distance measurement signal is received by the device A will be described. First, when the device B starts transmitting the distance measurement signal of the phase θOFF at the timing NTSB, the device A samples a phase θGMSK,a1 at the sampling timing and converts the phase θGMSK,a1 into the detection elapsed time ta1.
On the other hand, when the device B starts transmitting the distance measurement signal of the phase θOFF at the timing “NTSB−tb1”, the device A determines that the distance measurement signal arrives earlier than the elapsed time ta1 of the phase θOFF by the elapsed time tb1. Accordingly, the phase sampled by the device A at the sampling timing is not the phase θGMSK,a1 but the phase θGMSK,ab1 corresponding to the reception earlier by the elapsed time tb1. Thus, a relation of Expression (37) holds.
ta1+tb1≈{1/(2πf01)}sin−1{(θGMSK,ab1−θOFF)/A01} (37)
Thus, data of the elapsed time tb1 detected by the device B can be acquired at the device A by detecting the phase θGMSK,ab1. When the distance measurement signal of the phase θOFF is not transmitted from the device B at the timing “NTSB−tb1”, the device B needs to transmit data of the detected elapsed time tb1 to the device A.
Similarly, when the distance measurement signal of the phase θGMSK,a2 is transmitted from the device A at the timing NTS, the device B detects a phase θGMSK,ab2, and this phase and an elapsed time “ta2+tb2” to be detected through a second round trip sequence have a relation of Expression (38).
ta2+tb2≈{1/(2πf01)}sin−1{(θGMSK,ab2−θOFF)/A01} (38)
However, this result needs to be transmitted to the device A when distance calculation is to be performed by the device A, and thus the phase of the distance measurement signal to be transmitted does not need to be shifted in a second round trip sequence. The result leads to a reduced distance measurement time period when distance calculation is performed by the device B. A result detected by Expression (28) needs to be transmitted to the device B when distance calculation is to be performed by the device B. Thus, phase shift of the distance measurement signal may be performed in accordance with whether to perform distance calculation at the device A or the device B.
For verification, improvement of distance measurement accuracy by using Expressions (37) and (38) will be described below. The averaged flight time tx can be rewritten as Expression (39) by using Expressions (25) to (27).
tx=(tx1+tx2)/2={2TS−(ta1−tb1)−(ta2+tb2)}/4 (39)
The term (ta1+tb1) in Expression (39) can be calculated by Expression (37), and the term (ta2+tb2) in Expression (39) can be calculated by Expression (38). Thus, any one of Expressions (37) and (38) can be used depending on whether to perform distance calculation at the device A or the device B. and the amount of data communication in a detection time can be reduced.
Note that although not illustrated, it is clear that the method of performing phase detection K times for each m samples and averaging elapsed times obtained from detected phases in the second embodiment is also applicable to the present embodiment.
According to the fourth embodiment, effects substantially same as effects of the first to third embodiments described above are achieved, and in addition, a data communication time is reduced by transmitting a loop-back distance measurement signal at the phase of a received distance measurement signal, and the distance measurement time period can be further reduced.
In a fifth embodiment, any part same as a part in the first to fourth embodiments is denoted by the same reference sign, description of the part is omitted, and difference will be mainly described.
In the present embodiment, the distance measurement time period is further reduced by employing 1.5-round-trip distance measurement in the third embodiment and loop-back distance measurement at a received phase in the fourth embodiment.
Difference between the sequence in
In contrast, in
2ta1≈{1/(2πf01)}sin−1{(θGMSK,TXa−θOFF)/A01} (40)
When the distance measurement signal is transmitted from the device A to the device B at the phase θGMSK,TXa, an estimated arrival time at the device B is a time longer than the elapsed time tb2 estimated with θGMSK,TXa=θOFF by 2ta1, and accordingly, the received phase is θGMSK,ab2. Thus, Expression (41) holds.
2ta1+tb2≈{1/(2πf01)}sin−1{(θGMSK,ab2−θOFF)/A01} (41)
Alternatively, in a case of the 1.5 round trip, a left-hand side of Expression (43) is rewritten as a right hand side with interpretation of Expression (42) as described above.
