Time Syntonization and Frequency Stabilizing Using GPS Carrier Phase with Extension Controller

Transcription

1 WEA TANACTION on ELECTONIC Manuscript received Apr. 25, 2007; revised July 14, 2007 Guo-hing Huang Time yntonization and Frequency tabilizing Using GP Carrier Phase with Extension Controller GUO-HING HUANG Department o Electronic Engineering, National Chin-Yi University o Technology 35, Lane 215, Chung-han d., ec. 1, Taiping, Taichung, TAIWAN,. O. C. hgs@ncut.edu.tw Abstract: - This study discusses time syntonization and requency stability calibration using GP carrier phase measurements. Thus ar most papers on this subject discussed using two GP receiver measurements, and perorming requency stabilizing and vehicle positioning with the double dierences. This paper proposes using a dual requency GP receiver and a novel extension controller neural network algorithm that can achieve the requency stabilizing and coordinate positioning. The oscillation requency o the rubidium atom clock is selected irst as the satellite atom clock oscillation requency as the criterion or adjusting the GP receiver oscillator's requency. The receiver s oscillation requency is synchronized with the reerence atomic clock oscillation requency using the designed extension controller and extension neural network. To inish the requency stabilizing and time syntonization, the time can be calibrated and the position precision on the vehicle improved. The position precision can be improved rom about 3.5 meters to about 1.5 meters using the extension controller. The time error is improved rom about seconds to about seconds. Using the extension neural network to veriy the position precision allows improvement rom about 3.5 meters to about 1.3 meters. The time error is improved rom about seconds to about seconds. The system was veriied experimentally as satisying the exactness, easibility and robustness o the initial concept. Key-Words: - GP, Carrier Phase, Extension Controller, Extension Neural Network 1 Introduction Wireless communication lourishes in highspeed communications, navigation, power systems, data acquisition instrumentation and in numerous other applications. Frequency usage and bandwidth requirements have increased. The extreme accuracy o navigation data is not inluenced by time, place, or weather except or shielding the line o sight between the satellites and the navigator. There are global, all-weather, continuous, high accuracy threedimensional navigation systems with encrypted security. GP is a high- accuracy navigation system or all vehicles. However, GP receiver errors reduce the precision o GP positioning. Transmission errors due to ionospheric and tropospheric activity can cause delay. Because the satellites possess a high-accuracy atom clock and produce the L1 and L2 carrier phase signals, the navigators can access reasonably accurate navigation data through the GP system in the world. The internal o each GP receiver produces a pulse per second when the L1 and L2 carrier phase signals have been received. Thus, the time between the master station and slave station receivers can be adjusted simultaneously to improve the navigator positioning accuracy. [1][2][3] Hence, a higher perormance time and requency techniques are expected i the GP carrier phases are considered. The requency stability o the GP receiver is the most important actor or positioning. The cycle slip and multipath eects are not critical actors that inluence the GP solution. A new requency synchronization method is proposed in this paper that uses the GP carrier phase measurement is proposed in this paper. The idea is realized into a carrier phase requency synchronization system. [4] The goal o the system is to steer the receiver clock such that its requency will ollow the IN:

2 WEA TANACTION on ELECTONIC Guo-hing Huang requency o a given primary clock. The GP receiver dual carrier phase measurement and the oscillation requency o the master clock are used to achieve the requency stabilizing and time synchronization. The clock error between satellites and receivers can be estimated through the GP carrier phase observation. A master atom clock replaces the satellite atom clock, to estimate requency error between the receiver and master atom clock. The extension control law and extension neural network are employed to implement the controllers in this system. The oscillation requency o the GP receiver is synchronized with the master atom clock requency. The position precision can be improved by reducing the requency error between the receiver and master atom clock. [5][6] This paper is organized as ollows: 1 ection 2 describes GP carrier phase observation. 2 ection 3 derives the extension controller. 3 ection 4 depicts the extension neural network. 4 ection 5 discusses the experimental results. 5 ection 6 gives our conclusions. 2 GP Carrier Phase Observation The phase dierence between the GP satellite s carrier phase and the reerence requency o its GP receiver oscillator can be expressed as ollows: [7] [] Φ Φ = φ ( t φ ( T : Carrier phase o the -th receiver station to observe the -th satellite. φ ( t : Carrier phase o the -th satellite time transmission in t epoch. φ ( T : The phase o -th receiver produced at T epoch I we consider the phase relationship between the GP carrier phase requency and the oscillator, the above equation can be rearranged using φ ( T = φ ( t + ( T t The propagation delay errors contain the ionosphere delay eect, the troposphere error and the uncertain error. It can be ormulated as ollows: Φ = ρ + cdt ( dt + λn d + d + ε ion trop ρ : The distance between the -th satellite and the -th receiver dt : Clock bias o the -th satellite dt : The clock dierence between the GP time and the -th receiver clock. N : Initial carrier phase integer ambiguity λ : The GP L1 carrier phase wavelength ε : Uncertain error amount c : peed o light d d ion trop : Ionospheric delay : Tropospheric delay The wide lane method is used to dispel the ionospheric and tropospheric delay errors, and ormulate a new relationship with the carrier phase. This is expressed as ollows: Φ W = Φ Φ L 2 L 2 = ρ + ( L 2 Δ δ c α N N L 2 ( c L 2 Δ δ : Time dierence between the satellite and receiver α : Total ions number in the path L1 : The requency o L1 carrier phase L1 : The requency o L2 carrier phase N L1 : The integer ambiguity o L1 N L2 : The integer ambiguity o L2 IN:

