JP2015068768A - Positioning system, device, method, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a system and method that can avoid disconnection of a positioning signal from a satellite as much as possible in a space where the positioning signal is disconnected from the satellite by a structure such as a tunnel, bridge, and pedestrian bridge, and can perform highly accurate positioning in real time when a positioning signal is disconnected.SOLUTION: A positioning device comprises a first antenna for receiving a positioning signal from a satellite in an area where the positioning signal can be received from the satellite and a relay for relaying the positioning signal received by the first antenna to be transmitted from a second antenna in a space where the positioning signal is disconnected from the satellite. The positioning device that performs positioning on the basis of the positioning signal received from the satellite acquires motion information of the satellite and the positioning device and calculates a distance between the satellite and the positioning device to estimate an integer bias of a carrier phase when the device cannot receive the positioning signal relayed by the relay and detects disconnection of the positioning signal from the satellite in the space where the positioning signal is disconnected from the satellite.

Description

  The present invention relates to a positioning system, apparatus, method, and program.

<Quasi-Zenith Satellite System (QZSS)>
Quasi-Zenith Satellites (QZS) is placed in the Quasi-Zenith orbit so that it is always visible in the zenith direction near Japan (Quasi-Zenith Satellite System: In QZSS, a plan is underway to supplement and augment the US Global Positioning System (GPS) with three satellites that stay only in certain areas that can be received in Japan. That is, the first QZS aircraft will be launched in 2010, and all will be put into operation in 2013. In this quasi-zenith satellite system, three or more quasi-zenith satellites are prepared and signals are transmitted from the quasi-zenith orbit so that one quasi-zenith satellite that can be observed from the ground at a high elevation angle can always be seen. For example, it is possible to provide a high-accuracy positioning service that covers almost 100% of the whole country without being affected by mountainous areas, shadows of buildings, etc.

  As is well known, GPS satellites are equipped with positioning L1 and L2 transmitters, multiple cesium and rubidium atomic clocks, an orbital altitude of approximately 20.000 km, and an orbital period of 0.5 stars. The system consists of 24 satellites, 4 each on 6 orbital planes. QZSS has two services that complement and reinforce this GPS.

  The GPS supplementary service in QZSS is combined with GPS and improves the geometrical arrangement of the satellite using the quasi-zenith orbit, thereby increasing the positioning area and time in urban areas and mountainous areas, and the quasi-zenith satellite ( A positioning signal (L1C / A signal, L1C signal, L2C signal, and L5 signal) is transmitted from QZS to improve positioning accuracy.

  The GPS augmentation service in QZSS provides high accuracy by transmitting distance measurement correction information by transmitting, for example, an L1-SAIF signal and a LEX signal from the quasi-zenith satellite (QZS), and highly reliable by notification of health information and failure determination The user's convenience is notified by notifying the user of the support information for capturing the GPS and capturing the GPS satellite, etc. (Non-patent Document 1). Since there is always one zenith (quasi-zenith satellite) at the zenith, this is captured, then the other GPS satellites are quickly captured using the GPS information in this QZS, and four are secured, Start positioning. In this way, the satellite acquisition time is shortened.

From the Quasi-Zenith Satellite (QZS), as shown in Figure 7,
・ L1C / A (frequency 1575.42 MHz (Mega Herz)),
・ L1C (frequency 1575.42 MHz),
・ L1-SAIF (SBAS (Satellite Based Augmentation System) compatible signal: Frequency 1575.42 MHz: Quasi-zenith original),
・ LEX (frequency 1277.85 MHz: Quasi-zenith original),
・ L2C (frequency 1222.70 MHz),
・ L5 (frequency: 1766.45MHz)
6 types of satellite positioning signals are planned to be transmitted. The L1C / A, L1C, L2C, and L5 positioning signals are GPS interpolation signals. The L1-SAIF and LEX signals are reinforcement signals that are transmitted by superimposing added value information. The superimposable transmission speed is 250 bps (bits per second) for L1SAIF (correction information and integrity information are distributed at a speed of 250 bps), and a high-speed message of 2 kbps (kilo bits per second) can be transmitted for LEX.

<LEX signal>
The center frequency of the LEX signal is 1277.85 MHz, and the modulation of the LEX signal is BPSK (Binary Phase Shift Keying) using a Kasami sequence spreading code, and the specification is to alternately switch between a short code with a period of 4 ms (millisecond) and a long code with a period of 410 ms. It has become. A 1-frame 2000-bit navigation message (LEX message) is superimposed on the short code. The message is composed of a total of 2000 bits including a 49-bit header, a 1695-bit data portion, and a 256-bit Reed-Solomon code for error detection / correction. The header is a 32-bit preamble indicating the head of the message, and an 8-bit PRN number (Pseudo Random Noise: GPS satellite pseudo-random noise signal number for transmitting satellite identification. This number generates a specific pseudo-noise code inside the receiver. And a desired satellite is captured and received as compared to the received waveform), an 8-bit message type ID representing the message type, and a 1-bit alert flag. Since one frame of the LEX message is transmitted in one second, the effective data transmission rate that can be used for the correction data for high-precision positioning reinforcement is 1695 bps (Non-patent Documents 1 and 2).

In GPS, the estimated position of the GPS satellite orbit is
・ Ephemeris (almanac),
・ Broadcasting calendar (ephemeris: orbital element of the satellite itself in the navigation message of the GPS satellite: the position of the satellite is calculated based on the orbital element),
・ Precise ephemeris (orbital elements calculated based on high-precision orbit tracking of GPS satellites by ground tracking network)
The three types are provided. The GPS receiver confirms satellites that can be used for positioning based on almanac data, obtains accurate time information from the ephemeris data, and synchronizes with the clock inside the receiver in nanosecond units. The broadcast calendar (ephemeris) is always broadcast by GPS satellites, and the precise calendar is calculated by post-processing by the ground station, and is obtained through the Internet together with almanac. The accuracy of almanac is about several km, and the broadcast calendar (ephemeris) is 2-50 m, for example, when SA (Selectable Availability: noise is superimposed on the radio wave signal of GPS satellites to lower the positioning accuracy of general users) is on. When the SA is off, for example, 2 to 5 m or less, and the precise calendar is, for example, 0.5 to 1 m or less.

<PPP type high precision positioning>
Various experiments conducted using LEX signals transmitted from the Quasi-Zenith Satellite (QZS) include, for example, demonstration and evaluation of real-time PPP (Precise Point Positioning) type high-accuracy positioning The LEX signal header message types 10 and 11 store, for example, the following correction data (Non-Patent Document 2).