2ta1=ta2 (42)
2ta1+tb2=ta1+ta2+tb2 (43)
A phase detected by the device B having received the initial distance measurement signal from the device A is obtained by changing b to b1 in Expression (3), and thus the elapsed time tb1 obtained from the detected phase is given by Expression (44).
tb1≈{1/(2πf01)}sin−1{(θGMSK,b1−θOFF)/A01} (44)
At the device B, tb1 and (ta1+ta2+tb2) can be estimated from Expression (41), Expression (43), and Expression (44). Expression (39) can be rewritten to obtain Expression (45).
tx=(tx1+tx2)/2={2TS−(ta1+tb1+ta2+tb2)}/4 (45)
Thus, the flight distance can be estimated by using Expression (45) with addition of tb1 and (ta1+ta2+tb2) estimated at the device B.
Note that although not illustrated, it is clear that the method of performing phase detection K times for each m samples and averaging elapsed times obtained from detected phases in the second embodiment is also applicable to the present embodiment.
According to the fifth embodiment, 1.5 round trip distance measurement in the third embodiment and phase loop-back distance measurement in the fourth embodiment can be combined to estimate ta1+tb1+ta2+tb2 at one of the device A and the device B (in the above description, the device B). Accordingly, the data communication time can be further reduced, and the distance measurement time period can be further reduced.
In a sixth embodiment, any part same as a part in the first to fifth embodiments is denoted by the same reference sign, description of the part is omitted, and difference will be mainly described.
The elapsed times ta1, ta2, tb1, and tb2 until sampling since crossing of the offset phase θOFF are calculated by using, for example, Expressions (2) and (3) based on phases θGMSK,ai and θGMSK,bi (i=1, 2) sampled first after the offset phase θOFF.
Assume that the device A has an accurate clock and the device B has frequency error as defined in Expressions (7) and (8). Expression (7) is given as Expression (46) by using the reference clock frequency fA of the device A and the reference clock frequency fB of the device B.
fA/fB=1−rerr (46)
The frequency of the RF signal (distance measurement signal) generated at each of the device A and the device B is a frequency obtained by multiplying the reference clock frequency by a predetermined integer multiple, and thus error occurs to the frequency of the RF signal at a ratio same as a ratio for the reference clock frequency. Specifically, when an RF frequency of the device A is represented by fRFA and an RF frequency of the device B is represented by fRFB, Expression (47) is obtained.
fRFA/fRFB=1−rerr (47)
Thus, the RF frequency fRFB of the device B is higher than the RF frequency fRFA of the device A by rerrfRFB. Thus, when the RF frequencies of the device A and the device B are set to be equal, the RF signal of the device B is received by the device A not as a direct current (DC) signal but as a signal of the frequency rerrfRFB.
When a frequency corresponding to this difference is represented by fA=rerrfRFB and a difference between initial phases of the device B and the device A is represented by ΔθBA, the phase of the distance measurement signal received by the device A is given by Expression (48).
θGMSK,a≈A01 sin(2πf01t)+2πfΔt+θOFF+ΔθBA (48)
A time needed to be calculated is a time of crossing the offset phase θOFF with no frequency offset between the device A and the device B. Phase change is maximum at the time of crossing the offset phase θOFF. The maximum phase change at the time of crossing the offset phase θOFF occurs irrespective of the frequency offset fΔ and the initial phase difference ΔθBA. Thus, a time at which a value obtained by differentiating Expression (48) with respect to time is maximum is a time at which the distance measurement signal arrives at the device A. The time differential of Expression (48) is given by Expression (49).
dθGMSK,a/dt≈2πf01A01 cos(2πf01t)+2πfΔ (49)
Expression (49) has a maximum value of 2πf01A01+2πfΔ at t=0 [s].
When there is no frequency offset because the reference clocks of the device A and the device B are completely identical to each other and when initial phases are identical to each other, the distance measurement signal of Expression (1) is received by the device A. A time differential of Expression (1) has a maximum value of 2πf01A01 at a time of t=0 [s]. Although the maximum value has a difference due to a frequency difference, a time tarvA of arrival at the device A can be detected by detecting a time at which a time differential of the phase has a maximum value.
However, since the sampling period cannot be infinitesimally small but is finite, the time at which the differential of the phase has a maximum value needs to be estimated from phases acquired at sample points. When, for example, phases at three points are sampled per quadrant to increase accuracy of the estimation, the sampling frequency is 12f01. The following describes processing of estimating the arrival time tarvA from sampled phases.