3 WEA TANACTION on ELECTONIC Guo-hing Huang 3 Extension Controller ometimes the engineering process is not able to setup a mathematical model that can accurately describe and control an integrated plant system. In other words, the traditional controller is not able to obtain the satisactory results. Utilizing the extension controller to control a plant, can oten obtain unexpected terriic results. The listed reerences used the PI controller, uzzy controller and extension controller and the results were compared. The extension controller was veriied to produce better perormance than the traditional PI controller, and is similar to the uzzy controller via the experimental results [9]. Using a GP receiver to carry out requency stability and time syntonization will inluence the precision due to an unstable oscillation requency in the GP receiver, clock bias and integer ambiguity and so on. This paper proposes using the extension set and element model concept to design the extension controller, as shown in Figure 1. [10][11] First, obtain the classical domains in the control output plane: G C1 V1 C2 V 2 = ( G, C, V = Cn Vn G C 1 < a01, b01> C 2 < a02, b02 > =... <... > Cn < a0n, b0n > G G is the GP receiver; G is the control characteristic o the GP receiver. Where C, 1 C,, 2 C is to express n dierent characteristics n such as the oscillation requency o GP receiver, integer ambiguity o G. And V, 1 V,, 2 V n respectively is G about the range o C, 1 C,, 2 C value, namely classical domains. n thenvi =< a0n, b0n > (i = 1, 2,, n The extensional domain in the control output plane is expressed as: Figure 1. Extension Control ystem Functional Block Diagram The basic extension controller concept is to transer the signal point o view to deal with the control problem. Using a relational unction o the control output signal as the control input correction let the control signal transer to a reasonable range. Go Co1 Vo1 Co 2 V o 2 = ( Go, Co, Vo = Con Von Go Co1 < ap1, bp1 > Co 2 < ap2, bp2 > =... <... > Con < a, b > G is the GP receiver. o G is the control o characteristic o the GP receiver. Where C, o 1 C,, o 2 C on is n dierent characteristics such as the GP receiver oscillation requency, integer ambiguity o G o. And V, o 1 V,, o 2 V on respectively is Go about the range o C, o 1 C,, o 2 C value, namely extensional on domains. then V =< a, b >(i = 1, 2,, n oi IN:

4 WEA TANACTION on ELECTONIC Guo-hing Huang According to the distance deinition o the classical and extensional domains, determines a relational unction computation. ρ a + b b a ( vi, V i = vi i i i i a + b b a ρ ( vi, Voi = vi 2 2 pi pi pi pi Figure 2 shows the structure o the extension neural network. It is comprised o an input layer and output layer. The neuron o the input layer is made o the control plant characteristics. The output layer neuron is the control result. Ater adjusting the weighting actor, learning rate, and the extension distance, an ideal control result will be obtained. [12][13] Calculate the relational unction: ( K v i ( vi, Vi ρ, vi Vi V i = ρ ( vi, Vi, vi V ρ( vi, Voi ρ( vi, Vi i p x m 1 p x mn p x mt w L 11 w L w rn L w st U 11 U w rn O m1 O mr Judge the relational unction to determine the control output. U w st O ms u( t = u( t 1, K( vi 0 u( t = ( y, Kv ( i, 1 Kv ( i < 0 u( t = umax, K( vi 1 1. K( vi 0, the output does not change and maintains the last output. 2. ( 1 K v i < 0, according to the element model algorithm, resolve the outputs element. 3. K( v i < 1, is the output element o the biggest control amount. 4 Extension Neural Network Algorithm The extension neural network is a solution method that combines the extension theory with a neural network. The matter element model o the extension theory is combined with the neural network as the learning mechanism. By adjusting the receiver oscillation requency, it is synchronized to the oscillation requency o the master atomic clock. Figure 2. The structure o the extension neural network The extension neural network algorithm procedure is as ollows: tep 1: Utilize extension matter element model to determine the weighting actor. ( N c V Nr c1 Vr 1 c V M M ct Vrt 2 r2 r = r r = N is the GP receiver; c is the GP receiver r control characteristics o such as oscillation requency, integer ambiguity, and so on. And L U Vrn = wrn, wrn expresses a region o the characteristics (weighting interval. The method or determining this region is obtained in the training set: w L rn r = min{ xmn} IN:

5 WEA TANACTION on ELECTONIC Guo-hing Huang w U rn r = max{ xmn} tep 2: Calculate the center o the weighting interval z. rn {,,, } Z = z z K z r r1 r2 rt L U z = ( w + w /2 rn rn rn tep 3: Calculate the extension distance. ED t P U L xmn zrn ( wrn wrn/2 = + I n= I ( wrn wrn /2 G U L tep 4: Deine the extension distance o the atom clock oscillation requency ED. Determine whether the extension distance o the controlled receiver ED is equal to G ED or not. I ED = ED, then G maintain the original output. I it is not the same then go to tep 5. transmission errors can be dispelled via the GP carrier phase observation and pair o GP receivers to improve the position precision. However, i there is no oscillation requency syntonization between the GP receiver and satellite clock, the position precision will be reduced. Thereore, the extension controller and extension neural network are used to adjust the receiver oscillation requency to synchronize the satellite oscillation requency. Figure 3 shows the structure o the experimental system. The oscillation requency o the atomic clock is used to reduce the bias between the receiver and the atom clock requency. The proposed approach can more accurately resolve the integer ambiguity, clock bias and wide lane carrier phase. Enhancing the accuracy o these parameters allows the vehicle position to be estimated more precisely. tep 5: eadjust the center o the weighting interval. (1 z z x z new old p( old old = + η( mn z z x z new old p( old old = η( mn (2 Adjust the weighting actor interval. L( new L( old p( old old w = w + η( xmn z U( new U( old p( old old w = w + η( xmn z L( new L( old p( old old w = w η( xmn z U( new U( old p( old old w = w η( xmn z (3 Let ED = ED, G O is the result o the last output. ms O z x z new p( old new ms = + η( mn Figure 3. ystem Functional Block Diagram Figure 4 shows the navigator s position error using GP receiver observation. Using GP ephemeredes and carrier phase measurements, the time errors between the GP receiver and satellite can be estimated, as shown in Figure 5. Position precision is analyzed about 3.5 meters beore using the extension controller. The time error is about seconds. 5 Experimental esults Accurate single point positioning is generally perormed using a pair o dual-requency GP receivers. The ionospheric and tropospheric delay IN:

6 WEA TANACTION on ELECTONIC Guo-hing Huang Figure 4. eceiver position error without using extension controller. Figure 6. The position error using extension controller. Figure 5. Time dierence between GP receiver and satellite without using extension controller. Utilizing the extension theory to design the extension controller, the relational unction is deined via adjusting the GP receiver oscillation requency to synchronize with the atomic clock oscillation requency. Position precision can be improved rom 3.5 meters to 1.5 meters ater using the extension controller, as shown in Figure 6. The 7 time error is improved rom seconds to seconds ater using the extension controller. It is obvious that the accuracy is improved by about 17 times, as shown in Figure 7. Figure 7. Time dierence between GP receiver and satellite using extension controller. The neural network extension distance idea is used in cooperation with adjusting the weighting actor o the neural network to synchronize the receiver oscillation requency with the oscillation requency o the reerence atomic clock. Position precision can be improved rom 3.5 meters to 1.4 meters ater using the extension neural network, as shown in Figure. The time error is improved rom seconds to 3 10 seconds ater using the extension neural network. The accuracy is improved by about 16 times, as shown in Figure 9. IN:

7 WEA TANACTION on ELECTONIC Guo-hing Huang Figure. The position error using extension neural network. Figure 9. Time dierence between GP receiver and satellite by using extension neural network. algorithm estimates the relational unction among the oscillation requency stability, time syntonization and integer ambiguity, then combines the deault value o the relational unction. The control targets are controlled one at a time, until satisactory system control is obtained. The experiment results show that the time error is 7 improved rom seconds to seconds using the extension controller. The advantage o the proposed approach is the combined neural network learning mechanism and extension theory element model. The actor that most inluences positioning accuracy is the oscillation requency stability o the GP receiver, the time syntonization, and integer ambiguity. The relational extension distance and weighting actor adjustment are merged to adjust non-ideal value into an ideal interval ast and eiciently. The entire system perorms requency stability and time syntonization to obtain the optimum control result. The time error is improved to about 3 10 seconds ater using the extension neural network. Then the position precision is greatly promoted. In the uture, we can use the cesium atom clock with higher precision as the oundation or adjusting the receiver oscillation requency. At the same time, the cesium clock requency can dispel the multipath eects and estimate the cycle slip error to better improve vehicle position precision. Through wired or wireless transmissions, the proposed method gives all remote stations accurate analysis data. And then the requency o remote GP receivers can be syntonized using the extension neural network algorithm. Figure 10 shows an overview o the entire system to achieve requency stability and time syntonization. 6 Conclusions This paper proposed using GP carrier phase measurements to perorm requency stability and time calibration. Originally, position precision was not high and time error was great. Using an extension controller and extension neural network to adjust GP receiver oscillation requency will enhance the position precision and requency stability. The advantage o the extension controller is that it produces an extension element model or any required control system. The extension controller Figure 10. ystematic block diagram o the requency control process using carrier phase. IN:

8 WEA TANACTION on ELECTONIC Guo-hing Huang Acknowledgements Thanks to the Chunghwa Telecom Laboratory or providing critical data, and the National cience Council o the OC or supporting this research under Grant NC E eerences: [1] K. enior, D. Matsakis, and L. Breakiron, Frequency cales Generated rom Carrierphase GP Data, Proceedings o IEEE/EIA International on Frequency Control ymposium and Exhibition, pp , June [2] P. Jarlemark, K. Jaldehag, C. ieck, and J. Johansson, First esults o eal-time Time and Frequency Transer Using GP Code and Carrier Phase Observations, Proceedings o IEEE International on Frequency Control symposium and PDA Exhibition Jointly with the 17th European Frequency and Time, pp , May [3]. Dach, T. childknecht, T. pringer, G. Dudle, and L. Prost, Continuous Time Transer Using GP Carrier Phase, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control pp , Nov [4]. G. Zencik, and Jr., K. Kohlhepp, GP Micro Navigation and Communication ystem or Clusters o Micro and Nano-satellites, IEEE Proceedings on Aerospace Conerence, pp , March IEEE Transactions on Instrumentation and Measurement pp.33-3, [] Chia-Lung Cheng, Fan-en Chang, and Kun- Yuan Tu, Highly Accurate eal-time GP Carrier Phase Disciplined Oscillator, IEEE Transactions on Instrumentation and Measurement, pp.19-24, [9] Hu Chen, Wang Xingyn, Design o an Extension Linguistic Controller, From Matter Element Analysis to Extenics, December [10] Yang Lin, Wu Li-Ming, Huang Ai-Hua, The Matter Element Model and Algorithm o Extension Control, ystem Engineering Theory and Practice, No. 6, June [11] Zhang Jiwen, Yu Yongquan, Algorithm Implementation o Extension Control with Matter-element Model, Automation and Inormation Engineering o Guangdong, No. 3, [12] M. H. Wang, C. P. Hung, Extension Neural Network, Proceedings o the International Joint Conerence on Neural Networks, Vol.1, No.1, pp [13] Martin T. Hagan, Howard B. Demuth, and Mark Beale, Neural Network Design, PW Publishing Company, [5] J. Johansson, K. Jaldehag, Precise Time Transer Using GP Carrier Phase-based Techniques, Proceedings o Joint Meeting o the European on Frequency and Time Forum, 1999 and the IEEE International Frequency Control ymposium, pp , April [6] Hackman, C., Levine, J., New Frequency Comparisons Using GP Carrier-phase Time Transer, Proceedings o IEEE International on Frequency Control ymposium and PDA Exhibition Jointly with the 17th European Frequency and Time, pp , May [7] Kun-Yuan Tu, Fan-en Chang, Chia-hu Liao, Li-heng Wang, Frequency yntonization Using GP Carrier Phase Measurements, IN: