JP2000193733A - Determining device and method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a determining device with greatly improved determination accuracy. SOLUTION: This device is equipped with reception parts 4 and 5 that measure a carrier phase and code pseudo distance at known and unknown points according to the output signal of antennas 2 and 3 for receiving a GNSS satellite signal at the known and unknown points, a calculation part 6 that calculates carrier phase double phase difference according to the carrier phases at the known and unknown points, a calculation part 7 that calculates code pseudo distance double phase difference according to the code pseudo distance at the known and unknown points, a smoothing constant calculation part 11 that calculates the smoothing constant of the code pseudo distance double phase difference according to the carrier phase double phase difference and the code pseudo distance double phase difference, a calculation part 8 that uses the smoothing constant and calculates smoothing code pseudo distance double phase difference according to the code pseudo distance double phase difference and the carrier phase double phase difference, and a determination calculation part 9 that calculates the distance between the known and unknown points according to the smoothing code pseudo distance double phase difference.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a GNSS (Global
The present invention relates to a positioning device using a satellite, which is used for navigation, civil engineering, surveying, or the like, which requires positioning accuracy of several centimeters to several tens of centimeters.

[0002]

2. Description of the Related Art Here, a high-accuracy positioning device using a GPS (Global Positioning System) satellite, which is a type of GNSS and has already begun to be used, will be described. The explanation holds.

Positioning devices using GPS satellites are widely used mainly in car navigation systems because they can obtain accurate positions. Among them, a method called interference positioning that uses a carrier frequency phase (called a carrier phase) is used. Since positioning can be performed with high accuracy from millimeters to centimeters, it is rapidly spreading in the field of surveying and civil engineering.

[0004] Interferometric positioning measures the distance (called the base line) between two points (a point whose position is known (called a known point) and a point whose position is to be measured (called an unknown point)), for example. X-, Y-, and Z-dimensions are measured with high precision from millimeters to centimeters (called positioning).
A GPS receiver is placed at each of the unknown and known points, while simultaneously measuring the carrier phase of the satellite. The carrier phase difference (carrier phase difference) at unknown and known points is calculated for each satellite, a certain reference satellite is appropriately selected, and the carrier phase difference of another satellite is determined based on the carrier phase difference. (Called carrier-phase double phase difference). carrier·
Since the phase double phase difference takes the difference between known points and unknown points and between different satellites, it can cancel most of the positioning errors depending on the receiver and satellite, and also includes the information of the baseline, By solving this, a highly accurate baseline can be obtained.

However, there is a problem that initialization is indispensable for positioning based on a carrier-phase double phase difference. That is, the carrier phase includes an ambiguity (an integer ambiguity (ambiguit
y)), it is necessary to determine this integer ambiguity (called ambiguity resolution) before starting positioning. The integer ambiguity is constant and does not change as long as the signal is continuously received. The ambiguity resolution is usually based on the approximate values of the baselines: X, Y, Z, and X,
This is performed using carrier phases from a large number of satellites, which is sufficiently larger than three unknown numbers of Y and Z. At this time, X, Y, Z
The more accurate the approximate value and the greater the number of satellites, the shorter and more reliable the ambiguity resolution becomes. In addition, while ambiguity resolution is impossible, positioning cannot be performed and the user must wait for it. Also, the unreliable ambiguity resolution,
If the integer ambiguity of the carrier phase is determined incorrectly, an incorrect positioning position will be obtained, and a serious problem that may lead to trial in surveying residential lands and the like.

On the other hand, there are many fields such as navigation, civil engineering work, and surveying, in which positioning accuracy of millimeters is unnecessary and positioning accuracy of several centimeters to tens of centimeters is sufficient. Also,
While positioning accuracy from millimeter to centimeter is required, while ambiguity resolution is impossible,
Even if the positioning accuracy is several centimeters to several tens of centimeters, it is very convenient if the positioning position is displayed together with the caution indication of the positioning accuracy to the effect that the positioning accuracy is not displayed. This baseline: To get an approximate value of X, Y, Z, or to get a position with a positioning accuracy of several centimeters to several tens of centimeters, a code pseudorange is usually used instead of the carrier phase. Code pseudo distance is GP
Obtained by measuring the phase of the pseudo-noise code broadcast from the S satellite, and unlike the carrier phase, there is no integer ambiguity, so no ambiguity resolution is required. Positioning is possible. However, the code pseudorange has a disadvantage that noise is larger than that of the carrier phase.
Typically, the noise of the code pseudorange is on the order of meters while the noise of the carrier phase is on the order of millimeters. As a method of suppressing the noise of the code pseudo distance, there is a method called carrier smoothing using the parallelism of the code pseudo distance and the carrier phase.

Hereinafter, this method will be described with reference to FIGS.

FIG. 2 shows the relationship between the code pseudorange and the carrier phase. The horizontal axis is time, and the vertical axis is code pseudorange and carrier phase. In FIG. 2, the carrier phase is obtained by multiplying the number of cycles by the wavelength.
The value is converted to the same meter unit as the code pseudo distance, and the value of the integer ambiguity of the carrier phase is displayed as 0. As is clear from FIG. 2, it can be seen that the superimposed noise is significantly different between the code pseudo distance and the carrier phase, and that the noise is substantially parallel when the noise is ignored. The reason for the large difference in noise is that the wavelength of the code is about 300 meters while the wavelength of the carrier is very short, about 0.2 meters. Also, the reason why they are parallel is that both the code pseudo-range and the carrier phase represent the distance between the GPS satellite and the antenna, although they include the offset.

In practice, the code pseudorange and the carrier
The phases are not perfectly parallel and slightly, but staggered. The cause of the shift is that when a signal is propagated from a GPS satellite to an antenna, the code pseudorange is delayed in the ionosphere of the earth on the way, and the carrier phase advances in the opposite direction. However, if the length of the baseline is about 10 km or less, on the way from the GPS satellite to the antenna at the known point, on the way to the passing ionosphere and the antenna at the unknown point,
Since the passing ionosphere is almost the same, if a double phase difference is taken, the effect of the ionosphere is canceled and the ionosphere becomes completely parallel. The difference between the parallel code pseudorange double phase difference and carrier phase double phase difference every time is taken and smoothed, and extremely low noise, code pseudorange double phase difference and carrier phase double phase difference are obtained. A parallel difference is obtained. Adding this difference to each carrier phase results in a value that is low in noise and overlaps the code pseudorange double phase difference. This is called a smoothing code pseudorange double phase difference, and this smoothing method is called carrier smoothing.

FIG. 3 shows a conventional positioning device. In FIG. 3, 1 is a GNSS satellite, 2 is an antenna A, 3 is an antenna B, 4 is a receiving section A, 5 is a receiving section B, 6 is a carrier / phase dual phase difference calculating section, and 7 is a code pseudo distance duplex. A phase difference calculation unit, 8 is a smoothing code pseudo-range double phase difference calculation unit, 9 is a positioning calculation unit, and 10 is a smoothing constant setting unit.

The antenna A: 2 installed at a known point is GN
A signal from the SS satellite 1 is received and output to the receiving unit A: 4. The receiving unit A: 4 measures the carrier phase and the code pseudorange of the antenna A: 2, which are known points, and calculates the carrier phase and the code pseudorange, respectively, in the carrier / phase double phase difference calculation unit 6 And the code pseudo-range double phase difference calculator 7. Similarly, the antenna B: 3 installed at the unknown point receives the signal of the GNSS satellite 1 and outputs it to the receiving unit B: 5. The receiving unit B: 5 measures the carrier phase and the code pseudorange of the antenna B: 3, which are unknown points, and calculates the carrier phase and the code pseudorange, respectively, as a carrier / phase double phase difference calculation unit 6. And the code pseudo-range double phase difference calculator 7. The carrier / phase double phase difference calculator 6 calculates the carrier / phase double phase difference and outputs it to the smoothing code pseudorange double phase difference calculator 8. Similarly, the code pseudorange double phase difference calculator 7 calculates the double phase difference of the code pseudorange, and outputs it to the smoothed code pseudorange double phase difference calculator 8. The smoothed code pseudo-range double phase difference calculator 8 smoothes the code pseudo-range double phase difference using the constant set by the smoothing constant setting unit 10 and outputs it to the positioning calculator 9. . Positioning calculation unit 9
Performs positioning (i.e., calculation of the base lines X, Y, and Z) using the smoothed code pseudo-range double phase difference output from the smoothed code pseudo-range double phase difference calculation unit 8.

The antenna A: 2 and the receiver A: 4 constitute a known point receiver A, and the antenna B: 3 and the receiver B: 5 constitute an unknown point receiver B. The carrier / phase double phase difference calculator 6, the code pseudorange double phase difference calculator 7, the smoothed code pseudorange double phase difference calculator 8, the positioning calculator 9, and the smoothing constant setting unit 10 calculate the positioning result. If it is needed on the known point side, it is treated as part of the configuration of the known point receiver A, and if it is needed on the unknown point side, it is treated as part of the configuration of the unknown point receiver B.

The connection between the receiving section A: 4 and the carrier / phase double phase difference calculating section 6 and the code pseudo-range double phase difference calculating section 7, and the receiving section B: 5 and the carrier / phase double phase difference calculating section The connection between the heavy phase difference calculation unit 6 and the code pseudo-range double phase difference calculation unit 7 is performed by either a wired line or a wireless line depending on the installation locations of the known point receiver A and the unknown point receiver B. May be.

Next, ED Kaplan edited by UNDERSTANDING G
PS, PRINCIPLES AND APPLICATIONS, Artech House, pages 354-366, and explain using formulas. However, some symbols have been changed and used in accordance with the description of the present invention.

The carrier phase and code pseudo distance measured by the receiving unit A: 4 and the carrier phase and code pseudo distance measured by the receiving unit B: 5 can be expressed by the following equations.

[0016]

(Equation 1)

Here, comparing the carrier phase with the code pseudorange, it can be seen that the carrier phase includes an integer ambiguity and that the ionospheric propagation delay is included with the opposite sign. . For this reason, the code pseudorange and the carrier phase are not completely parallel, and are shifted by the ionospheric propagation delay. The ionospheric propagation delay depends on the season, sunspot activity, etc., and is generally constant at about 1.5 meters at night, but increases with sunrise during the day and reaches a maximum value of about 10 meters around 2:00 pm. After that, it decreases again and returns to about 1.5 meters with sunset.

When the difference between the receivers A and B (referred to as single phase difference) is taken for the carrier phase, the following equation (2) is obtained as the carrier phase single phase difference.

[0019]

(Equation 2)

If the length of the base line is about 10 km or less, the distance between the GPS satellite and the antenna is 20,000 km or more.
Since the ionosphere passing on the way to antenna 2 and antenna B: 3 on the way to antenna B: 3 can be regarded as almost the same place, β ^p _A
(n) = β ^p _B (n). The same can be said for the troposphere, where δ ^p _A (n) = δ ^p _B (n). When these are substituted into the above equation, the above equation is converted into the equation (3).

[0021]

(Equation 3) Similarly, the code pseudo-range single phase difference is expressed by equation (4).

[0022]

(Equation 4) When β ^p _A (n) = β ^p _B (n) and δ ^p _A (n) = δ ^p _B (n) are substituted into the above equation, the above equation is transformed into the following equation (5).

[0023]

(Equation 5)

Further, if a satellite k is considered as a reference satellite instead of the satellite p, the carrier phase single phase difference and the code pseudorange single phase difference are represented by Equation 6 with k instead of p.

[0025]

(Equation 6)

Regarding the carrier phase single phase difference,
Taking the difference between satellites k and p (referred to as double phase difference), the carrier-phase double phase difference is expressed by equation (7).

[0027]

(Equation 7)

The above-described calculation of the carrier-phase double phase difference is performed by the carrier-phase double phase difference calculation unit 6.
Do with.

Similarly, the code pseudorange double phase difference is represented by equation (8).

[0030]

(Equation 8)

The calculation of the code pseudorange double phase difference described above is performed by the code pseudorange double phase difference calculator 7.

When the carrier-phase double phase difference and the code pseudo-range double phase difference are written again, the following equation (9) is obtained.

[0033]

(Equation 9)

The following can be understood from these equations. That is, the carrier-phase double phase difference λΦ ^{p, k} _{B, A} (n) converted to the unit of meter by multiplying the wavelength and the code pseudo-range double phase difference R ^{p, k} _{B, A} (n) are common. GNSS satellite-antenna geometric distance ρ ^{p, k} _{B, A} (n), and the carrier-phase double phase difference is
N ^{p, k} _{B, A} (n). That is, since the ionospheric propagation delay is not included, it is completely parallel. As mentioned earlier, the code pseudorange double phase difference noise η ^{p, k} _{B, A} (n) is of the order of meters, which is the carrier phase double phase difference noise ε ^{p , k} _{B, A} Very large compared to the millimeter order of (n).

Next, carrier smoothing performed by the smoothing code pseudorange double phase difference calculator 8 will be described.

Carrier smoothing can be realized by equation (10).

[0037]

(Equation 10) The smoothing constant W (n) is set by the smoothing constant setting unit 10.

Next, the positioning calculation performed by the positioning calculation section 9 will be described.

By a method of positioning using only the unknown point receiver B like a positioning apparatus for car navigation, the approximate position of the antenna B: 3 at the unknown point can be obtained with an error of about 100 meters. Also, since the position of the known point is known,
When the smoothed code pseudo-range double phase difference is linearly approximated based on these positions, it can be expressed as Equation 11 (such a linear approximation method is described in, for example, BH Wellenhof et al .: GPS T
heory and Practice, Springer-Verlag, page 216
218).

[0040]

[Equation 11] When this is expressed using a matrix with respect to satellites of p = 1 to m,
Equation 12 is obtained.

[0041]

(Equation 12) From this equation, the base lines X, Y, and Z can be calculated by Equation 13 using, for example, the least squares method.

[0042]

(Equation 13)

[0043]

As described above, the noise in the code pseudorange can be suppressed by using the low noise characteristic of the carrier phase. In this case, the degree of suppression is set by the smoothing constant setting unit 10. Greatly depends on the smoothing constant W (n). That is, if W (n) is set to a value close to 1, the response is good but the smoothing characteristics are sacrificed. Conversely, if W (n) is set to a value close to 0, the response is good although the smoothing characteristics are good. Is sacrificed. Therefore, setting the smoothing constant W (n) is extremely important.

However, this constant W (n) is determined empirically, and is usually set to W (n) = 0.01 to 0.003. This means that if time n is taken in units of one second, W (n)
From = 1−e ^{−1 / T} , the time constant T corresponds to 99 to 330 seconds. The reason for this is that the code pseudo distance and carrier phase that do not take double phase difference
A method of applying smoothing is separately used in differential GPS. In this case, as described above, the code pseudorange and the carrier phase do not become parallel due to the influence of the ionospheric propagation delay, but shift, and a large time constant is smoothed. This is because the difference between the code pseudorange and the parallelism of the carrier phase cannot be obtained correctly due to the effect of the shift. For this reason, a value of 99 to 330 seconds has been empirically used, and the value is used as it is for the code pseudo distance with the double phase difference and carrier smoothing of the carrier phase.