(1) Ephemeris, SV (satellite vehicle) clock parameters: High precision ephemeris and SV clock parameters of QZSS and GPS satellites (nominal broadcast cycle 12 seconds, update cycle 3 minutes, nominal effective period 6 minutes).

(2) Ionospheric delay correction parameters (nominal broadcast cycle 12 seconds, update cycle 30 minutes)

(3) Signal health (nominal broadcast cycle 1 second, update cycle 1 second)

  In such PPP-type high-precision positioning, by using the precise satellite orbit and clock information sent by the LEX signal from "Michibiki" which is the first quasi-zenith satellite (QZS), a reference station is not required. It realizes PPP type high-accuracy positioning, which is normally realized using a reference point on the ground.

  In the normal PPP type positioning, an integer bias (Integer Ambiguity) included in a carrier phase observation value to be described later cannot be solved. For this reason, the convergence time of the positioning solution is long, and continuous observation is usually required for several tens of minutes just to obtain a sub-decimator class accuracy solution. In addition, in order to cancel the influence of ionospheric delay, it is essential to use a two-frequency receiver, and operation using an inexpensive one-frequency receiver is difficult.

<RTK-GPS>
On the other hand, in a network RTK (Real Time Kinematic) type positioning (RTK-GPS) that has already been put into practical use, a solution with centimeter-class accuracy can be obtained at high speed by solving an integer bias (Non-patent Document 3). . However, since a mobile phone is used for correction data transmission, there is a restriction that the service cannot be used outside the mobile phone service area.

<PPP-RTK positioning>
Therefore, the PPP-RTK type positioning solves these problems, and provides a highly accurate positioning service by transmitting correction information at a frequency optimized by separating correction information for each error item. By updating the correction data frequently, not only stationary users but also mobile users are targeted for service. If PPP-RTK type correction data can be broadcast to a user using a LEX signal, positioning with centimeter-class accuracy is possible. Correction data broadcast from the Quasi-Zenith Satellite (QZS) using the LEX signal includes satellite orbit / clock error, ionospheric delay, tropospheric delay, satellite code bias (satellite code bias for L1, L2, L5), satellite carrier phase Examples include bias (satellite initial phase), satellite ID, quality control information, ground correction grid point version, correction time, frame number, and the like (Non-Patent Document 2). These correction data are calculated by sequentially estimating model parameters based on GPS / GNSS observation data of a reference station network at a data center, for example.

  Below, GPS positioning is outlined. In a terminal that receives a positioning / ranging signal broadcasted by a positioning satellite such as GPS, when calculating the distance to the positioning satellite, four or more distances from the positioning satellite are acquired, and the position of the terminal (x, y, x) and time are estimated. As is well known, there are two methods for calculating the distance.

<Pseudo distance>
A measurement value of a positioning signal obtained in a general GPS / GNSS receiver is called a pseudo range.

  In single positioning, the distance of four GPS satellites is measured. The distance is obtained from the difference between the time when the radio wave leaves the satellite and the time when it reaches the receiver. Since the clock of the receiver is inaccurate, the distance thus obtained is also inaccurate, so it is called “pseudo distance”. The pseudo-range observation value P is measured between a satellite S and a receiver r measured by a positioning code called a PRN (Pseudo-Random Noise) code in a positioning signal transmitted from a GPS / GNSS (Global Navigation Satellite System) satellite. It is defined as the signal propagation time multiplied by the speed of light.

ρ is the geometric distance between the satellite receiver (m), c is the speed of light (m / s), dt _r is the receiver clock error, dT ^S satellite clock error, I _r ^S is ionospheric delay (m), T _r ^S represents a tropospheric delay (m), and ε _p represents a pseudorange observation error (m) including a multipath.

  The geometrical distance ρ represents the physical distance between the satellite S and the receiver, and in the inertial space between the satellite antenna phase center position when the positioning signal is transmitted and the receiving antenna phase center position when the positioning signal is received. Is defined as the distance.

In Expression (2), ρ ^S and ρ _r indicate the positions (m) of the satellite and the receiver in the fixed earth coordinate system. t is the positioning signal reception time, which is obtained by subtracting the receiver clock error dt (sec) from the observation time tr measured by the receiver clock (t = tr−dt). τ is the radio wave propagation time (sec), which is the geometric distance divided by the speed of light c (τ = ρ / c). During the radio wave propagation time τ due to the rotation of the earth, the fixed earth coordinate system rotates ω _E τ (rad) with respect to the inertial coordinate system. The calculation of the satellite position at the time of transmitting the positioning signal includes a correction Rz (ω _E τ) for the rotation of the coordinate system. Rz (θ) is a coordinate system rotation matrix (rotation angle θ) around the z axis (z axis of the xyz coordinate of the earth fixed coordinate system).

<Single positioning>
FIG. 8 is a diagram schematically showing a positioning device (receiver) and satellite coordinates (ECEF (Earth-Centered Earth-Fixed) system: earth-centered earth fixed)). With reference to FIG. 8, the independent positioning of the positioning device will be described. The position vectors of the satellite and the positioning device are ρ ^S = [x ^S , y ^S , z ^S ] and ρ _R = [x _R , y _R , z _R ], respectively. The geometric distance ρ between the satellite and the positioning device is given by

ρ = | ρ ^S −ρ _R | = √ ((x ^S −x _R) ² + (y ^S −y _R) ² + (z ^S −z _R ) ² ) (4)

  The positioning device measures the following pseudorange R.

R = ρ + Δρ = ρ + cΔδ (5)
Δδ = δ ^S −δ _R + δ _D (6)

However,
δ ^S is the offset time of the satellite clock (estimated from the clock correction factor of the navigation message), δ _R is the offset time of the positioning device clock,
δ _D is the offset time of the arrival time of the signal from the satellite to the positioning device,
It is.

The unknowns in the positioning operation are
・ Position coordinates of positioning device ρ _R = [x _R , y _R , z _R ],
・ Positioning device correction term δ _R
It is four.

The amount of observation with the positioning device is
・ Pseudo distance R,
・ Satellite position coordinates ρ ^S = [x ^S , y ^S , z ^S ],
A term that cannot be modeled for the clock correction terms δ ^S , δ _D ,
The rest is treated as noise n.

For the four satellites i (= 1 to 4)
R = ρ ⁱ −cΔδ ⁱ + cδ _R + n ⁱ (7)

However,
ρ ⁱ = | ρ ⁱ −ρ _R | = √ ((x ⁱ -x _R ) ² + (y ⁱ -y _R ) ² + (z ⁱ -z _R ) ² ) (8)

A linear approximation is performed around the value ρ ₀ (approximate value) of the coordinates ρ _R of the positioning device.

