INNOVATION RESEARCH ON STRAPDOWN INERTIAL NAVIGATION TECHNOLOGY

Transcription

1 IOVATIO RSARCH O STRAPOW IRTIAL AVIGATIO TCHOLOGY Yucui YAG* 1, Yi SOG 1, Yanhua ZHU 2 1 Huaiyin ormal Uniersity, HuaiAn, China; 2 Southeast Uniersity, anjing, China. Corresponding author: Yucui YAG mail: yangyucui01@126.com Abstract. The independent innoation o inertial naigation system is a crucial direction and approach and means o its deelopment, and it is targeted on the existing problems o inertial naigation system. Based on the quaternion theory which has been maturely applied in the attitude computation o strapdown inertial naigation system, this paper puts orward the innoatie thinking o geometric theory and graphic theory in the ield o naigation. Then, through the successul research results o the internal damping network in the strapdown system, it is necessary to ully explore the importance and practical signiicance o the inertial naigation potential by drawing on the platorm design idea. Finally, the adices o the crucial aspects o strapdown inertial naigation system independent innoation are gien. Keywords: Inertial aigation System; Quaternion; Geometric, Internal amping. 1. Introduction Strapdown inertial naigation system attaches inertial components directly to the carrier, and relies on computer to achiee the unctions o the naigation platorm. The system size, weight and cost are greatly reduced and are conenient or redundant coniguration since the electromechanical naigation system is remoed, which improes system perormance and reliability, and meanwhile proiding more naigation guidance inormation. The strapdown inertial naigation system is the main trend o the uture inertial naigation system deelopment [1, 2]. But the low accuracy o strapdown inertial naigation is the major actor which constrains its deelopment. Thereore, improing and enhancing the system s accuracy through all new ideas, new methods and new techniques is an important aspect o inertial naigation independent innoation. This paper pays wide attention to the deelopment and technology achieements o arious current subjects, and considers applied them to the improement o strapdown inertial naigations system. 2. Application o Mathematical Methods in Strapdown Inertial aigation Technology 2.1 Quaternion Theory The attitude computation is an important part o the strapdown inertial naigation system, which is related to the real-time updating o the carrier s attitude and the timely correction o the naigation coordinate system. Thereore, the accuracy o the attitude algorithm directly aects the naigation accuracy o the system. uler angle method and direction cosine algorithm were the two orginal methods to resole the carrier s attitudes. Howeer, the uler angle method had a singular point in the dierential equation when the carrier pitch angle was 90 degrees, which made it impossible to work in all attitudes. The direction cosine algorithm needed to resole nine dierential equations and the computational complexity was accordingly enormous [3]. Under the historical conditions at that time, there was an urgent need or an eectie and ull-scale way to sole the problem o carrier s attitudes computation. 72 International Journal o Mechatronics and Applied Mechanics, 2017, Issue 2