According to the above-mentioned ED Kaplan, the noise of the smoothed code pseudorange double phase difference due to carrier smoothing depends on multipath and is usually 1-2 meters. This means that multipath is 1-2
Since the period is on the order of minutes despite the presence of meters, the smoothing time constant of carrier smoothing is set to 99 to 330.
This is because they cannot be suppressed even in seconds.

The positioning accuracy caused by this noise depends on the satellite constellation, but is about the same, that is, 1 to 2 meters. For this reason, as compared with the case where the positioning accuracy can be obtained from several centimeters to several tens of centimeters as described above, the ambiguity resolution requires a longer time and lower reliability, and the navigation and civil engineering There was a major problem that limited the application of the positioning device in construction and surveying.

According to the present invention, in order to improve such disadvantages,
If we take the double phase difference, the code pseudorange double phase difference and the carrier phase double phase difference will be completely parallel,
A positioning device and a positioning method in which the positioning accuracy is improved from several centimeters to several tens of centimeters by making use of the fact that the smoothing time constant can be set to any large value and setting the time constant sufficiently large as necessary. It is.

[0048]

According to the present invention, the maximum period of noise can be calculated from the noise component of the code pseudo-range double phase difference, including not only the multi-pulse that could not be suppressed by the conventional positioning device but also other factors. The smoothing time constant of carrier smoothing is determined on the basis of the
Convert to (n) and use. Thereby, not only the multi-pulse but also the noise of the code pseudo-range double phase difference due to other factors is suppressed, and the positioning accuracy is greatly improved from several centimeters to several tens centimeters.

That is, according to the present invention, GN
A first antenna for receiving a signal from an SS (Global Navigation Satellite System) satellite; and a second antenna for measuring a carrier phase at the known point and a code pseudorange at the known point from an output signal of the first antenna. 1, a second antenna for receiving a signal from the GNSS satellite at an unknown point, and a carrier phase at the unknown point and a code pseudo distance at the unknown point from an output signal of the second antenna. A second receiving unit for measuring
And connected to the second receiving unit, a carrier phase double phase difference calculation unit that calculates a carrier phase double phase difference from the carrier phase at the known point and the carrier phase at the unknown point, A code pseudo-range double phase difference calculator connected to the first and second receiving units and calculating a code pseudo-range double phase difference from the code pseudo range at the known point and the code pseudo range at the unknown point. Unit, connected to the carrier phase double phase difference calculation unit and the code pseudo distance double phase difference calculation unit,
A smoothing constant calculator for calculating a smoothing constant of a code pseudo-range double phase difference from the carrier-phase double phase difference and the code pseudo-range double phase difference, and the carrier-phase double phase difference calculator; A pseudo-range double phase difference calculator connected to the smoothing constant calculator, and using the smoothing constant to smooth the code pseudo-range double from the code pseudo-range double phase difference and the carrier phase double phase difference. A smoothing code pseudo-range double phase difference calculator for calculating a phase difference, connected to the smoothed code pseudo-range double phase difference calculator, and the known point and the A positioning device comprising a positioning calculation unit that calculates a distance between unknown points is obtained.

Further according to the invention, the GNSS (G
receiving a signal from a satellite from a GNSS satellite at an unknown point, and measuring a carrier phase at the known point and a code pseudorange at the known point. Measuring a carrier phase at an unknown point and a code pseudorange at the unknown point; and calculating a carrier phase double phase difference from the carrier phase at the known point and the carrier phase at the unknown point. Calculating a code pseudorange double phase difference from the code pseudorange at the known point and the code pseudorange at the unknown point; and performing the carrier phase double phase difference and the code pseudorange double phase. A smoothing constant calculation step of calculating a smoothing constant of the code pseudo distance double phase difference from the phase difference, and using the smoothing constant, Calculating a smoothed code pseudorange double phase difference from the code pseudorange double phase difference and the carrier phase double phase difference; and the known point and the unknown point from the smoothed code pseudorange double phase difference. Calculating the distance between the two.