ρ _R = ρ ₀ + Δρ = [x ₀ , y ₀ , z ₀ ] + [Δx _R , Δy _R , Δz _R ] (9)

From Taylor expansion f (a + h) = f (a) + hf ′ (a) of function f (x), when ρ ⁱ is expanded to ρ ⁱ ₀ (= ρ ⁱ | ρ _R = ρ ₀ ),
ρ ⁱ = ρ ⁱ ₀ + (− 1 / ρ ⁱ ₀ ) (ρ ⁱ −ρ ₀ ) ^T Δρ (10)
(However, T represents transposition.)

ρ ⁱ ₀ = | ρ ⁱ −ρ ₀ | = √ ((x ⁱ −x ₀ ) ² + (y ⁱ −y ₀ ) ² + (z ⁱ −z ₀ ) ² ) (11)

R ⁱ −ρ ⁱ ₀ −cδi = − (1 / ρ ⁱ ₀ ) (ρ ⁱ −ρ ₀ ) ^T Δρ + cδ _R + n ⁱ (12)

The single positioning is performed by solving the linear simultaneous equations of the four satellites and obtaining (Δρ, δ _R ) from Equation (12) until ρ ₀ + Δρ converges within a predetermined calculation accuracy.

<Carrier phase distance>
A GPS / GNSS receiver (positioning device) for precise positioning mainly for the purpose of precise surveying measures an observation amount called a carrier phase in addition to a pseudorange. The carrier phase is obtained by continuously measuring the carrier phase angle of the positioning signal demodulated by the receiver. The carrier phase includes distance information between the satellite and the observation point as well as the pseudorange, but is used for precise positioning because it can be measured with higher accuracy than the pseudorange. The carrier phase observation can be expressed as follows:

λ is the wavelength of the carrier wave, the epsilon _[Phi represents an observation error including multipath.

<Integer Ambiguity>
Unlike the pseudorange, the carrier phase includes a bias that is a fixed value in continuous measurement called carrier phase bias. The carrier phase bias N (cycle) can be expressed as follows using the receiver initial phase φ _0r (cycle), the satellite initial phase φ ^S ₀ (cycle) and the integer ambiguity n.

  Since the above pseudo distance is measured in code units (one wavelength unit), the accuracy is rough. On the other hand, since the carrier phase angle is measured up to the phase angle within one carrier wave, the accuracy is high. There are error factors such as satellite position error, satellite clock error, ionosphere delay error, troposphere delay error, multipath error, and noise in measuring the distance to the positioning satellite.

  Multipath is a phenomenon in which the radio wave propagation time fluctuates when a positioning signal transmitted from a satellite is reflected by an object near the receiver and a plurality of propagation paths are formed. Multipath is a significant error factor in pseudorange measurements, and its magnitude can reach several meters. Similar to the pseudorange measurement, the carrier phase measurement value is also affected by multipath, but the magnitude is much smaller than the pseudorange, and when using a precision positioning antenna and receiver with multipath countermeasures Then, it is the order of several cm at the maximum. The observation error in the carrier phase measurement is usually a value of cm or less, and the distance between the satellite and the observation point can be measured with the accuracy of cm or less by giving other terms with sufficient accuracy. It is φ that can be actually measured. The ambiguity is estimated separately by rough measurement such as code positioning. The number of codes (1 code = 1 ms) is measured to calculate the arrival time from the satellite to the receiving device, and the distance is calculated by multiplying the speed of light.

<Cycle slip>
Carrier phase bias becomes an integer by eliminating double phase difference of carrier phase in relative positioning, thereby eliminating receiver and satellite initial phase terms, but generally not an integer if no difference is taken. . When the positioning signal is temporarily interrupted or the observation noise becomes large, and the carrier phase cannot be measured continuously at the receiver, a new value is introduced for the integer ambiguity of the carrier phase bias, Carrier phase measurements may skip. This phenomenon is called cycle slip. The detection and correction of cycle slip is one of the important issues of precision analysis using carrier phase.

  The GPS receiver stores almanac data and ephemeris data immediately before the power is turned off. The state in which this data is completely lost is called “cold”, the state in which the almanac data is not lost is called “warm”, and the state in which the ephemeris data is not lost is called “hot”. While the GPS receiver stores a valid ephemeris, it can be hot-started, but if it has expired, it will be a warm start because only the almanac. A cold start occurs when there is no orbit information. For example, since it takes 12.5 minutes to receive all the trajectory information, the trajectory information is obtained by receiving about 15 minutes when a cold start is performed.

  In Patent Document 1, as a positioning device that speeds up the calculation of ambiguity, the carrier phase and pseudorange from the satellite are measured, the initial value of ambiguity is calculated, and the calculated initial value is used. Estimate candidate solutions. The positioning device sets the range of the height position of the positioning device based on its approximate horizontal position (latitude, longitude) and the altitude information of the road at that horizontal position, and many carrier waves from each satellite have the same phase. A configuration is disclosed in which, from among the intersections (solution candidates), the solution is limited to the solution candidates within the set range, and whether or not it is a true solution is tested.

  In Patent Document 2, a satellite communication unit includes a code phase measurement unit that measures a pseudorange with each satellite, a carrier phase measurement unit that measures the phase of the carrier wave of each satellite, and a carrier wave that measures the frequency of the carrier wave of each satellite. A frequency measurement unit is provided, and the processing unit calculates the velocity vector of the positioning target by measuring the frequency of the carrier wave of each satellite and obtaining the Doppler shift, and sets the position of the positioning target before positioning as A, and the velocity vector A configuration is disclosed in which the center B of the solution search range is obtained by B = A + T · V, and the ambiguity is determined by limiting the solution search range, where V is V and the time interval for calculating the velocity vector is T. Yes.

  Further, in Patent Document 3, a moving body travels as a GPS positioning accuracy early stabilization method that always obtains a highly accurate current position display even on roads where objects such as tunnels, bridges, and pedestrian bridges exist. A means for relaying GPS radio waves is provided near the exit of the structure on the road, and when the mobile object approaches the vicinity of the exit of the structure, the positioning process by the GPS positioning system equipped on the mobile object is performed in advance. A configuration that has been started is disclosed. In Patent Document 3, a repeater having a GPS antenna and a repeater antenna is provided in the vicinity of an exit of a structure such as a pedestrian bridge or a tunnel, and a moving body such as an automobile traveling on a road under the structure has an exit. When coming to the vicinity, the radio wave received by the GPS antenna from the GPS satellite is relayed to the moving body via the repeater antenna, and the position calculation processing by the GPS receiver mounted on the moving body passes the structure through the moving body. At this time, it is started before that, and when the moving body moves to a place where the radio wave from the GPS satellite can be directly received, the accuracy of the position calculated by the GPS receiver is quickly restored.

