JP2006284452A - Satellite positioning method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a position determination method by satellite positioning capable of attaching an accurate position of a moving body while dispensing with time synchronization between a server and the moving body, and capable of determining the accurate position, only by supplying an Ephemeris data, a satellite time data error data and rough position information to the moving body through the server. <P>SOLUTION: Signals from at least the five satellites are used in the three-dimensional positioning. A pseudo-distance is measured by an equation having at least X, Y, Z, T of unknowns, where (X, Y, Z) is the three-dimensional moving body position in a coordinate system defined preliminarily, and T is the synchronization measured time for determining the each pseudo-distance as to the all the satellites. The each satellite position in the equation is a vector value function f<SB>k</SB>(T) of the time T, and the f<SB>k</SB>is determined based on the satellite Ephemeris data 3 transmitted to the moving body 2 through a communication line 5 or an equivalent thereof, and an approximate position of the moving body 2. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a satellite positioning method, and more particularly to a position measurement method that eliminates accurate time synchronization in a positioning system using so-called (satellite) assist information.

  Global positioning systems (hereinafter simply referred to as GPS) and satellite positioning systems such as the European equivalent Galileo, where the location of the user anywhere on the earth is an autonomous low-cost receiver In the case of a surveying receiver (differential GPS surveying) operating in conjunction with a base station, the accuracy can be determined in units of centimeters. In both these calculation modes, the receiver must capture and track signals from multiple satellites to measure the distance from each visible satellite to the receiver. The ability of the receiver to perform this function is often limited by buildings, mountains, trees, or other obstacles that block or significantly weaken the received signal. In addition, a significant amount of time is required to locate and capture the satellite signal, read the navigation data in the signal, and make the measurements necessary to determine the user's position.

  These limitations are particularly acute when the user needs to determine his position in an emergency. In a typical emergency, the user needs urgent assistance from others who need accurate location information about the location of the emergency, i.e., a lifesaving officer, police officer, or firefighter. In such situations (eg heart attack), time is paramount. Standard satellite navigation receivers usually take too long to calculate the user's position, which can be several minutes or even longer. In addition, satellite signals at emergency locations are often too weak for point positioning receivers. This is quite normal in buildings where walls significantly weaken electromagnetic radiation from satellites.

  Recently, efforts have been made to overcome the limitations of weak signal reception and greatly shorten the time (first positioning time) from when the receiver is started until the user's position is determined. In addition, reliable emergency position measurement is possible. One way to achieve this goal is known as positioning using assist information. A base station (server) in a position where it can receive good satellite signals collects data from the satellite and moves with the server. It is sent to the user (mobile body) together with other data through an independent communication line between bodies.

Positioning principle without assist information:
In order to best understand the principle of the positioning method using assist information, it is helpful to review the positioning without using standard assist information. A series of calculation processes are required from the time when a typical single-position GPS receiver is first activated until the information in the GPS satellite signal can be used for position determination. The calculation process is as follows in the order of execution.
1. Built-in almanac data is used to determine which satellites are visible from the antenna.
2. Determine the approximate Doppler for each visible satellite.
3. Search for each satellite signal in both frequency and C / A code phase.
4). Detect and confirm the presence of each signal.
5. Observe and track the C / A code from each satellite.
6). Observe and track the carrier phase from each satellite.
7). Performs navigation data bit synchronization.
8). The ephemeris data (satellite precise calendar) and time information are obtained by inversely modulating the flow of the navigation data bits.
9. The arrival time at a specific point where each satellite signal reception waveform can be identified is measured by the receiver clock.
Ten. Using the time information of process 8, the GPS communication time of the same point on the waveform described in process 9 is determined.
11． The pseudo distance of each satellite is calculated by subtracting the GPS communication time (process 10) from the arrival time (process 9).
12． Using the ephemeris data (satellite precise calendar) for each satellite (process 8), the satellite position at the GPS communication time (process 10) is determined.
13. Using the pseudorange of each satellite (step 11) and the satellite position (step 12), the user's position and very accurate time are calculated.

In a standard GPS receiver, the above calculation process is very time consuming. In particular, the satellite search of process 3 takes several minutes or more depending on the number of conditions. At the beginning of the search, the Doppler shift of each satellite signal is not exactly known, and it takes time to find the frequency window to find the signal. Before the first satellite is found, the main source of uncertainty is the frequency uncertainty in the reference oscillator of the user's receiver, which is one millionth of a unit, or 1575.42 MHz GPSL ₁ ± 1575 Hz at the carrier frequency. The second cause of frequency uncertainty is knowing if the receiver has no recent (within 2 hours from now) ephemeris data (satellite precision calendar) or how much Doppler shift is expected Occurs when there is not enough accurate approximate position data for (the Doppler shift can vary by about 1 Hz / km in the worst case).

  The average search time to obtain a sufficient number of satellite signals for positioning can be longer if the signal is weak. This is normal when the receiver is inside a building or is surrounded by obstacles that block the signal. In order to detect weak signals reliably, they must be averaged over longer time intervals in order to be sufficiently sensitive to noise. Thus, the average search time of step 3 can be much longer than if the signal is not disturbed.

  In addition to the long search potential to capture the satellite, the ephemeris data (satellite precision calendar) in process 8 and the navigation data flow from each satellite for time data acquisition are inversely modulated, so Time may be required. The ephemeris data (satellite precision calendar) from each satellite is used to determine the satellite position at the signal transmission time obtained in step 10. Ephemeris data (satellite precision calendar) is basically a formula, more precisely a parameterized algorithm, where the transmission time is substituted to calculate the satellite position at that time. In the standard (without assist information) GPS positioning method, ephemeris data (satellite precise calendar) is obtained from navigation data of 50 bits per second received directly from the satellite by the user. The navigation data stream consists of continuously transmitted 1500-bit frames 30 seconds long (1500 bits / 50 bits per second), each containing 5 300-bit subframes. The first three subframes consist of time and ephemeris data (satellite precise calendar). The ephemeris data (satellite precise calendar) is repeated at a frame repetition rate except that it is updated as appropriate. Thus, the reception for complete collection of ephemeris data (satellite precision calendar) from one satellite is approximately 30 seconds depending on where in the received frame the user's receiver begins looking for this data. Take it.

A more serious problem occurs when the GPS signal is too weak to reliably demodulate the navigation data bits in the time, ephemeris data (satellite precision calendar) extraction from the navigation message. This problem becomes apparent with a C / No of 25 dB Hz. In urban buildings and buildings, C / No can easily fall below this value, and ephemeris data (satellite precision calendar) and time data with no positioning errors can no longer be obtained. The receiver becomes unusable.
For the reasons described above, the standard method of GPS positioning with an independent positioning (without assist information) receiver is not appropriate when quick and reliable positioning is required, especially when the signal is weak. .

Positioning principle using assist information:
The limitations of the standard positioning method described above can be overcome by using positioning using assist information. In positioning using assist information, a base station (server) transmits assist information to a user's receiver (mobile body) (see Patent Document 1). This information varies to some extent depending on the system using the assist information, but typical assist information is as follows.
1. The server sends a very accurate frequency reference to the mobile to scale the reference oscillator of the mobile receiver. The carrier frequency of the server and mobile communication lines is often used for this purpose. Once the frequency uncertainty of the mobile reference oscillator is removed, the frequency search width is much smaller, thus considerably reducing the time for initial satellite acquisition by the mobile receiver.
2. In many cases, the server can determine the approximate location of the mobile relative to the approximate server. For example, if the mobile receiver is embedded in a mobile phone (common in emergency positioning systems), the location of the mobile antenna that receives the strongest mobile phone signal contributes to this purpose. The approximate position data of the mobile is combined with the ephemeris data (satellite precise calendar) collected by the server to further reduce the frequency uncertainty in the satellite signal search. In addition, if the server can determine the approximate position of the mobile at a distance of 100-200 km, the mobile will provide the satellite navigation data message (the above process) with the highly accurate time information normally required to determine the pseudorange. (Refer to 10).
3. Ephemeris data (satellite precise calendar) and satellite time correction data from each satellite are collected by a server and transmitted to a mobile unit. This is a huge advantage because the mobile can receive data directly from the satellite without consuming valuable time (at least 30 seconds). The server is in a position where many satellites can be clearly identified, and the satellite signal is strong enough to demodulate the ephemeris data (satellite precision calendar) at that position. So the server can easily transfer data to the mobile at a rate much higher than GPS's 50 bps and high enough to receive the ephemeris data (satellite precision calendar) directly from the satellite. Can be sent to.
4). In some positioning systems using assist information, the server sends a copy of the actual navigation data bit stream received from the satellite to the mobile. The bit pattern data allows the mobile to reliably obtain the modulated data from the satellite signal it receives, so that much longer coherence in the satellite signal arrival time measurement process (see step 9 above). Enable integration operation time. The result of this calculation allows signals that are too weak for other methods to take values, can be used for this purpose.
5. The server also sends accurate timing information to the mobile. Timing information from the server is essential when the mobile cannot recover the indeterminate time portion directly from the GPS navigation message due to signal shielding or attenuation.
US Pat. No. 5,663,734

  To explain from the role of timing information in positioning using assist information, as described above, in positioning without using standard assist information, the exact time must be recovered directly from the GPS signal for two purposes. Don't be. The exact time of signal transmission (see step 10 above) is determined for the purposes of (1) measuring pseudoranges and (2) determining the current position of each satellite. For the purpose of determining the pseudorange, the time must be accurate in tens of nanoseconds to prevent excessive distance errors due to the speed of light transmission. For the purpose of determining the satellite position, the transmission time must be inserted into the ephemeris data (satellite precise calendar) equation received from the satellite. In this case, the accuracy of the required time is lower. The satellite has a tangential velocity of about 3800 m / s, and for satellite positioning purposes, the time must be accurate in units of milliseconds to keep the satellite position error within tens of meters.

  However, in most positioning systems using assist information, an accurate time must be obtained from an information source other than a GPS signal for two reasons. The first reason is that it is undesirable for the mobile to spend valuable time to read time information from the received signal. Second, the signal may be too weak for this. Therefore, in a positioning system using typical assist information, a timing signal is sent from the server to the mobile body. Since it is unknown how much the signal transmission time differs from the absolute time on the server or mobile, such timing signals cannot be used to determine the signal transmission time from the satellite (even if the timing signal is used for this purpose). Even if it can be used, it is difficult or impossible for the communication line to provide the required accuracy of tens of nanoseconds).