[0051]

[Function] Interferometric positioning systems that have been used only for surveying and civil engineering in terms of price, even if they cannot be said to be car navigation systems that will reach one million units per year, have high positioning from millimeters to centimeters. It is expected to spread to various fields from the performance of accuracy.

At the same time, it is considered that the requirements for shorter time and higher reliability for the ambiguity resolution will be stricter. In particular, when it spreads to surveying of residential land and the like, if a wrong positioning position is obtained due to a wrong ambiguity resolution, a serious problem that may result in a trial may be caused. For this reason, the accuracy of positioning by the code pseudo-range double phase difference required for ambiguity resolution is reduced from the current 1-2 meters to several centimeters.
If it can be improved to tens of centimeters, ambiguity
Shortening of resolution and high reliability can be greatly improved.

In many fields such as navigation, civil engineering, or surveying, where positioning accuracy of millimeters is not necessary and positioning accuracy of several centimeters to several tens of centimeters is sufficient, a positioning device having a positioning accuracy suitable for this is provided. If possible, it will call demand, and demand will drive production, further expanding its spread.

According to the present invention, since only the smoothing constant is changed in accordance with the noise characteristic of the code pseudo-range double phase difference, only a change by software is required, and the price, size, and method of use by the user are adversely affected. With respect to the positioning accuracy by the code pseudo-range double phase difference, the conventional one to two meters can be greatly improved from several centimeters to several tens centimeters, and the effect is extremely large.

[0055]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, embodiments of the present invention will be described with reference to the drawings.

Referring to FIG. 1, there is shown a positioning device for realizing a positioning method according to an embodiment of the present invention. The positioning device includes similar parts indicated by similar reference numerals.

In other words, this positioning device has a smoothing constant setting unit 1
Instead of 0, the carrier / phase double phase difference calculator 6
It is the same as the positioning device of FIG. 3 except that it has a smoothing constant calculation unit 11 connected to the code pseudo distance double phase difference calculation unit 7. The operations other than the smoothing constant calculation unit 11 are the same as those of the positioning device in FIG.

Carrier-phase double phase difference calculator 6
Carrier-phase double phase difference λΦ ^{p, k}
_{When the} difference between _{B, A} (n) and the code pseudorange double phase difference R ^{p, k} _{B, A} (n) which is the output of the code pseudorange double phase difference calculation unit 7 is obtained, Equation 14 is obtained. Can be

[0059]

[Equation 14]

This difference (R ^{p, k} _{B, A} (n) −λΦ
^{p, k} _{B, A} (n)), for example, with respect to time n, save a predetermined number, and subtract the average value to remove a constant λN ^{p, k} _{B, A} (n), When the fast Fourier transform is performed, a spectrum combining noise η ^{p, k} _{B, A} (n) and ε ^{p, k} _{B, A} (n) is obtained. However, this can be regarded as a spectrum of η ^{p, k} _{B, A} (n). Because η ^{p, k} _{B, A} (n) is very different from meter order and ε ^{p, k} _{B, A} (n) is very different from millimeter order, ε ^{p, k} _{B, A} (n) is η
^{This is because p, k} _{B, A} (n) can be ignored.

From the spectrum of η ^{p, k} _{B, A} (n), one having the maximum period is obtained. This usually corresponds to the period of the multipulse, on the order of minutes. Assuming that the maximum period, for example, three times the carrier smoothing time constant is a carrier smoothing time, sufficient noise can be obtained by carrier smoothing.
It can be said that it can be suppressed and the responsiveness is the best under the suppression. If this time constant is T and, for example, the time n is in units of one second, it can be converted into a smoothing constant W (n) from W (n) = 1-e- ^{1 / T.} Carrier smoothing is performed using the smoothing constant W (n).

A multi-pulse is usually a non-periodic wave form of 1 to 2 meters, but if it is approximated by a sine wave and smoothed with a time constant three times the period of the multi-pulse, the multi-pulse Equation 15

(Equation 15) Double. That is, it goes from 5.3 cm to 10.6 cm. Even if the multi-pulse is greater than 1 to 2 meters, it is possible to suppress the noise of the smoothing code pseudorange double phase difference from several centimeters to tens of centimeters by setting the smoothing constant in this way. It is possible, and as a result, the positioning accuracy can be reduced from several centimeters to several tens of centimeters.

[0063]

As described above, according to the present invention, since the smoothing constant is merely changed in accordance with the noise characteristic of the code pseudo-range double phase difference, only the software needs to be changed, and the price, size, user Without adversely affecting the usage of GPS, with regard to positioning accuracy by code pseudo-range double phase difference,
It is possible to realize a positioning device and a positioning method in which the conventional one or two meters is significantly improved from several centimeters to several tens centimeters.

[Brief description of the drawings]

FIG. 1 is a block diagram of a positioning device that realizes a positioning method according to an embodiment of the present invention.

FIG. 2 is a diagram for explaining a general relationship between a code pseudo distance and a carrier phase.

FIG. 3 is a block diagram of a conventional positioning device.

[Explanation of symbols]

 Reference Signs List 1 GNSS satellite 2 Antenna A 3 Antenna B 4 Receiver A 5 Receiver B 6 Carrier-phase double phase difference calculator 7 Code pseudo-range double phase difference calculator 8 Smoothing code pseudo-range double phase difference calculator 9 Positioning calculation unit 10 Smoothing constant setting unit 11 Smoothing constant calculation unit

Claims (2)

[Claims] At a known point, a GNSS (Global Navigation S
a first antenna for receiving a signal from a satellite, and a first receiving unit for measuring a carrier phase at the known point and a code pseudorange at the known point from an output signal of the first antenna. And a second antenna for receiving a signal from the GNSS satellite at an unknown point; and measuring a carrier phase at the unknown point and a code pseudorange at the unknown point from an output signal of the second antenna. 2 and a carrier that is connected to the first and second receivers and calculates a carrier-phase double phase difference from the carrier phase at the known point and the carrier phase at the unknown point. A phase double phase difference calculator, connected to the first and second receivers, and based on a code pseudo distance at the known point and a code pseudo distance at the unknown point. A code pseudo-range double phase difference calculator for calculating a code pseudo-range double phase difference, and the carrier-phase double phase difference calculator and the code pseudo-range double phase difference calculator are connected to the carrier pseudo-range double phase difference calculator. A smoothing constant calculator for calculating a smoothing constant of the code pseudo-range double phase difference from the phase double phase difference and the code pseudo-range double phase difference, the carrier-phase double phase difference calculator, the code pseudo-range A heavy phase difference calculation unit, connected to the smoothing constant calculation unit, and using the smoothing constant to calculate a smoothed code pseudo range double phase difference from the code pseudo range double phase difference and the carrier phase double phase difference. A smoothing code pseudo-range double phase difference calculator for calculating, connected to the smoothing code pseudo-range double phase difference calculator, and Positioning device is characterized in that a positioning calculation unit that calculates the distance between the known point and the unknown point. 2. GNSS (Global Navigation S)
receiving a signal from a satellite and measuring a carrier phase at the known point and a code pseudorange at the known point; receiving a signal from the GNSS satellite at an unknown point; Measuring the carrier phase and the code pseudorange at the unknown point, and calculating the carrier phase double phase difference from the carrier phase at the known point and the carrier phase at the unknown point. Calculating a code pseudorange double phase difference from the code pseudorange at the known point and the code pseudorange at the unknown point; and A smoothing constant calculating step of calculating a smoothing constant of the code pseudo distance double phase difference; and Calculating a smoothed code pseudorange double phase difference from the distance double phase difference and the carrier phase double phase difference; and between the known point and the unknown point from the smoothed code pseudorange double phase difference. Calculating a distance.