Modelig Simulatio ad Optimizatio Techologies ad Applicatios (MSOTA 2016 Simulatio ad Aalysis o Sigal Acquisitio of DS Receiver with The Aid of INS Shulei Che Xiaqig Tag Xuwei Cheg Juqiag Gao ad Zepeg Su Departmet of Cotrol Egieerig Academy of Armored Force Egieerig eijig 100072 Chia Abstract Improvig the dyamic performaces of DS receiver with INS-aided is the hotspot of the curret avigatio research ad the key problem is how to improve the performace of sigal acquisitio. This paper has some research ad aalyses about the theory ad mathematic model of sigal acquisitio. Though the simulatio of vehicle trajectory the author acquired the results of sigal acquisitio performace of DS receiver with the aid of INS composig of 10 deg/h bias drift gyros ad 100 ug bias drift accelerometer. The experimet results illustrate that the average sigal acquisitio time of DS receiver with the low accuracy INS aided is shorteed greatly the searchig scope of Doppler frequecy shift ad code phase are arrowed thus the sigal acquisitio performace of DS receiver is improved. This research ca serve as good istructio for the developmet of itegrated avigatio. acquire sigal by determiig the carrier frequecy ad code phase. There are may methods of sigal acquisitio the simplest oe is the serial acquisitio scheme based o glidig correlatio. The satellite sigal become IF sigal though the receiver RF the RF outputs IF sigal to acquisitio module after samplig. The carrier geetator ad pseudo code of receiver geerate sigal which frequecy ad code phase could be chaged the get a result after hadlig the IF sigal ad local sigal by modulatio itegral. If the result is greater tha the fixed threshold sigal acquisitio is success. If ot we must chage the frequecy ad code phase of local sigal ad repeat the previous step. [1]Figure 1 shows sigal acquisitio structure model. I IDF Threshold eywords-ds; sigal acquisitio; INS-aided; performace aalysis IF sigal I. INTRODUCTION As the cotiuous improvemet of sciece ad techology iformatio war has become the maistream i military the army eeds the avigatio istrumet with high accuracy sesor. Therefore the startup-time of avigatio system must be shorter ad sigal acquisitio ad trackig must be quick. With the rapid developmet of avigatio techology we usually use INS aided satellite receiver to improve its performace i harsh eviromet. This paper uses traditioal serial acquisitio method based o time domai to acquire eidou satellite sigal the aalyzes the performace idexes of the DS receiver. What s more The author use MATLA simulate the course of sigal acquisitio with the aid of low precisio INS though simulatig the vehicle trajectory of the carrier. I the ed this paper has some compariso ad aalysis of the results of sigal acquisitio with or without INS-aided. The work has the guidig sigificace for DS/INS itegrated system desig. II. THE THEORY OF SIGNAL ACQUISITION WITH THE AID OF INS A. The Serial Acquisitio Scheme ased O Glidig Correlatio As for the satellites of DS they have the same carrier frequecy ad trasmittig time of the sigal at the begiig. The carrier frequecy of sigal will be chaged alog with the motio of the satellite ad receiver (Doppler effect what more the code phase of carrier will be chaged too. So we Carrier Pseudo code Sigal detector IDF Q Cotrol sigal FIGURE I. THE SIGNAL ACQUISITION MODEL The sigal becomes IF sigal though RF frot. Ad the IF sigal ca be obtaied as: sif (t 2 PS C (t D(t cos[ IF t (t ] (t Where PS is power of IF sigal; C (t is pseudo code; is time delay; D(t is avigatio message; I F is frequecy of IF sigal; (t is iitial code phase; (t is white oise. Two ways of orthogoal sigals produced by local s ad are multiplied with iput sigals through mixer I ad Q ad the model is as follows: I (t sif (t 2 cos[( IF t 0 ] Copyright 2016 the Authors. Published by Atlatis Press. This is a ope access article uder the CC Y-NC licese (http://creativecommos.org/liceses/by-c/4.0/. (2 121
Q(t sif (t 2 si[( IF t 0 ] Ad the mathematic model of Doppler frequecy shift is: (3 (V rev V s e fb c The multiplyig uit ca be regarded as a low pass filter due to the itegrator behid it. Therefore the high-frequecy i the above formula ca be igored which has bee simplified as follows (oise is eglected: T1 I P D PS C (t C (t cos[ t 0 ]dt N I 0 (4 Where Vrev Vs ad (8 respectively represet the satellite receiver ad the speed of the satellite. e is the uit directio vector. Supported by INS ad ephemeris almaac we ca kow about the satellite ad the speed of the receiver i real time. Furthermore we ca figure out the value for T1 fs f rev ad subsequetly shorteig the Doppler search scope. If the QP D PS C (t C (t si[ t 0 ]dt N Q speed of the satellite provided by the satellite ephemeris is 0 (5 Select the modulus from the results of the above two formulas ad make threshold judgmet. If the value of the result high eough the sigal ca be acquired. The coordiates of the peak correspod to the carrier frequecy ad code phase of the sigal. Otherwise adjust the local carrier frequecy ad code phase by the cotrol device util the presece of peak exceedig the detectio threshold. [2]. Sigal Acquisitio With Is-Aided I order to acquire satellite sigals rapidly whe it is started DS receiver is required to cut dow the search scope for satellite sigals. Meawhile three kids of iformatio are ecessary to idetify the search scope icludig satellite ephemeris the speed ad positio of the receiver as well as the curret DS time. If INS avigatio parts ca assist iputtig avigatio iformatio such as Doppler frequecy shift iformatio ad code phase iformatio ito the satellite receiver i advace it will greatly shorte the search scope above the Doppler frequecy domai. With the same step size the smaller the search scope is the less time will be spet. I such circumstaces the TTFF (Time To First Fix will also be reduced. [3] Whe the satellite receiver receives the satellite sigals the Doppler frequecy shift of carrier ca be represeted i the followig: accurate the performace of INS will directly affect the acquisitio performace of the satellite receiver. We will make the study from the perspective of satellite receiver s performace idex to aalyze the iflueces of INS o the receiver i multiple ways. III. PERFORMANCE INDEXES OF SATELLITE RECEIVER A. Detectio Probability Aalysis Detectio probability ad false alarm probability are two importat idicators to detect the performace of the satellite receiver. oth of these idicators determie the reliability of the sigal acquisitio. Larger detectio probability ad smaller false alarm probability will lead to more reliable acquisitio. Uder the coditio of o-coheret itegratio we adopt the simulatio of detectio probability to reflect the acquisitio performace of the receiver with or without assistace. The detectio value of o-coheret itegratio is: 1 Z 1 (9 I 2 Q 2 Figure out the squares of the ambiguity fuctios for I ad Q withi periods ad add them together from the couterpoits to obtai the fial detectio value. [4] Defie two assumptios: H0 assume the presece of oise (A=0without sigal f f s f rev f s f rev (6 Where f s is the Doppler frequecy shift arisig from the movemet of the satellite. H1 assume the presece of sigal (A>0 Whe A =0 the detectio quatity Z is distributed as Rayleigh ad the false alarm probability is: f rev is the Doppler frequecy shift fs is to the caused by the movemet of the carrier. frequecy drift due to the clock errors of DS satellite while f rev is the frequecy drift produced by the clock errors of satellite receiver. Sice the miimum errors of satellite clocks ca be igored the formula ca be simplified as: f f rev f s f rev P fa V Vt p(z H 0 dz e Vt2 2 (10 2 2 Where t is the detectio threshold value ad is the oise power. We ca obtai that the detectio threshold value is: (7 122
Vt (11 2 l P fa P If the value of false alarm probability fa is obtaied the detectio threshold value of the system ca be figured out. If H1 is valid the detectio probability ca be expressed as follows: As show i the figure whe the Doppler error is less tha 100Hz it exerts the miimum ifluece o the detectio probability.. Calculatio Aalysis With the serial acquisitio algorithm based o time domai assume fuc ad tuc respectively refer to the ucertai sectio f Pd ( Q 1 ( N CN Q1( N 0 fs N 0 fs (12 bi ad tbi scopes searched by frequecy ad code respectively represet the frequecy search step size ad code search step size[5] the the total search cell is: Q1 ( is first-order Marcum Q-Fuctio which is: (15 N Q (a b 1 a 1 b x e x2 a2 2 The receiver always processes discrete data i practical I 1 (ax dx (13 I 1 [1 e N e operatio. I ( ad Q( ca be discretized as I(k ad Q(k. With k=01-1 if we adopt regular serial I the above formula 1 is the first class essel fuctio of -1 order. For easy calculatio the detectio probability ca be expressed as follows: PD ( 2 fu ct u c f bi tb i 2 2 2 2 ]N Q1 ( A acquisitio method every chage i the value of k would require times of multiplicatio ad additio operatios. ecause there are values of k 2 times of multiplicatio ad additio operatios are required i a carrier frequecy. For M times of frequecy searches M2 times of calculatios are eeded. Thus we ca make calculatio aalysis based o the chages of the acquisitio scope. (14 With the help of the software simulatio we ca work out a relatioship graph illustratig the chages of detectio probabilities for differet Doppler errors as the carrier-to-oise ratios i cases where the false alarm probability is 0.001 the search step size of code phase is 0.5 chip ad the pre-detectio itegratio is 2ms. C. Average Acquisitio Time Aalysis The average residece time for each cell is: T d w e ll ( Where 2 Pd (k Pd p P fa 1 T (16 Pd is detectio probability the loss factor of k p is P 1 fa is false alarm probability ad T is itegral time the required acquisitio time is: T T d w e ll IV. FIGURE II. RELATIONSHIP GRAPH ILLUSTRATING THE CHANGES OF DETECTION PROAILITIES FOR DIFFERENT DOPPLER ERRORS AS THE CARRIER-TO-NOISE RATIOS 2 f uc tuc f b i t b i (17 SIMULATION EXPERIMENT This experimet has adopted MATLA software to simulate the motio curve of the vehicle with low-precisio INS avigatio equipmet costituted by 100ug precisio accelerometer ad 1deg/h precisio gyroscope. The curve starts from the five-poited star movig toward the orth at first. It returs to the iitial positio after 600s. The x-axis is latitude lie ad the y-axis is the logitude lie. The iitial speed is 0 the maximum acceleratio is 10m/s2 ad the maximum agular velocity is 30deg/s. The motio curve is show i Figure 3 as follows: 123
V. RESULT ANALYSIS Apply the speed ad positio iformatio of INS as a result of 300s operatio to assist DS i capturig the satellite sigal. After aalyzig the acquisitio probability before ad after the assistace we make the graph i Figure 6. The sesitivity of its sigal acquisitio has bee improved by 4-5d-Hz. FIGURE III. THE SIMULATION OF VEHICLE TRAJECTORY The speed error ad positio error i the ortheast calculated by low-precisio iertial avigatio withi 600s are respectively show i Figure 4 ad Figure 5. Withi 600s the orther speed error does ot exceed 4m/s ad the easter speed error is o more tha 3m/s. Sice it is a route test o the simulated floor the speed error is early close to zero. The variace of Doppler frequecy shift ca also be calculated by INS speed error. While the latitude error reaches up to 350s ad logitude error approaches to 250s withi 600s. The aalysis o the detectio probability of acquisitio supported by INS from the perspectives of Doppler error ad code phase is show as ext chapter. FIGURE VI. COMPARISON GRAPH AOUT THE ACQUISITION SENSITIVITY EFORE AND AFTER THE INS-AIDED If the receiver is supported by low-precisio INS calculatig iformatio ad ephemeris the search scope of Doppler frequecy shift ca be declied to [-150kHz+150kHz] i a short time which is less tha the step size of the frequecy search. I coclusio the table which has illustrated the calculatio quatity with/without INS assistace is listed i Table 1 as follows: TALE I. CALCULATION QUANTITY WITH/WITHOUT INS-AIDED FIGURE IV. SPEED ERROR OF INS Way of Acquisiti o Serial acquisitio Serial acquisitio Assistace Search scope Number of search cells Calculatio quatity No [10kHz+10kHz] 163680 669778560 Yes [150Hz+150Hz] 4092 16744464 Obtaied from the above table with the help of INS ad ephemeris the calculatio quatity ad eergy will be declied by a order of magitudes. Give that the detectio probability of DS receiver is 0.95 false alarm probability is 0.01 the itegral time of time domai acquisitio is 2msad the system clock of receiver is 5.714MHz the required time without INS assistace ca be figured out as: T T d w e ll FIGURE V. LONGITUDE AND LATITUDE ERRORS OF INS 2 f uc tuc 362s f b i t b i (18 The required time with INS assistace ca be figured out as: 124
T IN S T dw ell 2 f uc t uc 9s f bi t bi (19 Therefore eve with low-precisio INS-aided the acquisitio time of satellite sigal ca be cosiderably reduced. VI. CONCLUSION This paper have show that eve the low-precisio INS could effectively improve the acquisitio sesitivity of the receiver which would greatly lower the calculatio quatity ad improve the acquisitio time of the receiver. The research achievemets made by this article ca istruct the desig of the INS/DS combied avigatio from the perspective of acquisitio sigal which ca help with sigal track of receiver ad the further study o the filter techology as well as provide vital practical sigificaces to the iformatio war. REFERENCES [1] [2] [3] [4] [5] Zhag G L Zeg J. Priciple ad Techology of Itegrated Navigatio.Xi a: Xi a Jiatog Uiversity Press2008pp31-46. Lashley M evly D M. Performace Compariso of Deep Itegratio ad Tight Couplig[J]. Navigatio 2013 60(3pp 159-178. Liu J Y Zeg Q H. Navigatio System Theory ad Applicatio. Xi a: Nwupress2010pp152-154. Lu Y.DS/GPS Dual Mode Software Reiver. eijig Electroic Idustry Press 2016pp134-136. He X F. Performace aalysis o high dyamic sigal acquisitio aided by SINS for GNSS satellites. Joural of Chiese Iertial Techology 201119 4 pp446-451. 125