The estimation of the arrival time tarvA is performed through a difference operation replacing a differential operation based on Expression (48). The offset phase θOFF+ΔθBA in the phase signal of Expression (48) is replaced with θFFA=θOFF−ΔθBA for simplification.
First, the device A observes the phase θGMSK,a of a received phase signal for a duration equal to or longer than the modulation period T01=1/f01. The modulation period is known through beforehand communication between the device A and the device B, and thus the number of samples is determined accordingly. In the present assumption, a maximum value of a phase change amount can be detected through phase observation at 12 samples or more in the sampling period TS. The 12 samples are represented by ti (i=0 to 11). Sampling is performed a larger number of times in reality, in which phase observation is performed at 12 samples or more, but for description, the arrival time tarvA estimated by the device A based on particular 12 samples is calculated.
The maximum value of the change amount of the received phase θGMSK,a can be calculated by calculating a value of Expression (50) for i=0 to 10 and determining a maximum value among the values.
ΔθGMSK,a(ti)=θGMSK,a(ti+1)−θGMSK,a(ti) for i=0 to 10 (50)
Three samples are extracted based on the sample time ti that provides the maximum value of the phase change amount. Note that estimation accuracy of the arrival time tarvA can be further increased with samples in the number of three or larger, but the present description is made on a process of estimating the arrival time tsumA with three samples.
In this case, three sample points used to estimate the arrival time tarvA are t1, t2, and t3. Note that the same result can be obtained when the sample points are t0, t1, and t2, but description of such a case is omitted.
Formulae that associate the detection phase θGMSK,a(ti) with the sample points of times t1, t2, and t3 are Expressions (51) to (53) below.
θGMSK,a(t1)≈A01 sin(2πf01t1)+2πfΔt1+θOFFA (51)
θGMSK,a(t2)≈A01 sin(2πf01t2)+2πfΔt2+θOFFA (52)
θGMSK,a(t3)≈A01 sin(2πf01t3)+2πfΔt3+θOFFA (53)
Since TS=t2−t1=t3−t2 holds, Expression (54) is obtained by subtracting, from a result obtained by subtracting Expression (52) from Expression (53), a result subtracting Expression (51) from Expression (52).
θGMSK,a(t3)−2θGMSK,a(t2)+θGMSK,a(t1)=A01{sin(2πf01t3)−2 sin(2πf01t2)+sin(2πf01t1)} (54)
Expression (57) is obtained when the sample times t1 and t3 in Expression (54) are expressed as Expressions (55) and (56), respectively, by using t2 and substituted into Expression (54).
t1=−TS+t2 (55)
t3=TS+t2 (56)
θGMSK,a(t3)−2θGMSK,a(t2)+θGMSK,a(t1)=2A01 sin(2πf01t2){cos(2πf01TS)−1} (57)
Since an elapsed time from the arrival time tarvA between the sample time t1 and the sample time t2 to the sample time t2 is ta, t2 is expressed by Expression (58).
t2=tarvA+ta (58)
Since the arrival time tarvA is a time at which the phase of the sinusoidal signal as the distance measurement signal becomes the offset phase θOFF, Expression (59) is obtained.
sin(2πf01tarvA)=0 (59)
When sin(2πf01t2) in Expression (57) is rewritten by using Expression (58), Expression (60) is obtained.
sin(2πf01t2)=sin{2πf01(tarvA+ta)}=sin(2πf01ta) (60)
Expression (61) is obtained from Expressions (57) and (60).
sin(2πf01ta)=[θGMSK,a(t3)−2θGMSK,a(t2)+θGMSK,a(t1)]/[2A01{cos(2πf01TS)−1}] (61)
Expression (61) can be rewritten as Expression (62), which is an expression that calculates ta.
ta={1/(2πf01)}sin−1[{θGMSK,a(t3)−2θGMSK,a(t2)+θGMSK,a(t1)}/(2A01{cos(2πf01TS)−1})] (62)
Expression (62) indicates that ta can be calculated from a result of the phase detection at three points, the sampling period TS, the frequency f01 of the GMSK signal of 0 and 1, and the amplitude A01. From Expression (58), the arrival time tarvA of the distance measurement signal is earlier than the sample time t2 by the elapsed time ta. Note that, as described up to the fifth embodiment, ta calculated by Expression (62) is needed to calculate the flight time tx.
It is trivial that the same processing can be performed to calculate the elapsed time tb from an arrival time point of the distance measurement signal detected by the device B to the sample point, and ta1, tb1, ta2, and tb2 detected in an alternation sequence.
According to the sixth embodiment, the times tarvA and tarvB at which the distance measurement signal arrives can be accurately calculated at Devices A and B described in the first to fifth embodiments.
In the seventh embodiment, any part same as a part in the first to sixth embodiments is denoted by the same reference sign, description of the part is omitted, and difference will be mainly described.
In the sixth embodiment, the elapsed time ta from the arrival time point of the distance measurement signal to the sample point is calculated by extracting only three points from among 12 sample points. The present embodiment describes a method to which the method of the sixth embodiment is extended and that calculates ta by using four or more sample points. Note that the description assumes that conditions on the sample points are identical to conditions in the sixth embodiment.
As illustrated in
The sixth embodiment uses samples at t1 and t3, one sample time TS before and after the sample time t2 when the elapsed time ta has elapsed since the arrival time tarvA. In contrast, the present embodiment uses samples at tmod(2−i) and t2+i, i sample times iTS before and after the sample time t2, where mod represents a residue of 12, and for example, mod(−1)=11. Exemplary calculation in a case of i=2 will be described below.
In a case of i=2, sample times other than the sample time t2 are t0 and t4, and phases are given by Expressions (63) and (64). Note that Expression (52) at the sample time t2 is listed below again.
θGMSK,a(t0)≈A01 sin(2πf01t0)+27πfΔt0+θOFFA (63)
θGMSK,a(t2)≈A01 sin(2πf01t2)+2πfΔt2+θOFFA (52)
θGMSK,a(t4)≈A01 sin(2πf01t4)+2πfΔt4+θOFFA (64)
Similarly to derivation of Expression (54) by using Expressions (51) to (53), Expression (65) can be obtained by using Expressions (63). (52), and (64).
θGMSK,a(t4)−2θGMSK,a(t2)+θGMSK,a(t0)=A01{sin(2πf01t4)−2 sin(2πf01t2)+sin(2πf10t0)} (65)
In addition, Expressions (66) and (67) below hold.
t0=−2TS+t2 (66)
t4=2TS+t2 (67)
Expression (65) can be rewritten as Expression (68) by using Expressions (66) and (67).
θGMSK,a(t4)−2θGMSK,a(t2)+θGMSK,a(t0)=2A01 sin(2πf01t2){cos(2πf012TS)−1} (68)
Processing same as processing for obtaining a result of Expression (62) is performed to obtain the elapsed time ta as in Expression (69).
ta={1/(2πf01)}sin−1[{(θGMSK,a(t3)−2θGMSK,a(t2)+θGMSK,a(t1)}/(2A01{cos(2πf012TS)−1})] (69)
When calculated through the same processing for i≤5 in the present assumption, the elapsed time ta is given by Expression (70).
ta={1/(2πf01)}sin−1[{θGMSK,a(t2+i)−2θGMSK,a(t2)+θGMSK,a(tmod(2−i))}/(2A01{cos(2πf01iTS)−1})] (70)
When the elapsed time ta calculated by Expression (70) for i=1, 2, 3, 4, and 5 is newly written an elapsed time ta,i, the elapsed time ta can be calculated by Expression (71) as an average value over a large number of sample points.
ta=(⅕)×Σi=15ta,i (71)
However, when the number of phase sample points for the frequency f01 of the GMSK signal of 0 and 1 is 12 as in the present assumption, a sample at t8, which is shifted from the sample time t2 by half the period, is not used in averaging. To avoid this, the number of sample points in one period needs to be an odd number.
Note that the averaging of the elapsed time ta may be performed by averaging the phase term of sin−1 in Expression (70) and then converting the average into time. In this case, Expression (72) is obtained.
ta={1/(2πf01)}sin−1[(⅕)×Σi=15{θGMSK,a(t2+i)−2θGMSK,a(t2)+θGMSK,a(tmod(2−i))}/(2A01{cos(2πf01iTS)−1})] (72)
Thus, averaging over a large number of sample points is possible through phase averaging as well.