JP 2009-74930 A JP 2010-71686 A JP 2007-93436 A

Quasi-Zenith Satellite System User Interface Specification (IS-QZSS) March 27, 2013 Japan Aerospace Exploration Agency Internet (searched April 27, 2013) <URL: http://qz-vision.jaxa.jp/USE /is-qzss/DOCS/IS-QZSS_15_E.pdf> Tomoji Takasu, Takuji Ebinuma, Akio Yasuda (Tokyo Marine University), Kei Kogure, Tomoyuki Miyano (Japan Aerospace Exploration Agency) 2.6 QZSS LEX Signal Overview, Evaluation and Extension, Internet (Search April 27, 2013) <URL: http://gpspp.sakura.ne.jp/paper2005/gpssymp_2009_revA.pdf> Tomoji Takasu (Tokyo University of Marine Science and Technology), A. 4 RTK-GPS and network type RTK-GPS positioning technology Internet (searched on April 27, 2013) <URL: http://gpspp.sakura.ne.jp/paper2005/gpssymp_2007.pdf>

  The analysis of related technology is given below.

  In the positioning device using the carrier phase, as long as the positioning signal is captured (locked), it is not necessary to estimate the carrier bias N every time. When reception of a positioning signal (radio wave) is interrupted (cycle slip), it is necessary to estimate N again.

  In the case of positioning at a fixed point, it is only necessary to consider only the satellite side, so it is easy to re-estimate N. However, in the case of positioning with a moving body, since N greatly changes, it takes time to estimate N. Cost. Moreover, in a mobile body, there are many opportunities for the positioning signal to be interrupted.

  In PPP-RTK type positioning and the like, there is a demand for quickly knowing position and time information from a positioning signal (correction data) from a quasi-zenith satellite (QZS).

  In Patent Document 3, a GPS antenna and a repeater provided with a repeater antenna are provided in the vicinity of an exit of a tunnel or the like. However, when a mobile object or a structure is under or inside a direct wave from a GPS satellite, Since it cannot receive and is far away from the vicinity of the exit, it cannot receive radio waves from the repeater antenna, and the GPS receiver cannot receive any radio waves from the GPS satellite. The position calculation unit cannot calculate the position of the vehicle. That is, when entering a structure such as a tunnel, reception of positioning signals (radio waves) is interrupted. For this reason, the carrier wave bias N is re-estimated in the tunnel when receiving the positioning signal from the repeater antenna.

  Therefore, an object of the present invention is to make it possible to avoid a positioning signal from a satellite as much as possible in a space where a positioning signal from the satellite is blocked by a structure or a structure such as a tunnel, a bridge, a pedestrian bridge, and the like. However, an object is to provide an apparatus, a system, a method, and a program that enable real-time positioning with high accuracy.

According to one of several related aspects of the present invention (viewpoint 1), the satellite includes a first antenna that receives a positioning signal from the satellite in an area where the positioning signal from the satellite can be received. A relay for relaying the positioning signal received by the first antenna and transmitting from the second antenna to the space where the positioning signal from is cut off,
The positioning device for positioning based on the positioning signal received from the satellite cannot receive the positioning signal relayed by the repeater in the space where the positioning signal from the satellite is blocked, and the positioning signal from the satellite When a disconnection is detected, a positioning system is provided that acquires movement information of the satellite and movement information of the positioning device, calculates a distance between the satellite and the positioning device, and estimates an integer bias of a carrier phase.

According to another aspect (viewpoint 2), the positioning signal received by the first antenna provided in the area where the positioning signal from the satellite can be received is obtained in a space where the positioning signal from the satellite is blocked. Relay from the repeater and transmit from the second antenna,
The positioning device for positioning based on the positioning signal received from the satellite cannot receive the positioning signal relayed by the repeater in the space where the positioning signal from the satellite is blocked, and disconnects the positioning signal from the satellite. Is detected, the movement information of the satellite and the movement information of the positioning device are acquired, the distance between the satellite and the positioning device is calculated, and the positioning method for estimating the integer bias of the carrier phase is provided.

  According to still another aspect (viewpoint 3), the positioning signal received from the first antenna provided in the area where the positioning signal from the satellite is received, in a space where the positioning signal from the satellite is blocked. When moving to the space provided with a repeater that relays the positioning signal and transmits from the second antenna, the positioning signal relayed by the repeater cannot be received and the disconnection of the positioning signal from the satellite is detected. There is provided a positioning apparatus comprising means for acquiring satellite movement information and positioning apparatus movement information, calculating a distance between the satellite and the positioning apparatus, and estimating an integer bias of a carrier phase.

  According to still another aspect (viewpoint 4), the positioning signal received from the first antenna provided in the area where the positioning signal from the satellite is received, in a space where the positioning signal from the satellite is blocked. When moving to the space provided with a repeater that relays the positioning signal and transmits from the second antenna, the positioning signal relayed by the repeater cannot be received and the disconnection of the positioning signal from the satellite is detected. A program is provided that acquires satellite movement information and positioning apparatus movement information, calculates a distance between the satellite and the positioning apparatus, and executes processing for estimating an integer bias of a carrier phase.

  According to still another aspect (viewpoint 5), a computer-readable medium (for example, a semiconductor memory or a magnetic / optical disk) on which the program of viewpoint 4 is recorded is provided.

  According to the present invention, a positioning signal from a satellite can be avoided as much as possible in a space where the positioning signal from the satellite is blocked by a structure or a structure such as a tunnel, a bridge, a pedestrian bridge, and the like. High-precision positioning can be realized in real time.

It is a figure for demonstrating the principle of this invention typically. It is a figure for demonstrating the principle of this invention typically. 2 is a diagram illustrating a configuration of a receiver according to Embodiment 1. FIG. FIG. 6 is a diagram illustrating a processing procedure (operation) according to the first embodiment. It is a figure explaining the system of Embodiment 1. FIG. It is a figure explaining another system of Embodiment 1. FIG. It is a figure explaining the signal from QZS. It is a figure for demonstrating independent positioning.

  According to the embodiment of the present invention, for example, a positioning signal from the satellite can be received in a space where the positioning signal from the satellite is blocked, such as a structure such as a tunnel, a bridge, a pedestrian bridge, or the like. In a positioning device that relays a positioning signal received by a first antenna provided in a region by a repeater and transmits from a second antenna, receives a positioning signal from the satellite, and calculates an integer bias of a carrier phase, When the positioning signal from the satellite cannot be received in the space where the positioning signal from the satellite is interrupted and the positioning signal from the satellite is detected, the movement information of the satellite and the movement information of the positioning device are obtained. Obtaining and calculating the distance between the satellite and the positioning device to estimate the integer bias of the carrier phase. For this reason, high-precision positioning can be continued in real-time.

  FIG. 1 is a diagram for explaining the principle of the present invention. In FIG. 1, an in-vehicle navigation device is used as a positioning device that receives a positioning signal from a satellite and calculates an integer bias of a carrier phase. In FIG. 1, a positioning device (receiver) (on-vehicle navigation device) mounted on a moving body 4 such as a car is not shown. In FIG. 1, a passenger car is shown as the moving body 4, but it is needless to say that the moving body is not limited to the vehicle. Further, in FIG. 1, a tunnel is illustrated as a space (region) where a positioning signal from a satellite is blocked (shielded), but a space (region) where a positioning signal (radio wave) from a satellite is blocked (shielded). Of course, this is not limited to tunnels, but can be applied to structures such as bridges and pedestrian bridges.

  As shown in FIG. 1, an antenna 12 that receives positioning signals from the quasi-zenith satellite 1 and the GPS satellite 2, and a signal received by the antenna 12 (a positioning signal from the GPS satellite 2, a positioning signal from the quasi-zenith satellite 1 (L1C / A repeater (repeater) 13 that relays the A signal, L1C signal, L2C signal and L5 signal, L1-SA1F, and LEX signal), and a repeater antenna that propagates the signal relayed by the repeater (repeater) 13 in the air 1 includes a set of an antenna 12, a repeater (repeater) 13, and a repeater antenna (relay antenna) 14 for the sake of simplicity. Of course, a plurality of sets may be arranged at different locations depending on the length of the positioning signal, etc. In the following, positioning signals from the quasi-zenith satellite 1 and the GPS satellite 2 (complementation, reinforcement) No. of the containing), simply referred to as a positioning signal from a satellite.

When the moving body 4 is in the A position before entering the tunnel 15 (time t0), the distance R between the positioning device (receiver) in the moving body 4 and the satellite 1 is
R = λN + φ (= c (t _R −t ^S )) (15)
And

Where λ is the wavelength of the positioning signal, N is an integer, φ is the carrier phase, R is the pseudorange, ρ is the geometric distance between the satellite and the positioning device, Δρ is the distance error, c is the speed of light, t _R , Is the positioning signal arrival time at the positioning device 3, and t ^S is the transmission time of the satellite.

  What can be observed by the positioning device is the phase φ (0 ≦ φ <λ) of the carrier wave transmitted by the satellite, and the integer bias N cannot be measured directly. In the positioning device, the integer bias N is estimated from the measured value of the carrier phase φ by a known method (for example, LAMBDA (least square ambiguity de-correlation adjustment) method using a Kalman filter). In addition, the obtained integer bias is tested. Then, the positioning device performs positioning (positioning device position coordinates and clock error δR) based on the integer bias N.

When the moving body 4 enters the tunnel 15 and the positioning signal from the satellite is cut off at the point B near the entrance 16,
・ The distance R between the positioning device and the satellite at point A,
Movement information (movement vector) ΔX from point A (time at the positioning device that received the last positioning signal: t0) to point B (time at the positioning device at which the positioning signal was interrupted: t1 = t0 + Δt) , The movement vector ΔS of the satellite (quasi-zenith satellite) 1 from time t ^S to t ^S + Δt,
From the above, the pseudorange R ′ between the positioning device (receiver) and the satellite at the point B is estimated.

R ′ = ρ ′ + Δρ ′ (16)

  Here, ρ ′ is a geometric distance between the satellite and the positioning device, and Δρ ′ is a distance error.

  An integer bias N is estimated from this R '.

R ′ = λN ′ + φ (17)
(0 ≦ φ <λ)

  At the point A where the positioning device (not shown) in the moving body 4 can receive the positioning signal from the satellite, the positioning device in the moving body 4 obtains the integer bias N based on the measured carrier phase φ. At the point B where the positioning signal cannot be received, the positioning device in the moving body 4 obtains the integer bias N based on the estimated distance R ′. In the positioning device in the moving body 4, the repeater 13 takes the signal delay in the antenna 12, the wiring, the repeater 13, and the repeater antenna 14 with respect to the measurement signal from the repeater antenna 14, at the point B. The pseudo-range R ′ between the positioning device (receiver) and the satellite may be estimated. In this case, the repeater 13 may transmit the positioning signal including information indicating that the positioning signal is a positioning signal relayed by the repeater 13 from the repeater antenna 14.

  When the mobile unit 4 reaches a point C near the repeater antenna 14 and the positioning device in the mobile unit 4 receives a radio wave relaying a positioning signal from the satellite (time t2 at the positioning device), the positioning unit from the satellite Based on the integer bias value N ′ of the carrier phase estimated when the signal is disconnected (for example, an initial value), the integer bias of the carrier phase is derived from the carrier phase data.

  When the mobile unit 4 exits the tunnel 15 and reaches a point D where a positioning signal from a satellite can be received, an integer bias of the carrier phase from the carrier phase data is obtained based on the integer bias value of the carrier phase obtained at the point C. Is derived. For this reason, in the positioning device, high-precision positioning (PPP-RTK) can be continued promptly when the reception of the positioning signal from the quasi-zenith satellite 1 (including the LEX signal carrying correction data) is resumed.

  In Patent Document 3 described above, a positioning signal from a GPS satellite is interrupted at the entrance of a tunnel, structure, or the like. For this reason, when the positioning device receives a relay signal from a repeater antenna in the tunnel, the integer bias of the carrier phase is estimated from the beginning, which takes a lot of time (depending on the length of the tunnel, the car may In some cases, the carrier phase phase integer bias may not be obtained.

  On the other hand, according to the present embodiment, when the positioning signal from the satellite is interrupted, high-precision positioning can be continued in real time using the movement information of the positioning device.

  In FIG. 1, the distance between the quasi-zenith satellite 1 and the positioning device in the moving body 4 is R, but the same applies to the distance between the GPS satellite 2.

  FIG. 2 is a diagram showing a positioning device (receiver) and satellite coordinates (ECEF (Earth-Centered Earth-Fixed) system: earth-centered earth fixed) at points A and B in FIG. The positioning device at point A in FIG. 2 corresponds to FIG. 8 and receives a positioning signal from a satellite. On the other hand, a positioning signal cannot be obtained at point B.

As an example of the calculation of the pseudo distance, the reception time of the positioning signal from the satellite by the positioning device at the point A (time at the positioning device) is t0 (the positioning signal transmission time at the satellite is t0−τ: where τ is Radio wave propagation time), and the time at the positioning device at time B when the positioning signal from the satellite is interrupted is t1 (= t0 + Δt). The positioning device acquires a movement vector (Δx) that the positioning device has moved from time t0 (position vector of the positioning device is ρ _R ) to time t1. Therefore, the position vector ρ ^′ _R of the positioning device at point B is given by

ρ ^′ _R = ρ _R + Δx (18)

In the equation (18), ρ _R is a position vector (ρ _R ) of the positioning device at the point A in FIG. 2 obtained by the positioning device together with the offset δ _R of the positioning device clock.

The positioning device also determines the time interval between time t0 and time t1 (Δt = t1−t0) based on the position information of the satellite and the satellite orbit at time t0−τ when the satellite transmits the positioning signal received at point A at time t0. ) To obtain the movement vector from the time t0-τ of the satellite. The position vector ρ ^′S at the satellite time t0−τ + Δt is given by the following equation (19).

ρ ^'S = ρ ^S + ΔS (19)

ρ ^S is data transmitted from the satellite at point A (position vector of the quasi-zenith satellite 1 at time t0−τ, which may include correction data transmitted from the quasi-zenith satellite), and ΔS is It is obtained from the satellite orbit calculation (vector corresponding to the distance that the satellite that was in the position vector ρ ^S at time t0−τ moved at time Δt).

Therefore, the geometric distance ρ ′ between the satellite and the positioning device at time t1 in the positioning device is given by the following equation (20). The calculation of the satellite position at time t1 includes the correction Rz (ω _E τ) for the coordinate system rotation described above.

^{ρ '= | ρ' S -ρ} 'R | = | (ρ S + ΔS) - (ρ R + Δx) | ··· (20)

In calculating the pseudo distance R ′ at the point B moved Δx from the point A by the positioning device,
R ′ = ρ ^′ + c (δ _R −δ _S + δ _D ) (21)
For example, the positioning device clock δ _R approximates the positioning result at the point A, and the satellite clock offset δ _S uses the satellite clock offset included in the positioning signal (or LEX signal) received at the point A. May be. Further, the offset [delta] _D of the arrival time from the satellite to the positioning device may be used an approximate value. Alternatively, [delta] _D is ionospheric delay that is included in the LEX signal received at point A, using the troposphere delay information may be approximated. In the positioning device, the integer bias is estimated from R ′ = N′λ + φ. The movement ΔS of the satellite can be obtained by numerical calculation from the satellite orbit (Kepler equation or the like). Of course, in equation (21), the offset δ _S of the satellite clock and the offset δ _D of the arrival time from the satellite to the positioning device may be obtained by parameter fitting or the like. A description will be given below according to the embodiment.

<Embodiment 1>
FIG. 3 is a diagram illustrating a configuration of the receiver 10 mounted on the positioning device 3 according to the first embodiment. The positioning device 3 includes an output device such as a display device, an input device, a CPU (Central Processing Unit), etc., which are not shown in FIG. Referring to FIG. 3, the receiver 10 includes an L1 signal processing unit 101 that processes the received L1 signal, an L2 signal processing unit 102 that processes the received L2 signal, a LEX signal processing unit 103 that processes the received LEX, and positioning. Satellite position / clock calculation unit 104 that calculates the position of the satellite that received the signal and the clock of the satellite, ionosphere / troposphere delay correction unit 105 that corrects the ionosphere / troposphere delay, ranging observation data (carrier phase), satellite Position correction unit 106 that calculates a correction distance from the position of the satellite and the clock of the satellite, the ionosphere / troposphere delay amount, a position calculation unit 107 that calculates a position of the positioning device, a clock based on the correction distance data, and a positioning signal from the satellite When the signal is interrupted by the positioning signal disconnection detection unit 108 and the positioning signal disconnection detection unit 108 that detect the disconnection, the distance between the satellite and the positioning device is calculated, and the integer bias is estimated from the calculated distance That the distance calculation unit 109, and an antenna 110. Among these, the L1 signal processing unit 101, the L2 signal processing unit 102, the LEX signal processing unit 103, the satellite position / clock calculation unit 104, the ionosphere / troposphere delay amount correction unit 105, the distance correction unit 106, and the positioning calculation unit 107 are related. Technology configurations may be used. The positioning device 3 includes an acceleration / gyro sensor 11 that functions as a distance sensor. The gyro sensor detects angular velocity (for example, how much it is bent to the left and right). When the positioning device 3 is mounted as a car navigation device, the travel distance may be calculated using tire rotation or the like.

  In FIG. 3, for the sake of simplicity of explanation, the positioning signal loss detection unit 108 detects the presence / absence of reception of L1, L2, and LEX signals from the output signal of the antenna 110. From the outputs of the L1 signal processing unit 101, the L2 signal processing unit 102, and the LEX signal processing unit 103, the presence or absence of reception of the L1, L2 signal, and LEX signal may be detected.

  When the positioning signal disconnection detecting unit 108 detects the disconnection of the positioning signal, the positioning signal disconnection detecting unit 108 stops the operations of the ionosphere / troposphere delay amount correcting unit 105, the distance correcting unit 106, and the satellite position / clock calculating unit 104 ( (Deactivation). When the positioning signal disconnection detection unit 108 detects that the positioning signal is disconnected, the distance calculation unit 109 calculates the movement vector Δx of the positioning device 3 based on the output of the acceleration / gyro sensor 11, and further calculates the movement vector ΔS of the satellite. The distance R ′ between the satellite and the receiver is calculated, and the integer bias is estimated from the distance R ′.