2 The quaternion theory is an ancient branch o mathematical theory. Beore it was introduced into the computation o strapdown inertial naigation system (SIS), the ield o application was quite small or quaternion theory, and it was not taken seriously by the majority o scholars. Howeer, the scientiic workers creatiely applied it to sole the practical problems o space technology and strapdown inertial naigation system, bringing the use o quaternion to sole the attitude matrix method into being. This method not only soles the problem o dierential equation degradation, but also has a small computation complexity, which can totally satisy the SIS sampling rate and real - time requirement. In order to reduce the rotation noncommutatiity error occurred in the quaternion computation o carrier s attitude, the equialent rotating ector algorithm is used to correct it in engineering projects. This algorithm can be diided into single sample algorithm, two-sample algorithm and three-sample algorithm according to dierent gyro sample number. At present, SIS widely takes quaternion algorithm and equialent rotating ector algorithm to resole the carrier s attitude. The actual eect has been widely recognized by the inertial naigation industry proessionals. 2.2 Geometric Theory The main purpose o naigation is the location and orientation o the carrier in the plane or space, that is, to determine the parameters o the carrier in a plane or space at a gien time. Then, the geometric theory or graphics theory o mathematical disciplines can be applied in the ield o naigation, in order to promote the strapdown inertial naigation technology improement and deelopment. The ollowing two examples canl illustrate this point. a. The Fast Locating and Orientating o a Carrier in a Certain Area ( i i, ) Based on the location o three known points in a region, the carrier (installed with SIS) can be accurately positioned and orientated. As shown in Figure 1: Figure 1 The Relationship Between Known Points and Car Position and Angle IS SIS proides heading inormation, The angle measuring deice proides the azimuth angle o the carrier or the known point i. Then the azimuth angle o the known point relatie to the north is: ISi i (1) And the azimuth angle o the known point relatie to the north (it may be in the irst quadrant) calculated according to the coordinate relation is: c arctan y x t t y x (2) Here x and x t y y t are the location measures output o SIS, and are known parameters, then the azimuth angle error c (3) Since the inertial naigation location error is not a small amount compared to the distance between the carrier and the known point, the arctangent unction cannot be linearized by the Taylor expansion method. In this case, the problem can be studied in another way: angle (heading angle) and the distance are geometric parameters, and geometric igure problem settlement can be taken into consideration. International Journal o Mechatronics and Applied Mechanics, 2017, Issue 2 73

3 Figure 2 The Triangle Formed by Heading Angle rror As shown in Fig. 2, assuming that the error o the azimuth angle measured by the inertia naigation is, the location error caused by the heading angle error will orm the error triangle shown in Fig. 2, and the triangular trilateral length o the triangle can be obtained mathematically. Thereore, it is not diicult to sole the problem by using the modern computer to sole the pure geometric problem, which makes the carrier position resoling problem transormed into "making side length o the error triangle be zero and minimize the position error ". It can be seen that a complex problem in naigation can be simpliied by the quick and eectie geometric methods. It is known that Proessor Shen Gongxun s research team rom Beijing Uniersity o Aeronautics and Astronautics has embarked the research method on a carrier to quickly ind the orth. The key technology is the use o geometric principles to set the orientation. We can predict that the urther study and reinement o the geometric model will be expected to achiee ast and accurate alignment o SIS and improe alignment and accuracy thanks to rapidity o modern computer soling mathematical problems [4, 5]. Undoubtedly, there are a lot o practical technological diiculties that need us to deep into. b. Aircrat Precise Landing In the aircrat landing system, the pilot plays an important role in the airport's scene judgment. Thereore, we can consider the deelopment o isual scene enhancing system, based on isible and inrared light detection and the use o image recognition technology to achiee the aircrat s landing alignment and monitoring on the runway [6, 7], which can proide more accurate location and orientation angle inormation or the pilot. In act, the ollowing three graphics will be obtained through obsering the aircrat runway rom the iewing rame: Figure 3 Runway Graphic 1 Obsered rom Viewing Frame Figure 4 Runway Graphic 2 Obsered rom Viewing Frame Figure 5 Runway Graphic 3 Obsered rom Viewing Frame 74 International Journal o Mechatronics and Applied Mechanics, 2017, Issue 2