Note that it is trivial that the same processing can be performed to calculate the elapsed time tb from the arrival time point of the distance measurement signal detected by the device B to the sample point, and ta1, tb1, ta2, and tb2 detected through an alternation sequence.
According to the seventh embodiment, effects substantially same as effects of the first to sixth embodiments described above are achieved, and in addition, it is possible to easily obtain a time until sampling since the distance measurement signal arrives at each device, which is necessary for calculating the distance. The same result can be obtained through phase averaging in place of time averaging.
While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel devices described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the devices described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the inventions.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2020-159572 | Sep 2020 | JP | national |
| Number | Name | Date | Kind |
|---|---|---|---|
| 6820031 | Hayakawa | Nov 2004 | B1 |
| 7561048 | Yushkov et al. | Jul 2009 | B2 |
| 7872583 | Yushkov et al. | Jan 2011 | B1 |
| 7969311 | Markhovsky et al. | Jun 2011 | B2 |
| 8305215 | Markhovsky et al. | Nov 2012 | B2 |
| 8648722 | Markhovsky et al. | Feb 2014 | B2 |
| 9288623 | Markhovsky et al. | Mar 2016 | B2 |
| 9507007 | Markhovsky et al. | Nov 2016 | B2 |
| 9699607 | Markhovsky et al. | Jul 2017 | B2 |
| 9813867 | Prevatt | Nov 2017 | B2 |
| 9913244 | Markhovsky et al. | Mar 2018 | B2 |
| 9955301 | Markhovsky et al. | Apr 2018 | B2 |
| 10091616 | Prevatt | Oct 2018 | B2 |
| 10117218 | Markhovsky et al. | Oct 2018 | B2 |
| 10165461 | Vamaraju et al. | Dec 2018 | B2 |
| 10281557 | Markhovsky et al. | May 2019 | B2 |
| 10433111 | Prevatt et al. | Oct 2019 | B2 |
| 10440512 | Prevatt et al. | Oct 2019 | B2 |
| 10506376 | Markhovsky et al. | Dec 2019 | B2 |
| 10712435 | Shimizu et al. | Jul 2020 | B2 |
| 10834531 | Markhovsky et al. | Nov 2020 | B2 |
| 10845453 | Markhovsky et al. | Nov 2020 | B2 |
| 10863313 | Markhovsky et al. | Dec 2020 | B2 |
| 10873830 | Markhovsky et al. | Dec 2020 | B2 |
| 20100172339 | Duan et al. | Jul 2010 | A1 |
| 20170248678 | Markhovsky et al. | Aug 2017 | A1 |
| 20180180702 | Markhovsky et al. | Jun 2018 | A1 |
| 20180267154 | Ootaka et al. | Sep 2018 | A1 |
| 20180335514 | Dees et al. | Nov 2018 | A1 |
| 20190204406 | Lubberhuizen | Jul 2019 | A1 |
| 20190242967 | Markhovsky et al. | Aug 2019 | A1 |
| 20200120509 | Stitt | Apr 2020 | A1 |
| 20200142023 | Markhovsky et al. | May 2020 | A1 |
| 20200166631 | Tong | May 2020 | A1 |
| 20200178028 | Markhovsky et al. | Jun 2020 | A1 |
| 20200182959 | Markhovsky et al. | Jun 2020 | A1 |
| 20200284888 | Shimizu et al. | Sep 2020 | A1 |
| 20230266421 | Naiki | Aug 2023 | A1 |
| 20230276395 | Kono | Aug 2023 | A1 |
| Number | Date | Country |
|---|---|---|
| 2001-033543 | Feb 2001 | JP |
| 2009-150872 | Jul 2009 | JP |
| 2018-100973 | Jun 2018 | JP |
| 2018-155724 | Oct 2018 | JP |
| 2018-155725 | Oct 2018 | JP |
| 2019-503472 | Feb 2019 | JP |
| 2019-506081 | Feb 2019 | JP |
| Entry |
|---|
| Kim et al., “Vehicle Relay Attack Avoidance Methods Using RF Signal Strength”, Communications and Network, 2013, 5, 573-577 (Year: 2013). |
| Number | Date | Country | |
|---|---|---|---|
| 20220091253 A1 | Mar 2022 | US |