  Fortunately, it is possible for the mobile body to know the approximate time of transmission from a GPS satellite without demodulating the navigation data message. This is possible because the start of the GPS C / A code is transmitted from each satellite at each satellite vehicle (SV) time, with millisecond accuracy, which is obtained by the server and transmitted to the mobile. This is because the GPS time differs from the GPS time by an error period included in the navigation message (GPS time is an accurate time at which all satellites are synchronized). The mobile receiver can correlate the received signal with a C / A code replica to determine the beginning of the code. If a long time correlation is performed, a large amount of calculation input can be obtained, so even weak signals can be performed with reliability. However, the transmission of the start time has an uncertainty of 1 millisecond. That is, it is only known that a particular start was transmitted at an SV time equal to an integer millisecond, and the integer value is unknown. Thus, the pseudorange of each satellite is subject to the same uncertainty, which is 300 km spatially. When this uncertain time is used in the position equation, the possible solutions of the mobile position equation in a three-dimensional frame or grid span a 300 km scale space (actual space is the position of the satellite and receiver) This value differs depending on the relationship). However, if the approximate position of the moving body is known within 100 to 200 km, this position uncertainty is resolved. However, the uncertainty over the 1 millisecond time remains unresolved.

  Therefore, the accurate timing signal from the server is used only for the purpose of establishing the satellite position at the time of transmission, and only requires accuracy within a few milliseconds to reduce the satellite position error to an acceptable level. It is. Unfortunately, however, communication lines such as cellular telephone lines available for this purpose contain unknown and fluctuating communication delays caused by packetization and matrixing of data from the server. This unpredictable delay is often too great for satellite position determination. On the other hand, using an existing communication line from the server to the mobile is desirable even if it was not originally designed to send accurate timing signals. However, it is desirable to modify such a communication line (eg, a cellular network) to provide a sufficiently accurate timing signal because it is too expensive and generally does not appeal to communication service providers. Absent.

  Therefore, an object of the present invention is to solve the problems of the conventional satellite positioning method described above. In particular, one object is to provide a method in which accurate positioning of a mobile object can be achieved without time synchronization between the server and the mobile object. The mobile object uses ephemeris data (satellite precision calendar) and a signal time tag. Another object is to provide a method that does not require reverse conversion of the navigation data bit stream from the satellite for reception, and the server also provides ephemeris data, satellite time error data, and approximate data. It is still another object to provide a method that only needs to provide position information to a moving object.

In order to achieve the above object, the present invention requires at least ephemeris data (satellite precise calendar), satellite time correction data, approximate position information or equivalent data from a server or other information source to a mobile unit. A satellite positioning method,
(A1) 3D positioning uses signals from at least 5 satellites, and 2D positioning uses signals from at least 4 satellites.
(B1) When (X, Y, Z) is a three-dimensional moving object position in a predefined coordinate system, and T is a simultaneous measurement time for determining pseudoranges for all satellites, three-dimensional positioning is performed. Performs pseudorange measurements on equations with minimum X, Y, Z, T unknowns,
(C1) When (X, Y) is the position of a moving body on a horizontal plane in a predefined coordinate system and T is the simultaneous measurement time for determining the pseudorange for all satellites, the minimum is two-dimensional positioning. Perform pseudorange measurements on equations with unknown X, Y, T limits,
(D1) Each satellite position in the above equation is a vector value function f _K (T) at time T, and f _K is the satellite ephemeris data (satellite precise calendar) or its equivalent sent to the mobile body through the communication line. And the approximate position of the moving body.

Also, a communication line is used for communication from the server or other information source to the mobile, and the communication line includes any of a mobile phone network, a wired or wireless Internet, or a telephone land line, or It is a combination.
In addition, an accurate but uncertain pseudo-time using the fact that the start of the GPS C / A pseudo-random code is transmitted as an integer millisecond value of the space vehicle (SV) time corrected to the GPS time by the satellite time correction data. Includes determination of distance differences.
In addition, the uncertainty of the pseudo-range difference is solved by a moving body approximate position supplied from a server or another information source.

また、反復アルゴリズムが、２次元測位に適合する様に量が修正される点を除いては同様である。 In addition, the least square iterative algorithm is used in which x (average value) as an initial estimated solution starts the above equation with the following equation 1, and each subsequent calculation process starts with the estimated solution at the previous calculation. Iterating until a convergence of the solution is obtained, the iterative algorithm is
(A5) Using the ephemeris data (satellite precise calendar) received from the server, or an equivalent thereof, calculate the satellite position (x _k , y _k , z _k ) at time T,
(B5) Calculate the LOS vector r _k (average value) and the length (distance) r from the estimated position of the moving object to each satellite,
(C5) When c is the speed of light, the satellite signal transmission time t _k = T−r _k / c is calculated. (D5) The satellite position (x _k , y _k , z _k ), r _k (average) Value) and r _k and the corresponding satellite velocity vector v _k (average value) to recalculate the ephemeris data (satellite precise calendar) using the signal transmission time t _k obtained in step C5. use,
(E5) The following equation (2) indicating the moving object-satellite unit vector u _k (average value) is calculated together with the LOS vector r _k (average value).
(F5) The vector v _k (average value) is a satellite velocity vector, and forms a matrix H defined by the following equation (3):
(G5) using r _k obtained by a process D5, it calculates the following equation 4 of the formula as the distance difference to use the current estimates solutions x,
(H5) The following equation (5) is calculated as a vector of change between the pseudo-range difference measurement vector supplied by the receiver and the distance difference calculated in the process G5. ,
ρ _1k = (n _k −n ₁ ) + c (ε _k −ε ₁ ) + c (τ _k −τ ₁ )
Calculated by
τ _k is the measurement value of the k-th satellite reception code phase, ε _k is the satellite time correction value of the k-th satellite received from the server, and an unknown integer (n _k −n ₁ ) is the following number 7 is solved by
(I5) In order to apply to the current estimated solution, Δx (average value) as a correction value is calculated by the following formula 8,
(J5) = represents an assignment instruction in calculation, and does not indicate algebraic equivalence, and generates the following equation (9) as a new estimated solution,
(K5) If there are not enough iterations to obtain good convergence, go back to step A5, otherwise finish the iteration with the solution x (mean value).
It is a method that consists of these stages.

