This application claims the priority benefit of Taiwan application serial no. 100102943, filed Jan. 26, 2011. The entirety of the above-mentioned patent application is hereby incorporated by reference herein and made a part of this specification.
This disclosure relates to a positioning method and a positioning apparatus using a differential global positioning system (DGPS).
Typhoons cause vast damages to the Earth each year. If more instant information about the incoming typhoon can be collected, it will be possible to take precautious measures and, when necessary, help people withdraw to reduce property losses and personal casualties. The instant typhoon information is also important to typhoon research.
The heat energy of typhoons is largely absorbed from the warm sea surfaces. Therefore, information close to the sea surface such as the wind field, humidity and temperature is useful in studying the developing process of typhoons. Detecting the rainfall amount in the typhoon area is useful in forecasting the possible flood caused by typhoon. Cloud structure and atmospheric convection within the typhoon have great effects on typhoon development. There are researchers who drop dropsondes with global positioning system (GPS) into the typhoon to measure the various typhoon information mentioned above.
A positioning method is introduced herein. In this positioning method, a differential global positioning system is used to calculate a double difference of satellite distance in connection with a reference station and a receiver station. A baseline vector pointing from the reference station to the receiver station is calculated according to the double difference of satellite distance and the cosine law. The baseline vector and the position of the reference station are used to calculate the position of the receiver station. A plurality of correction coefficients are obtained according to the position of the reference station, the position of the receiver station, and a current time. The position of the receiver station is corrected according to the correction coefficients and a length of the baseline vector.
A positioning method is introduced herein. In this positioning method, a differential global positioning system is used to calculate a double difference of satellite distance in connection with a reference station and a receiver station. A baseline vector pointing from the reference station to the receiver station is calculated according to the double difference of satellite distance and the cosine law. The baseline vector and the position of the reference station are used to calculate a position of the receiver station.
A positioning method is introduced herein. In this positioning method, a differential global positioning system is used to calculate a baseline vector pointing from a reference station to a receiver station. The baseline vector and the position of the reference station are used to calculate the position of the receiver station. A plurality of correction coefficients are obtained according to the position of the reference station, the position of the receiver station, and the current time. The position of the receiver station is corrected according to the correction coefficients and the length of the baseline vector.
A positioning apparatus is introduced herein. This positioning apparatus is the receiver station and employs the above differential global positioning system. The positioning apparatus includes a balloon and a payload disposed below the balloon. The payload includes a receiver, a processor, and a transmitter. The receiver receives satellite signals of the differential global positioning system or receives the satellite signals as well as signals from the reference station. The processor calculates based on the signals received by the receiver. The transmitter wirelessly transmits a calculation result of the processor. Any one of the aforementioned positioning methods may be executed by the processor or a monitoring station. Alternatively, the processor and the monitoring station may cooperate to execute any one of the aforementioned positioning methods, in which some steps of the positioning method are executed by the processor and the remaining steps of the positioning method are executed by the monitoring station.
Several exemplary embodiments accompanied with figures are described below to further describe the disclosure in details.
The accompanying drawings are included to provide further understanding, and are incorporated in and constitute a part of this specification. The drawings illustrate exemplary embodiments and, together with the description, serve to explain the principles of the disclosure.
The flow chart of
r
ur
(kl)
=[r
u
(k)
−r
r
(k)
]−[r
u
(l)
−r
r
(l)] (1)
In equation (1), the subscripts u, r represent the receiver station and the reference station, respectively. The superscripts k, l represent two satellites of the DGPS, respectively. rur(kl) is the double difference of satellite distance, ru(k) is the distance between the receiver station and the satellite k, rr(k) is the distance between the reference station and the satellite k, ru(l) is the distance between the receiver station and the satellite l, and rr(l) is the distance between the reference station and the satellite l.
The double difference of satellite distance rur(kl) is obtained by a series of calculation. Firstly, the traditional DGPS is used to calculate a double difference of pseudo-range and a double difference of carrier phase in connection with the reference station and the receiver station using equations (2) and (3) below.