4 According to the three dierent patterns aboe, three dierent categories o inormation can be acquired: Fig.3 shows the lateral deiation; Figure 4 shows the longitudinal deiation; Figure 5 shows the azimuth angle deiation. A relatiely accurate deiation alue can be obtained based on the conersion o a certain proportion o graphics to guide the sae landing o the aircrat. Undoubtedly, the aboe method is currently only put orward or a new research direction. The practical application still aces many technological diiculties and technical details to urther research and oertake, but the concept o using geometric graphics concept is a new way to assist strapdown inertial naigation. 3. The Use o Platorm-based Internal amping Theory in Strapdown aigation Technology The existence o Schuler cycle oscillations and Fourier cycle oscillations within SIS not only generate the oscillation error, but also the accumulation error will occur due to external disturbance on SIS. This is the key actor aecting system accuracy. When the system is in the case o little acceleration, the system undamped oscillation in the traditional platorm-based inertial naigation system can be eectiely restrained by adding the internal damping network in the platorm control circuit [8]. Other naigation inormation combination is usually imported in SIS to improe the naigation accuracy. We are concerned that in some special occasions, how to make ull use o the inertial measurement combination o its own inormation to improe its accuracy when the external auxiliary sensor inormation is not aailable. This approach ully exploits the potential o inertial naigation and does not add any cost and structural complexity, which is also an important aspect o inertial naigation innoation. This paper studies and compares the platorm inertial naigation and strapdown inertial naigation ully, and reers to the design ideas o platormbased system damping network in an innoatie way. The internal damping is successully obtained in SIS, making a breakthrough. The ollowing is a brie introduction. The naigation system (n) adopts orth ast own () geographic coordinate system, the scale orce equation is n en 2 ie en en gn, The equation expansion: nx ny nz 2 tan L 2 ie sin L R ( tan L ) 2 L L ie( sin cos ) R ie cos L g R (4) Here, are the north accelerated speed, east accelerated speed and down accelerated speed o the system respectiely; are the north speed, east speed and down speed respectiely.; L is latitude; R is the earth radius; ie is rotational angular elocity o the earth; g is the local acceleration o graity. is b The actual measurement input o accelerometer b, and b Cn n, the equation expansion is: bx by bz cos cos cos sin sin sin cos cos sin cos sin sin sin cos sin sin sin cos cos sin sin cos cos sin sin cos sin cos cos nx ny nz (5) b Cn Here, is the transition matrix o the naigation coordinate system relatie to the carrier coordinate system,,, are the roll angle, pitching angle and heading angle o the carrier respectiely. When the system is in the case o little acceleration, = = 0, the internal damping attitude can be calculated through the combination o the simpliied equation (1), and equation (2): arctan( arctan( by bz bz ) bx cos by ) sin, (6) Thus, when the system is in the case o little acceleration, the attitude angle o the carrier can be calculated using the acceleration inormation. International Journal o Mechatronics and Applied Mechanics, 2017, Issue 2 75

5 In addition, we combine the calculated attitude o strapdown inertial naigation and the inner damping attitude by Kalman ilter, which can eectiely suppress the oscillation o the gyro and improe the accuracy o the system. This will explained in detail due to limited space. The ollowing model gies the prototype o the actual test results to eriy the application o the attitude algorithm. 3.1 Static Test The three-axis gyroscopic drit o IMU is 10 /h, the three-axis accelerometer zero-bias is 5X10-4 g. Put the IMU on three-axis precision rotating table, and keep the attitude angle to be 0, heading angle to be 90, and do the static test or two hours. Figure 8 Pitching Angle Comparison Map o Internal amping System Figure 6 SIS Comparison Graphic o Static Roll Angle Figure 9 Pitching Angle Comparison Maps o Pure Inertia Undamped System Figure 7 SIS Comparison Graphic o Static Pitching Angle 3.2 Swing Test Place the IMU on the precision three-axis rotating table. Static test or more than 900 seconds, and control the rotating table around the Y-axis in the requency o 0.15Hz, the amplitude o the swing moement is ±30, Fig. 8 and Fig. 9 are the pitching angle comparison maps o 50s time pure inertia undamped system and the internal damping system respectiely. From the aboe two types o experimental results, we can see that the application o internal damping thought greatly improes the attitude accuracy o SIS. At the same time the system has also undergone a number o traic tests, the results o the traic tests also conirmed that the algorithm in the system greatly improed SIS accuracy in the case o little acceleration. The research results rely on the introduction o the idea o platorm inertial naigation system internal damping network in into strapdown inertial naigation. Thereore, another direction o inertial naigation system is to ully explore the ability o inertial naigation system itsel as ar as possible to improe its perormance and accuracy. 4. Conclusion The inertial naigation technology innoation and deelopment, on the one hand depends on the urther exploration and improement o inertial naigation system itsel. More importantly, it is dependent on the importation o other disciplines into the ield o inertial naigation research and application, which is the important trend o the uture deelopment. 76 International Journal o Mechatronics and Applied Mechanics, 2017, Issue 2