The same is true except that the iterative algorithm modifies the quantity to match the two-dimensional positioning.

The present invention has the following remarkable effects.
(1) Accurate position determination of the moving object can be achieved without time synchronization between the server and the moving object. (2) The mobile need not demodulate the flow of navigation data bits from the satellite to receive the ephemeris data (satellite precise calendar) and the signal time tag.
(3) The server only needs to provide ephemeris data (satellite precise calendar), satellite time error data, and approximate position information to the mobile body at a minimum.
As long as the server sends data in one-way communication, the mobile need not send a signal to the server. Eliminating the need for time synchronization between the server and the mobile unit provides tremendous flexibility in selecting the communication link between the server and mobile unit, and the communication link does not need to be designed to transmit at the correct time. Also included. Thus, usable links include existing mobile telephone networks, wired or wireless Internet networks, and landline telephone networks, and there is no need to modify these links. The moving receiver does not need to demodulate the navigation data bit stream from the satellite, and the receiver is reliable, fast, and accurate in a weak signal environment such as indoors or urban buildings. It becomes free to design to be able to.

The present invention uses at least one additional satellite beyond the number required for normal positioning to solve the problem of acquired indeterminate time, which typically includes errors that do not exceed a few milliseconds. The mobile does not get the time from the navigation message or from the server. Instead, the time is treated as an additional variable that is determined directly from the navigation solution, even if it is not as accurate as that based on the timing data contained in the navigation message. A navigation solution at a receiver that does not use assist information generally resolves the position (three coordinates of X, Y, and Z) and the error B of the receiver clock. In such a receiver, the resolution of the receiver clock error B is used to set the receiver clock to obtain a very accurate time, but to obtain this accuracy, the receiver clock is received for the navigation solution. The machine is required to read timing data directly from the GPS signal. In contrast, the present invention includes the exact time t as the fourth variable, and the timing data need not be read from the GPS signal itself. This new variable is independent of the receiver clock error B, which is no longer a variable of the navigation solution of the present invention. The three-dimensional positioning of the present invention requires a minimum of five satellites, and for two-dimensional positioning, four satellites are sufficient if the altitude is known in advance or an altitude map is available. is there. At least one additional satellite is not as disadvantageous as it seems. This is because additional satellites from other positioning systems such as Glonas have sufficient signal strength to use, and in the future more satellites will be available from other systems such as Galileo. is there.
In the description of the distance of the present invention and claims, the “left column” may be expressed as “right column” as shown in the following Table 1, but it is the same in that it indicates an arithmetic mean. Definition.

  A typical error-free model of pseudorange measurement by a receiver that does not use conventional GPS assist information and also uses assist information is expressed by the following equation (10) in the current technology. That is, ρ (average value) is as shown in Equation 10.

If the following equation (11) is a vector of the pseudorange measurement of the observed satellite n, (X, Y, Z) is the receiver position, B is the receiver clock bias, and f is a known function. To express. The purpose of positioning is to determine the navigation solution x (average value) = [XYZB] ^T given the measured value ρ.

The function f is defined by the following equation (12).

The k-th satellite position at the transmission time is (x _k , y _k , z _k ), and the pseudorange measurement of this satellite is ρ _k . B is in seconds, and the position of the satellite and server 1 is expressed in meters using the East-North-Up (ENU) coordinate system in which the east-north plane is in contact with the earth surface. Thus, Z and z _k represent the altitudes from the data representing the earth surface of the mobile and the k-th satellite, respectively. However, other coordinate systems can be used.
In this model, the satellite position is determined by putting the appropriate time of signal transmission into the satellite progression equation provided by the ephemeris data (satellite precise calendar). In conventional GPS receivers that do not use assist information, ephemeris data (satellite precise calendar) is obtained from navigation messages, and in conventional GPS systems that use assist information, ephemeris data (satellite precise calendar) (or equivalent) Are generally sent from the server to the mobile.