Δρ=ρur(kl)=[ρu(k)−ρr(k)]−[ρu(l)−ρr(l)] (2)
Δφ=φur(kl)=[φu(k)−φr(k)]−[φu(l)−φr(l)] (3)
Δρ and ρur(kl) both represent the double difference of pseudo-range. Δφ and φur(kl) both represent the double difference of carrier phase. Similar to the representation in equation (1), ρu(k) and φu(k) represent the pseudo-range and carrier phase calculated based on the signal of satellite k, and other similar variables are represented in a similar manner. Any one of the pseudo-range ρ, namely ρu(k), ρr(k), ρu(l) and ρr(l) can be represented by equation (4) below.
ρ=r+Iρ+Tρ+c(δts−δtu)+ερ (4)
In equation (4), r is the distance between the reference station or the receiver station and one of the satellites, i.e. one of ru(k), rr(k), ru(l) and rr(l), Iρ and Tρ represents the distance differences caused by the delay of satellite signal transmitting through the ionosphere and the troposphere, respectively, c represents the speed of light, δts represents the clock error of one of the satellites, δtu represents the clock error of the reference station or the receiver station, and ερ represents the distance error caused by noise.
On the other hand, any carrier phase φ of φu(k), φr(k), φu(l) and φr(l) can be represented by equation (5) below.
φ=λ−1[r+Iφ+Tφ+c(δts−δtu)]−Nφ+εφ (5)
In equation (5), λ is the wavelength of the satellite signal, Iφ and Tφ represent the distance errors caused by the delay of satellite signal transmitting through the ionosphere and the troposphere, respectively, Nφ is the integer ambiguity, and εφ is the phase error caused by noise.
If each pseudo-range ρ in equation (2) is represented by equation (4) and each carrier phase φ in equation (3) is represented by equation (5), some terms are very close in value and can therefore cancel each other out, thus resulting in the following equations (6) and (7).
Δρ=ρur(kl)≅rur(kl)+ερ,ur(kl) (6)
Δφ=φur(kl)≅λ−1rur(kl)−Nφ,ur(kl)+εφ,ur(kl) (7)
Positioning by means of the carrier phase φ is more accurate than positioning by means of the pseudo-range ρ, however, the double difference of integer ambiguity Nφ,ur(kl) must be calculated first. Therefore, the next step is to calculate the double difference of integer ambiguity Nφ,ur(kl) in the double difference of carrier phase, Δφ. Firstly, the following two references [1], [2] give equations (8), (9) below.
[1] B. Li, Y. M. Feng, and Y. Z. Shen, “Three carrier ambiguity resolution: Distance-independent performance demonstrated using semi-generated triple frequency GPS signals,” GPS Solut., vol. 14, pp. 177-184, 2010.
[2] Y. M. Feng, “GNSS three carrier ambiguity resolution using ionosphere-reduced virtual signals,” J Geod., vol. 82, pp. 847-862, 2008.
Δ
Δ
Δ
In equations (10) and (11), f1, f2 and f5 are frequencies of the GPS satellite signal at frequency bands L1, L2 and L5, respectively. Δ
Δ
In equation (15),
In equation (16), Ŝr(l) to Ŝr(K) are unit vectors pointing from the reference station to the first and to the kth GPS satellites, respectively. Next, Δ
According to the calculations above, the double differences of integer ambiguity Δ
Details of equations (8) to (18) are discussed in the above-mentioned references [1], [2] and, therefore, explanation thereof is not repeated herein.
In equation (7), the double difference of carrier phase Δφ is known, and GPS satellite signal wavelength λ and the double difference of integer ambiguity Nφ,ur(kl) are also known. Let the double difference of noise error εφ,ur(kl) be approximated to zero, the double difference of satellite distance rur(kl) can thus be obtained.
Referring to
As shown in
However, when the baseline length is as great as one hundred kilometers, the parallel line segment assumption adopted in the tradition DGPS positioning method is no longer appropriate. Therefore, the present embodiment does not adopt the parallel line segment assumption. Instead, the trigonometric cosine law is used which can make the calculation of the baseline vector
rr(k) can also be similarly expressed according to the cosine law. The reference station
In equation (20), rr(k) and rr(l) in the denominators are extremely large in value and, therefore, terms other than −[Ŝr(k)−Ŝr(l)]·
r
ur
(kl)
=−[Ŝ
r
(k)
−Ŝ
r
(l)
]·
ur+αur(kl) (21)
In equation (21), −[Ŝr(k)−Ŝr(l)]·
In this exemplary embodiment, the baseline vector
Referring to
A plurality of correction coefficients is obtained according to the reference station position, the receiver station position, and the current time at step 140. A simulation calculation shows that the receiver station position obtained at step 130 still has an error with respect to the real position, and the error is directly proportional to the cube of the length of the baseline vector. The correction coefficients represent the ratio of the error to the cube of the baseline vector length. In the exemplary embodiment, three coefficients αx, αy, αz are used, which respectively correspond to the coordinate axes x, y, z of the position at which the receiver station is located. The coordinate axes x, y are parallel to the earth surface, and z is the height axis.