  In the distance correction unit 106 that operates when receiving the positioning signal, the single phase difference (the phase difference of the carrier wave from one positioning satellite with two antennas as a set) is obtained from the distance measurement observation data (carrier wave phase data) and the satellite position / clock information. Or, calculate the observed amount of double phase difference (difference of single phase difference based on radio waves from two positioning satellites), and use single-phase difference and integer bias of double phase difference using Kalman filter and LAMBDA method And the integer bias information is passed to the positioning calculation unit 107. The positioning calculation unit 107 may update the positioning data of the positioning device based on the satellite information (position, clock), phase difference information, and integer bias. The positioning calculation unit 107 corrects the positioning data (position / clock) in consideration of signal delays at the antenna 12, the repeater 13, and the repeater antenna 14 when the positioning signal from the satellite passes through the repeater 13. You may make it do. This is done by including correction information such as signal delay in the positioning signal propagating from the repeater antenna 14 when the repeater 13 relays the positioning signal, and notifying the positioning calculator 107. Of course, one part or all of the functions of the respective processing units in FIG. 3 may be realized by a program executed on a computer constituting the positioning device 3.

  FIG. 4 is a diagram for explaining the operation of the first embodiment. The positioning device 3 calculates the distance R between the satellite and the positioning device 3 based on the positioning signal received from the satellite, and holds it in a storage device (not shown) (step S1). The positioning device 3 may be an in-vehicle navigation system or a mobile terminal.

  When the positioning signal disconnection detection unit 108 of the receiver 10 of the positioning device 3 detects a positioning signal disconnection (Yes in step S2), positioning based on the positioning signal cannot be performed, and thus the distance calculation unit 109 of the receiver 10 of the positioning device 3 is detected. Calculates the moving distance of the positioning device 3 from the time when the previous positioning signal was acquired (step S3). When the positioning signal can be received by the receiver 10 of the positioning device 3 (No in step S2), the positioning in step S1 is performed.

  The distance calculation unit 109 of the receiver 10 of the positioning device 3 calculates the movement distance ΔS of the satellite 1 from the position of the satellite 1 at the time when the previous positioning signal was acquired (step S4).

  The distance calculation unit 109 of the receiver 10 of the positioning device 3 calculates the previous distance R (the distance R between the quasi-zenith satellite 1 and the positioning device 3), the movement distance ΔS of the quasi-zenith satellite 1, and the movement distance ΔX of the positioning device 3. The distance R ′ between the quasi-zenith satellite 1 and the positioning device 3 is calculated (step S5).

  The distance calculation unit 109 of the receiver 10 of the positioning device 3 calculates an integer bias N ′ (R ′ = N′λ + φ) from the distance R ′ between the quasi-zenith satellite 1 and the positioning device 3 (step S6). Thereafter, when the receiver 10 of the positioning device 3 resumes receiving the positioning signal (No in step S2), the positioning in step S1 is performed. At that time, the positioning calculation unit 107 uses the integer bias N ′ obtained by the distance calculation unit 109 as a candidate (for example, an initial value of the candidate), thereby shortening the positioning time compared to the case of obtaining the integer bias from the beginning. be able to.

  FIG. 5 is a diagram illustrating a system configuration according to the first embodiment. Referring to FIG. 5, the monitor station / correction information generation device 6 generates correction information based on a signal (satellite position / clock information, etc.) from the QZS 1 and includes correction information from the master control station / tracking control station 5. Send a signal to QZS1. The monitor station / correction information generating device 6 receives the LEX signal from the QZS 1, creates correction information, and transmits it to the master control station / tracking control station 5. The master control station / tracking control station 5 transmits the generated correction information to QZS1. The QZS 1 receives correction information from the master control station / tracking control station 5, and uses a LEX signal that transmits a correction signal (radio wave) to the positioning device 3 and the antenna 11 above the tunnel 15. ) The correction data broadcast from 1 may include, for example, satellite orbit information and satellite clock error information. According to the first embodiment, one or more antennas 12, repeaters 13, and repeater antennas 14 are provided in the tunnel 15, so that highly accurate correction information from the quasi-zenith satellite (QZS) can be obtained in the tunnel 15 by the positioning device 3. Can be provided. As a result, the positioning accuracy can be improved.

  FIG. 6 is a diagram illustrating another system configuration according to the first embodiment. Hereinafter, differences from FIG. 5 will be described. Referring to FIG. 6, the monitor station / correction information generation device 6 is connected to a signal (satellite position / clock information, etc.) from the QZS 1 and a plurality of (for example, nationwide) electronic reference points (reference criteria) connected via the communication network 8 On the basis of the monitoring result of the positioning signal of the satellite 2 at point 7), correction information is generated, and a signal including the correction information is transmitted from the master control station / tracking control station 5 to the QZS1. Positioning accuracy can be improved by generating correction data for positioning based on the positioning information from the electronic reference point 7 and broadcasting it from QZS1.

  As correction data broadcast from the Quasi-Zenith Satellite (QZS) 1 using the LEX signal, for example, satellite orbit information, satellite clock error information, ionosphere delay model, troposphere delay model, and monitoring station from electronic reference point 7 observation data The correction information generation device 6 may generate the correction information. These correction data are calculated by sequentially estimating model parameters by the monitor station / correction information generation device 6 based on GPS / GNSS observation data of the network of the electronic reference points 7 nationwide. According to the present embodiment, the correction data generated based on the observation data at the electronic reference point 7 is broadcast by QZS, thereby enabling high-precision positioning with the positioning device 3. Further, according to this system configuration, as in FIG. 5, by providing one or more antennas 12, repeaters 13, and repeater antennas 14 in the tunnel, high-precision correction from the quasi-zenith satellite (QZS) in the tunnel. Information (correction data generated based on observation data at the electronic reference point 7) can be provided to the positioning device 3.

  It should be noted that the disclosures of the above-mentioned patent documents and non-patent documents are incorporated herein by reference. Within the scope of the entire disclosure (including claims) of the present invention, the embodiment can be changed and adjusted based on the basic technical concept. Various combinations and selections of various disclosed elements are possible within the scope of the claims of the present invention. That is, the present invention of course includes various variations and modifications that could be made by those skilled in the art according to the entire disclosure including the claims and the technical idea.

1 Quasi-Zenith Satellite (QZS)
2 GPS satellites 3 Positioning device 4 Mobile body 5 Master control station / tracking control station 6 Monitor station / correction information generating device 7 Electronic reference point 8 Communication network 10 Receiver 11 Acceleration / gyro sensor 12 Antenna 13 Repeater (repeater)
14 repeater antenna 15 tunnel 16 entrance 17 exit 101 L1 signal processing unit 102 L2 signal processing unit 103 LEX signal processing unit 104 satellite position / clock calculation unit 105 ionosphere / troposphere delay amount correction unit 106 distance correction unit 107 positioning calculation unit 108 positioning signal Break detection unit 109 Distance calculation unit 110 Antenna

Claims (17)

A first antenna for receiving a positioning signal from the satellite is provided in an area where the positioning signal from the satellite can be received, and the first antenna receives the space for blocking the positioning signal from the satellite. A repeater that relays the positioning signal transmitted from the second antenna,
The positioning device for positioning based on the positioning signal received from the satellite cannot receive the positioning signal relayed by the repeater in the space where the positioning signal from the satellite is blocked, and the positioning signal from the satellite When a disconnection is detected, the positioning system acquires movement information of the satellite and movement information of the positioning device, calculates a distance between the satellite and the positioning device, and estimates an integer bias of a carrier phase. .   In the space where the positioning signal from the satellite is interrupted, the positioning device receives the positioning signal relayed by the repeater from the disconnected state of the positioning signal from the satellite, or the positioning signal from the satellite Derivation of the carrier phase phase integer bias from the carrier phase data based on the carrier phase phase integer bias value estimated when the positioning signal from the satellite was interrupted when resuming the reception of the positioning signal in the area where The positioning system according to claim 1, wherein the positioning system is performed. When the positioning signal from the satellite is disconnected, the positioning device receives the positioning signal from the first time point (t0) when the positioning device receives the positioning signal immediately before the positioning signal from the satellite is disconnected. The movement information (Δx) that the positioning device has moved up to the second time point (t1) when the positioning signal is cut off is acquired,
The positioning signal received by the positioning device at the first time point is based on the satellite position information and the satellite orbit at the third time point transmitted by the satellite, and the second time point and the first time point. The positioning system according to claim 1, further comprising means for acquiring movement information (ΔS) of the satellite from the third time point in the section (Δt = t1−t0).   The positioning system according to any one of claims 1 to 3, wherein the satellite includes a quasi-zenith satellite, and the positioning device receives positioning correction information broadcast from the quasi-zenith satellite. . For a space where positioning signals from satellites are blocked, positioning signals received by a first antenna provided in an area where the positioning signals from satellites can be received are relayed by a repeater and transmitted from a second antenna. Send
The positioning device for positioning based on the positioning signal received from the satellite cannot receive the positioning signal relayed by the repeater in the space where the positioning signal from the satellite is blocked, and disconnects the positioning signal from the satellite. And detecting the movement information of the satellite and the movement information of the positioning device, calculating the distance between the satellite and the positioning device, and estimating the integer bias of the carrier phase.   In the space where the positioning signal from the satellite is interrupted, the positioning device receives the positioning signal relayed by the repeater from the disconnected state of the positioning signal from the satellite, or the positioning signal from the satellite Derivation of the carrier phase phase integer bias from the carrier phase data based on the carrier phase phase integer bias value estimated when the positioning signal from the satellite was interrupted when resuming the reception of the positioning signal in the area where The positioning method according to claim 5, wherein the positioning method is performed. When the positioning signal from the satellite is disconnected, the positioning device receives the positioning signal from the first time point (t0) when the positioning device receives the positioning signal immediately before the positioning signal from the satellite is disconnected. The movement information (Δx) that the positioning device has moved up to the second time point (t1) when the positioning signal is cut off is acquired,
Based on the position information of the satellite and the satellite orbit at the third time point when the satellite transmits the positioning signal received by the positioning device at the first time point, the second time point and the first time point The positioning method according to claim 5, wherein movement information (ΔS) of the satellite from the third time point in a section (Δt = t1−t0) is acquired.   The positioning method according to any one of claims 5 to 7, wherein the satellite includes a quasi-zenith satellite, and the positioning device receives positioning correction information broadcast from the quasi-zenith satellite. .   In the space where the positioning signal from the satellite is blocked, the positioning signal received by the first antenna provided in the area where the positioning signal from the satellite can be received is relayed and transmitted from the second antenna. If the positioning signal from the satellite is detected because the positioning signal relayed by the repeater cannot be received and the positioning signal from the satellite is detected, the movement information of the satellite and the positioning device are acquired. A positioning device comprising means for calculating a distance between the satellite and the positioning device and estimating an integer bias of a carrier phase.   In a space where the positioning signal from the satellite is cut off, an area in which the positioning signal from the satellite can be received when the positioning signal relayed by the repeater is received from the disconnected state of the positioning signal from the satellite Means for deriving an integer bias of the carrier phase from the carrier phase data based on the integer bias value of the carrier phase estimated when the positioning signal from the satellite is interrupted when resuming the reception of the positioning signal at The positioning device according to claim 9. When the positioning signal from the satellite is disconnected, the positioning device receives the positioning signal from the first time point (t0) when the positioning device receives the positioning signal immediately before the positioning signal from the satellite is disconnected. The movement information (Δx) that the positioning device has moved up to the second time point (t1) when the positioning signal is cut off is acquired,
Based on the position information of the satellite and the satellite orbit at the third time point when the satellite transmits the positioning signal received by the positioning device at the first time point, the second time point and the first time point The positioning device according to claim 9 or 10, further comprising means for acquiring movement information (ΔS) of the satellite from the third time point in a section (Δt = t1-t0).   The positioning device according to any one of claims 9 to 11, wherein the satellite includes a quasi-zenith satellite, and the positioning device receives positioning correction information broadcast from the quasi-zenith satellite. . In a computer that constitutes a device that performs positioning based on positioning signals received from satellites,
In the space where the positioning signal from the satellite is blocked, the positioning signal received by the first antenna provided in the area where the positioning signal from the satellite can be received is relayed and transmitted from the second antenna. If the positioning signal from the satellite is detected because the positioning signal relayed by the repeater cannot be received and the positioning signal from the satellite is detected, the movement information of the satellite and the positioning device are acquired. Then, a program for calculating a distance between the satellite and the positioning device and executing processing for estimating an integer bias of a carrier phase.   In a space where the positioning signal from the satellite is cut off, an area in which the positioning signal from the satellite can be received when the positioning signal relayed by the repeater is received from the disconnected state of the positioning signal from the satellite A process of deriving an integer bias of the carrier phase from carrier phase data based on the integer bias value of the carrier phase estimated when the positioning signal from the satellite is disconnected when resuming the reception of the positioning signal at 14. The program according to claim 13, which is executed by a computer.   The program according to claim 13 or 14, wherein the satellite includes a quasi-zenith satellite, and causes the computer to execute processing for receiving correction information broadcast from the quasi-zenith satellite.   A portable terminal comprising the positioning device according to claim 9.   An in-vehicle navigation device comprising the positioning device according to any one of claims 9 to 12.

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