In a GPS receiver that does not use conventional assist information designed for unobstructed signals, the signal transmission time for satellite positioning purposes is immediately determined from the timing information of the received navigation message. However, in the GPS system using the assist information, it is not desirable that the moving body runs out of valuable time to read the timing data. Furthermore, the signal is often too weak to read such data. Current GPS positioning technology using assist information typically solves this problem in one of two ways, assuming that the server has an accurate clock. (1) The mobile unit can acquire the time from the synchronization signal sent from the server, and then uses the ephemeris data (satellite precise calendar) to calculate the satellite position corresponding to the time at which the pseudorange measurement is performed. (2) The moving body can transmit a timing pulse to the server in accordance with the pseudorange measurement, and the server can then return numerical data representing the reception time of the pulse to the moving body.
However, such timing adjustment often imposes demands on the server and its communication network that are expensive and difficult to implement. The present invention is an alternative solution that uses at least one additional satellite beyond the minimum required for positioning. As a result, the pseudorange measurement, and hence the corresponding satellite position, is also part of the navigation solution, and accurate timing data received directly from the satellite or server is not required.

  The present invention uses a different equation where the clock bias B is no longer a relevant variable. In fact, this bias can no longer determine the high level of accuracy (about 10-100 nanoseconds) achieved using a receiver that does not use conventional assist information to obtain time directly from the GPS signal. In developing a new equation, the first step is to eliminate B as a variable by subtracting the first equation from each of the remaining equations from equation (12). This equation is shown in the following equation (13).

であり、ρ_1K＝ρ₁ −ρ_K である。
この数13の式では、衛星位置（ｘ_k ,ｙ_k , ｚ_k ）は、新時刻変数Ｔの関数として表され、ｎ衛星のそれぞれの同時に距離測定が遂行される時刻として次の数14の式によって定義される。

And ρ _1K = ρ ₁ −ρ _K.
In the equation (13), the satellite position (x _k , y _k , z _k ) is expressed as a function of the new time variable T, and the following equation 14 is used as the time at which the distance measurement of each of the n satellites is performed simultaneously. Defined by an expression.

The function f _k is obtained by inserting the estimated signal transmission time T into the ephemeris data (satellite precise calendar) equation for the kth satellite (this will be described in detail later). Equation 13 above, which is a function of T, where the satellite position is given by Equation 14, thus takes a more organized form.

dρ (average value) = [ρ ₁₂ ρ _13... ρ _1n ] ^T is a column vector of measured pseudoranges between the first satellite and the other satellites, and x (average value) = [X Y Z T] ^T is an unknown column vector.

Pseudo distance difference measurement:
The pseudo-range difference measurement value ρ _1k issued by the moving body 2 is obtained by measuring the pseudo-range ρ _k for each satellite k = 1, 2 _,. This is achieved by correlating the satellite C / A code copy with the received signal in the fundamental frequency band for each satellite to determine the position of the vertex of the correlation function. The position of the vertex determines the phase T _k of the satellite C / A code at the normal reference time T ₀ by the receiver clock. These phases are recorded. Since the C / A code is a 1-millisecond period, the recorded phase is a distance from 0 to 1 in milliseconds, and indicates the position of the reference time T ₀ in the code period.

For each satellite, it is known that the start (start) of the received code period, where T ₀ occurs, originates from the satellite at an integer n _k time in milliseconds by the satellite clock. This watch provides a time known as space vehicle (SV) time. A small time correction ε _k , which is part of the navigation data message sent from the server to the mobile, is applied to convert the SV time to the same GPS time for all satellites. And, for the k-th satellite, the transmission GPS time t _{k in} milliseconds on the received signal at the observation point having the phase of τ _k milliseconds is expressed as the following equation (16). The

_nk is unknown as a positive integer. The pseudo distance ρ _k of the k-th satellite is the transmission time from the satellite to the mobile receiver multiplied by the light velocity c as shown in the following equation (17).

Here, the term pseudo-range is used instead of distance. This is because mobile clocks are generally not synchronized with GPS time, and are relatively errors or errors in the receiver clock described above as B. This is because of having (bias).
In the preferred embodiment of the present invention, the measured value τ _k of the code phase is used as shown in _Equation 18 below to obtain the pseudorange difference ρ _1k .

Since T ₀ is deleted when determining the pseudorange difference, the bias B of the receiver clock is also deleted, so it is appropriate to refer to the pseudorange difference as the measured distance difference.
The pseudo-range difference in the equation (18) has a disadvantage of uncertainty because the integer (n _k −n ₁ ) is unknown at the initial stage. However, this uncertainty can be solved if the position of the moving body 2 is known within 100 to 200 km and the initial estimate of the measurement time of the code phase τ _k is known with an accuracy of 10 seconds or so. The The ambiguity resolution is achieved with an initial estimate of the distance r _k by the satellite position and the approximate position of the mobile 2 at the approximate time (within about 10 seconds) at which the pseudorange is measured. The estimated distance difference (r ₁ −r _k ) is substituted into the equation 18 instead of the actual pseudo distance difference measurement value ρ _1k , and the integer (n _k −n ₁ ) is expressed by the following equation 19. Calculated.

cintは、最近似の整数関数であり、ｃは光速度を１ミリ秒あたりのメートル数で示す（2.9979 ×10⁵ ）。

cint is the closest integer function, and c represents the speed of light in meters per millisecond (2.9979 × 10 ⁵ ).

Solution of navigation equations:
The solution of the navigation equation is a solution of four variables X, Y, Z, and T. The solution of the distance difference measurement time T is usually expressed in seconds, and the moving body position solution (X, Y, Z) is typically a local ENU (East-North-Up) where the east-north plane is in contact with the earth surface. ) Expressed in meters using the coordinate system.
There is a subtle but important distinction between equation 10 for a receiver using conventional assist information and equation 15 of the present invention. In the equation (10), sufficiently accurate timing information can be obtained from the server, so that the accurate signal transmission time from each satellite is known. Therefore, the position of each satellite at the time of transmission can be obtained by inserting the transmission time into the ephemeris data (satellite precise calendar). In contrast, in the present invention, the signal transmission time is obtained from the solution of the equation (14), and the timing information from the server 1 is not required.

  Note that in equation (13), four unknown values X, Y, Z, and T are solved by four equations by using five satellites. We want to find the solution of x (average value) from the measured value dρ (average value) using the formula (15). Since there may be more measured values than unknowns x (average value), the minimum multiplication solution is appropriate. The vector solution x (average value) by the minimum multiplication solution minimizes the following equation (20).

  Although g is a non-linear function, a solution that quickly converges by the Newton method can be obtained. In any case, the vector x (average value) is very close to the true solution, and a small change Δx (average value) in x (average value) and a corresponding change Δ in the vector dρ (average value) of the pseudorange difference measurement Δ The relationship with dρ (average value) is given by the following equation (21).

ただし、マトリックスＨは次の数22の式である。

However, the matrix H is the following equation (22).

数22の式においてベクトルｕ_k （平均値）は次の数23の式にて示されるが、このベクトルｕ_k （平均値）は、視線（ＬＯＳ）に沿った移動体−衛星単位のベクトルであり、ベクトルｖ_k （平均値）は、時刻ｔ_k における衛星速度ベクトルである。

In the equation (22), the vector u _k (average value) is expressed by the following equation (23). This vector u _k (average value) is a moving object-satellite unit vector along the line of sight (LOS). Yes, vector v _k (average value) is a satellite velocity vector at time t _k .

  The matrix H always has a total column rank (= 4), and the number of rows is always one less than the number of satellites. If more than 5 satellites are used, H will have more rows than columns. In such a case, there may be no solution of Δx (average value). However, there exists a minimum multiplication solution of Δx (average value), which can be obtained by the following well-known equation 24.

Referring to FIG. 1, FIG. 2 and FIG. 3, the minimum multiplication solution of x (average value) (not Δx (average value)) is obtained by the following iterative calculation. The loop index is j. The first loop passage starts with an initial estimated solution x (average value) = [X Y Z T] ^T obtained from the approximate position and time of the mobile 2 and refines this solution to provide a better estimated solution . Subsequent calculations are performed with the most recent estimates, and the solution is further refined. In the following process, the index k moves from 1 to the number n of satellites observed.

(A5) The satellite position (x _k , y _k , z _k ) at time T is calculated using the ephemeris data (satellite precise calendar) received from the server 1 or its equivalent.
(B5) The LOS vector r _k (average value) and the length (distance) r from the estimated position of the moving object to each satellite are calculated.
(C5) When c is the speed of light, the satellite signal transmission time t _k = T−r _k / c is calculated.
(D5) In order to recalculate the satellite position (x _k , y _k , z _k ), r _k (average value) and r _k , and the corresponding satellite velocity vector v _k (average value), each obtained in step C5 The ephemeris data (satellite precise calendar) is used while using the satellite signal transmission time t _k .
(E5) A vector u _k (average value) between the moving object and the satellite is expressed by the following equation 25, and this vector u _k (average value) is calculated together with the LOS vector r _k (average value). .

(F5) The matrix H defined by the formula of the equation 22 is formed.
Use r _k obtained by (G5) process D5, the distance difference dr to use the current estimates solution x (average) (average value) by a formula of the following numbers 26, calculates.

(H5) A change vector Δdρ (average value) between the vector of the pseudo distance difference measurement value supplied by the receiver and the distance difference calculated in the process G5 is calculated. Δdρ (average value) is expressed by Equation 27. The pseudo-range difference measurement value is calculated using the satellite time correction data supplied from the server according to the above equation (18).

(I5) In order to apply to the current estimated solution, the correction value Δx (average value) is calculated by the equation (28).

(J5) A new estimated solution (see Equation 29) is generated (= represents a calculation assignment instruction, not algebraic equivalence).

(K5) If there are not enough iterations to obtain good convergence, return to step A5 (see circle B in FIGS. 2 to 1). Otherwise, the iterative calculation ends with the solution x (average value) (see FIG. 2).

  In this iterative method, the initial position estimate (X, Y, Z) is good to some extent at a distance of 100 to 200 km from the actual moving body position, and the initial time estimate T is within some 10 seconds from the GPS time. If good, it generally converges very quickly. Under these conditions, if the value (PDOP) indicating the good geometric extent of each satellite is 40 or less, generally 5 or more iterations are not required. As a result, the loop is simply done only five times, avoiding the need to set criteria for when to stop.

Processes A5 to K5 can be corrected to obtain a two-dimensional position immediately when the altitude of the moving object is known. In the local ENU coordinate system, Z is the height coordinate.
Since the initial time estimate only needs to be accurate in about 10 seconds, it can be easily provided by a low-cost real-time clock in the mobile 2 (or a potential uncertainty of about the same time as about 10 seconds) (It can be provided in time increments sent from the server 1 having the characteristics). Thus, the present invention has the advantage that the server 1 does not require any kind of time synchronization. Positioning using the assist information can transmit the assist information using various existing communication lines 5 such as the Internet without remodeling for accurate time transmission.

  In the block diagram showing the features of the present invention shown in FIG. 3, the information required from the server 1 is only the ephemeris data (satellite precise calendar) and the correction value of the satellite time error. These data are valid for about two hours from the latest update and are stored in the server 1 and later transmitted to the mobile. The server 1 also sends additional assist information (such as ionospheric correction information) and an accurate time signal of about 10 seconds to the mobile 2. However, no timing signal is required because the mobile 2 can use its own low-cost real-time clock in the initialization of the position calculation algorithm.

Numeric value indicating accuracy:
The numerical value (GDOP) indicating the accuracy of the geometrical extent of the satellite in the present invention is different from the conventional method, although the basic principle of calculation is still the same. The basic unit of positioning GDOP without using conventional assist information is a numerical value (PDOP) indicating the accuracy of the satellite position, a numerical value (HDOP) indicating the accuracy of the horizontal spread of the satellite, and the vertical spread of the satellite. A numerical value (VDOP) indicating the accuracy of the condition and a numerical value (BDOP) indicating the accuracy of the receiver clock bias. The present invention holds PDOP, HDOP, and VDOP, but replaces BDOP with a numerical value (TDOP) indicating the accuracy of time. PDOP, HDOP and VDOP numbers are slightly different from those obtained previously, but TDOP numbers are very different from BDOP numbers. This is because the pseudo distance measurement value T and the clock bias B are clearly different amounts.

To determine the GDOP of the present invention, the quantity cτ _k is assumed to have an independent zero-mean variable noise unit δ _k , where τ _k is expressed in milliseconds, and c is expressed in milliseconds per millisecond. It is the speed of light. From the equation (17), it can be seen that Δ _k is also a noise constituent unit ρ _k . Therefore, according to the equation (18), the noise constituent unit of the pseudo distance difference measurement value ρ _1k = ρ ₁ −ρ _k is δ ₁ −δ _k . Accordingly, the noise constituent unit (see Equation 30) of the vector dρ (average value) = [ρ ₁₂ ρ _13... Ρ _1n ] ^T of the pseudo distance difference measurement value is given by the following Equation 31.

  From Equation 24, it can be seen that the noise vector of the pseudo-range difference measurement value (see Equation 30) causes the corresponding zero average noise vector (see Equation 32) to occur for the solution vector x (average value).

であり、Ｅ｛ ｝は期待値を意味し、数35の式で示される事実を用いた。Ｉ_nXn はｎ×ｎ同定マトリックスである。
対角要素Ｃ₁₁、Ｃ₂₂、Ｃ₃₃、Ｃ₄₄は、前述の擬似距離測定ノイズの単位可変数の仮定において、それぞれＸ，Ｙ，Ｚ，Ｔの解の可変数であり、ＰＤＯＰ，ＨＤＯＰ，ＶＤＯＰ，ＴＤＯＰを次のように定義するために使われる。 The covariant matrix C of the zero mean noise vector shown in the equation 32 is

And E {} means an expected value, and the fact shown by the equation 35 is used. In _xn is an _nxn identification matrix.
Diagonal elements C ₁₁ , C ₂₂ , C ₃₃ , and C ₄₄ are variable numbers of solutions of X, Y, Z, and T, respectively, on the assumption of the unit variable number of the pseudorange measurement noise described above, and PDOP, HDOP, It is used to define VDOP and TDOP as follows.

Typical performance:
To obtain a proof of the above concept, the performance of the present invention was simulated. In the simulation, a GPS satellite array model consisting of 6 orbital planes including 4 satellites equispaced on an angle for each orbit was used. The rising intersections of the six orbital planes are equally spaced around the equator of the rotating earth. The true positions of the server 1 and the mobile body 2 are at the same fixed point on the earth. The results presented here assume that server 1 and mobile 2 are at 34 degrees north latitude and the visible satellite mask angle is 10 degrees. Assume that the pseudorange measurement noise has a standard deviation of 1 meter. In each trial, visible satellites are randomly selected by randomization over a 24 hour period, and the positioning algorithm uses five satellites randomly selected from the visible satellites.
Table 2 shows the results of 20,000 Monte Carlo trials. The root mean square (RMS) position and time error are expected to increase with increasing PDOP, and the results are grouped into 4 PDOP categories.

From Table 2, it can be seen that if at least five satellites and good PDOP can be observed from the moving body, good three-dimensional positioning can be obtained by the method of the present invention. If the number of satellites is greater than 5, the error is greatly reduced. Note that the RMS positioning error shows a good match with the corresponding PDOP category. This is because the RMS positioning error is equal to the PDOP for the 1 meter 1 sigma pseudorange measurement noise used in the simulation. If altitude assist information is obtained (ie, a local altitude map stored in a mobile object), a minimum of four satellites are sufficient to produce a similar result.
Note also that when the PDOP is good (ie small), the pseudorange measurement time T is determined within a few milliseconds at the mobile. This time is also used to adjust the mobile clock to the same accuracy. For 5 satellites, the RMS error is a distance from 2.7 milliseconds when PDOP <5 to 22.1 milliseconds when 20 ≦ PDOP <40.

In the embodiment of the present invention described above, a GPS satellite is used, but the present invention can also be applied to other global navigation satellite systems (GNSS) that use a periodic pseudo-random code and broadcast ephemeris data (satellite precise calendar). Such systems include, but are not limited to, the Galileo positioning system in Europe, the Glonus in Russia, and the Beidou system in China.
As shown in FIG. 3, the communication line 5 for communication from the server 1 (or other information source) to the mobile unit 2 includes a form telephone network 5a, the Internet 5b, a telephone ground line 5c, and a wireless communication network. It is composed of one or a combination thereof such as 5d.

It is a principal part flowchart figure which shows one Embodiment of this invention. It is a flowchart figure of the other principal part which shows one Embodiment of this invention. It is a block diagram which served as an operation explanatory view.

Explanation of symbols

1 Server 2 Mobile 3 Ephemeris data (satellite precise calendar)
4 satellite time correction data 5 communication line 5a mobile telephone network 5b Internet 5c telephone landline T time f _x vector value functions X, Y, mobile location of Z 3 dimensional

Claims (6)

A satellite positioning method that requires minimum ephemeris data (satellite accuracy calendar), satellite time correction data, approximate position information or equivalent data from a server or other information source to a mobile unit,
(A1) 3D positioning uses signals from at least 5 satellites, and 2D positioning uses signals from at least 4 satellites.
(B1) When (X, Y, Z) is a three-dimensional moving object position in a predefined coordinate system, and T is a simultaneous measurement time for determining pseudoranges for all satellites, three-dimensional positioning is performed. Performs pseudorange measurements on equations with minimum X, Y, Z, T unknowns,
(C1) When (X, Y) is the position of a moving body on a horizontal plane in a predefined coordinate system and T is the simultaneous measurement time for determining the pseudorange for all satellites, the minimum is two-dimensional positioning. Perform pseudorange measurements on equations with unknown X, Y, T limits,
(D1) Each satellite position in the above equation is a vector value function f _K (T) at time T, and f _K is the satellite ephemeris data (satellite accuracy calendar) or its equivalent sent to the mobile body through the communication line. A satellite positioning method characterized by being determined from an approximate position of a mobile object.   Use a communication line for communication from a server or other information source to a mobile, and the communication line includes either a cellular network, a wired or wireless Internet, or a telephone landline, or a combination thereof The satellite positioning method according to claim 1.   An accurate but uncertain pseudorange difference using the GPS C / A pseudorandom code start time transmitted as an integer millisecond value of space vehicle (SV) time corrected to GPS time by satellite time correction data The satellite positioning method according to claim 1, further comprising:   An accurate but uncertain pseudorange difference using the GPS C / A pseudorandom code start time transmitted as an integer millisecond value of space vehicle (SV) time corrected to GPS time by satellite time correction data The satellite positioning method according to claim 1, wherein the determination of the uncertainty of the pseudo-range difference is performed by a moving body approximate position supplied from a server or another information source. X (mean value) as an initial estimated solution is started by the above equation with the following equation 1, and a least squares iteration algorithm is used in which each subsequent calculation process is started with the estimated solution at the previous calculation. Iterating until convergence is achieved, the iterative algorithm is
(A5) Using the ephemeris data (satellite accuracy calendar) received from the server, or an equivalent thereof, calculate the satellite position (x _k , y _k , z _k ) at time T,
(B5) Calculate the LOS vector r _k (average value) and the length (distance) r from the estimated position of the moving object to each satellite,
(C5) When c is the speed of light, the satellite signal transmission time t _k = T−r _k / c is calculated. (D5) The satellite position (x _k , y _k , z _k ), r _k (average) Value) and r _k and the corresponding satellite velocity vector v _k (average value) to recalculate the ephemeris data (satellite accuracy calendar) using the signal transmission time t _k obtained in step C5. use,
(E5) The following equation (2) indicating the moving object-satellite unit vector u _k (average value) is calculated together with the LOS vector r _k (average value).
(F5) The vector v _k (average value) is a satellite velocity vector, and forms a matrix H defined by the following equation (3):
(G5) using r _k obtained by a process D5, it calculates the following equation 4 of the formula as the distance difference to use the current estimates solutions x,
(H5) The following equation (5) is calculated as a vector of change between the pseudo-range difference measurement vector supplied by the receiver and the distance difference calculated in the process G5. ,
ρ _1k = (n _k −n ₁ ) + c (ε _k −ε ₁ ) + c (τ _k −τ ₁ )
Calculated by
τ _k is the measurement value of the k-th satellite reception code phase, ε _k is the satellite time correction value of the k-th satellite received from the server, and an unknown integer (n _k −n ₁ ) is the following number 7 is solved by
(I5) In order to apply to the current estimated solution, Δx (average value) as a correction value is calculated by the following formula 8,
(J5) = represents an assignment instruction in calculation, and does not indicate algebraic equivalence, and generates the following equation (9) as a new estimated solution,
(K5) If there are not enough iterations to obtain good convergence, go back to step A5, otherwise finish the iteration with the solution x (mean value).
The satellite positioning method according to claim 4, comprising the steps of:

6. The satellite positioning method according to claim 5, wherein the iterative algorithm is the same except that the quantity is modified to fit the two-dimensional positioning.

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