The position of the GPS satellites will affect the correction coefficients αx, αy, αz. Therefore, the correction coefficients have correlation with the current time and the latitude and longitude of the receiver station. In addition, the azimuth angle between the baseline vector
Referring to
εα=ααR3 (22)
In equation (22), α=x, y, z, εα represents the receiver station position errors corresponding to the three coordinate axes, i.e. the desired correction amount. αα represents the correction coefficients αx, αy, αz, R is the length of the baseline vector
The correction coefficients εx, εy, εz can thus be used to correct the corresponding coordinates of the receiver station to achieve the final estimated receiver station.
The receiver station position that undergoes the geometric correction of step 120 is already more accurate than the traditional DGPS positioning. Having undergone the residual error corrections of step 140 and 150, the receiver station position is even more accurate.
The positioning method of
The positioning method described above can apply in any fields that need precise positioning. For example, a plurality of positioning apparatus that support the above positioning method can be fabricated and dropped into a typhoon to timely monitor the developing process and travelling path of the typhoon.
The positioning apparatus 500 may be dropped into the typhoon to serve as the above receiver station. The positioning apparatus 500 includes a balloon 520 and a payload 540 disposed below the balloon 520. The balloon 520 can carry the payload floating in the sky to facilitate the payload 540 to collect monitoring data. The payload 540 includes a receiver 542, a processor 544, and a transmitter 546. The receiver 542 receives the GPS satellite signals or receives GPS satellite signals as well as signals from the reference station. The reason of receiving signals from the reference station is that the positioning apparatus 500 can estimate its position according to the above positioning method and needs to receive relevant data from the reference station for this estimation. The processor 544 calculates based on the signals received by the receiver 542. The transmitter 546 wirelessly transmits the calculation results of the processor 544. For example, the transmitter 546 may be a radio-frequency (RF) circuit for transmitting wireless signals.
These positioning apparatuses may first use the traditional DGPS positioning method to preliminarily estimate their positions and self-define the clusters according to the distances from one another and the positioning apparatus distribution. In each cluster, the positioning apparatus most close to the center of the cluster is selected as the reference station in the above-described positioning method, and the remaining positioning apparatus in the same cluster serve as the receiver stations in the above-described positioning method.
The reference station of each cluster may directly use the traditional GPS positioning method to estimate its position, or use the traditional DGPS positioning method to estimate its position under the assistance of another reference station. The above estimated reference station position may be used by the receiver stations in the same cluster to carry out the positioning method of
The processor 544 of the positioning apparatus 500 can execute the positioning method of
The positioning method of
In addition to the two implementations as described above, the processor 544 may also execute some steps of the positioning method and the monitoring station may execute the remaining steps of the positioning method. In this case, the positioning apparatus 500 must transmit the data obtained in those some steps to the monitoring station for the monitoring station to continue the subsequent steps.
In summary, this disclosure improves the traditional DGPS positioning method by adopting geometric correction and residual error corrections and can accurately estimate the coordinates of the positioning apparatus. Even when the baseline length is greater than 100 kilometers, the estimation can be accurate to centimeter-level, making the disclosed positioning method and apparatus beneficial in various applications. This disclosure replaces the parachutes of traditional dropsondes with balloons, which can prolong the floating time of the positioning apparatus such that the positioning apparatus can provide more observation data. This disclosure may be used for real-time monitoring of a typhoon. This disclosure may also be applied in any technical field that needs precise positioning.
It will be apparent to those skilled in the art that various modifications and variations can be made to the structure of the disclosed embodiments without departing from the scope or spirit of the disclosure. In view of the foregoing, it is intended that the disclosure cover modifications and variations of this disclosure provided they fall within the scope of the following claims and their equivalents.
Number | Date | Country | Kind |
---|---|---|---|
100102943 | Jan 2011 | TW | national |