6 In the ollowing, some recommended research directions in inertial naigation systems are gien. Mathematical technology, biotechnology, image & graphics and other disciplines are gradually emerging in the ield o naigation. These technical results should be ully applied to sole the practical problems in the ield o naigation; Beacon / GPS dierential combination proide users with low prices and high accuracy naigation inormation [9], the urther research and deelopment on beacon naigation technology will promote the progress o inertial technology; Reasonable and reliable application o MMS technology or small-scale inertial naigation system to make greater contributions to the releant research [10, 11]; Gyro drit real-time compensation technology: computer leel, modeling model and other deiciencies cannot guarantee the drit compensation be "real-time" lead to the long-term stagnation o the technology research. At present, the use o adanced computer technology and the deelopment o theoretical results to carry out the study, the theoretical and application leel o innoation are o great signiicance. With the continuous eorts and innoation o our scientiic researchers, these important technologies are bound to deelop in the uture deelopment o inertial naigation system. Acknowledgement This work was supported by the 2016 ational atural Science Fund Project "atural ector aided inertial ocean long endurance autonomous naigation technology research" (Project number: ). Reerence [1] Liu L, Liu R Q. Research o integrated naigation system based on strapdown inertial naigation system [J]. Modern lectronics Technique, 2009, 290(3): [2] Barbour, Schmidt G. Inertial sensor technology trends[j].i Sensors journal,2001, 1(4): [3] Curey R K,Ash M,Thielman L O, et a1. Proposed I inertial systems terminology standard and other inertial sensor standards[a].i Position Location aigation Symposium 2004[C]. Montery, CA, [4] Zhang C J, Yuan J, Li, Wang L, Ren L. eelopment trend o inertial deice test technology in iew o the study o accelerometer test [J]. Aerospace Control, 2005, 23(2): [5] Azouaoui O, Cherii A, Bensalem R, et a1. Reinorcement learning based group naigation approach or multiple autonomous robotic system [C]. Mechatronics and Automation, 2005 I International Conerence, Vol. 3, 29 July-1 Aug. 2005: [6] Li Z Q, Qing L F, Rong M. Study on Chariot Gun Control System Simulation in 3-Scene [J]. Journal o System Simulation, 2006, 18 (Suppl.1): [7] Kim T J,Fellerho J R,Kohler S M. An integrated naigation system using GPS carrier phase or real-time airbore/synthetic aperture radar (SAR) [J]. Journal o the Institute o aigation, 2001, 48(1): [8] u Y L, Liu J Y, Liu R H, Sun Y R. Fuzzy amped Algorithm in Strapdown Attitude Heading Reerence System [J]. Journal o anjing Uniersity o Aeronautics& Astronautics, 2005, 37(3): [9] Lan X Q, Zhang B L, Huang J H, Huang X S. xperimental research o GPS pseudo-range dierential position [J]. Journal o Hohai Uniersity (atural Sciences), 2004, 32(3): [10] u Y L, Liu J Y, Li R B, Lai J Z. Strapdown Inertia Attitude Heading Reerence System Based on SP [J].Chinese Journal o Scientiic Instrument, 2005, 26(8 Suppl): [11] Chao H Y, Cao Y C, Chen Y Q.Autopilots or small unmanned aerial ehicles: A surey [J]. International Journal o Control, Automation and Systems, 2010, 8(1): International Journal o Mechatronics and Applied Mechanics, 2017, Issue 2 77