Tightly coupled GPS/INS integration for missile applications. Tightly-coupled GPS/INS Integration für unbemannte Fluggeräte

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1 Aerospace Science and Technology 8 (2004) Tightly coupled GPS/INS integration for missile applications Tightly-coupled GPS/INS Integration für unbemannte Fluggeräte Jan Wendel, Gert F. Trommer Institute of Systems Optimization, University of Karlsruhe, Kaiserstr. 12, Karlsruhe, Germany Received 8 March 2004; received in revised form 7 July 2004; accepted 22 July 2004 Available online 25 August 2004 Abstract An approach to enhance the performance of tightly coupled GPS/INS systems is described. First, the advantages of tightly coupled systems compared to loosely coupled systems are clarified. Then, it is shown in hardware-in-the-loop tests and in a test drive that processing time differenced carrier phase measurements instead of delta-range measurements results in an increased velocity and attitude accuracy for the tightly coupled system, which is of great importance in the beginning of a time interval with purely inertial navigation, e.g. when GPS is lost due to jamming. A measurement equation is derived allowing to process the time differenced carrier phase measurements in the navigation Kalman filter. Finally, the proposed method is applied to missile navigation systems, where significant vibrations enter the inertial sensor data Elsevier SAS. All rights reserved. Zusammenfassung In diesem Beitrag wird ein Verfahren vorgestellt, mit dem die Performance von tightly coupled GPS/INS Systemen gesteigert werden kann. Zunächst werden die Vorteile der tightly coupled GPS/INS Systeme im Vergleich zu loosely coupled Systemen herausgearbeitet. Anschließend wird mit Hardware-in-the-Loop Tests und einer Testfahrt gezeigt, dass die Verarbeitung von Differenzen auf einander folgender Trägerphasenmessungen anstelle der üblicherweise verwendeten delta-range Messungen zu einer Steigerung der Geschwindigkeitsund Lagegenauigkeit bei tightly coupled Systemen führt, was besonders zu Beginn einer Inertialnavigationsphase, z.b. wenn GPS aufgrund von Jamming nicht genutzt werden kann, von Bedeutung ist. Es wird eine Messgleichung vorgestellt, die es erlaubt die zeitlichen Trägerphasendifferenzen direkt im Navigationsfilter zu verarbeiten. Abschließend wird die Einsetzbarkeit des vorgeschlagenen Verfahrens in Flugkörpernavigationssystemen untersucht, die teilweise heftigen Vibrationen ausgesetzt sind, welche in die Inertialsensordaten eingehen Elsevier SAS. All rights reserved. Keywords: GPS/INS integration; Kalman filter; Carrier phase measurements Schlüsselwörter: GPS/INS Integration; Kalman Filter; Trägerphasenmessungen 1. Introduction In integrated navigation systems, different navigation sensors are combined. Exploiting the complementary char- * Corresponding author. Phone ; Fax address: jan.wendel@ite.uni-karlsruhe.de (J. Wendel). acteristics of these sensors, the resulting system offers a significantly increased performance with respect to accuracy and robustness, compared to the stand-alone usage of each component. Especially, the benefit from integrating a GPS receiver and an inertial navigation system (INS) is well known: As the INS is not dependent on external information, this component assures the continuous availability of a complete navigation solution consisting of position, velocity and attitude estimates. The growth of navigation errors with time /$ see front matter 2004 Elsevier SAS. All rights reserved. doi: /j.ast

2 628 J. Wendel, G.F. Trommer / Aerospace Science and Technology 8 (2004) is prevented by using aiding information provided by the GPS receiver. Mostly, the data fusion algorithm processes GPS position and velocity information, which requires that signals from at least four satellites are available. Unmanned aerial vehicles as well as missiles have to operate in an environment where the choice of the flight path or hostile jamming leads to a reduced availability of GPS satellite signals. In this case, tightly coupled GPS/INS systems can provide a solution, where raw GPS data such as pseudorange and delta-range measurements are processed in the data fusion algorithm. Therefore, if the number of available satellite signals is not sufficient to calculate a GPS position and velocity measurement, a limited aiding of the INS using the pseudorange and delta-range measurements to the remaining satellites is still possible. In this situation, a loosely coupled system processing GPS position and velocity information remains unaided and as a result, the navigation errors grow according to the inertial navigation performance of the system. This contribution focuses on the improvement of a tightly coupled GPS/INS system by using GPS carrier phase measurements instead of delta-range measurements. This improvement can be expected because carrier phase measurements are usually less noisy than delta-range measurements. The problem by using carrier phase measurements are the unknown integer ambiguities, which prohibit a direct processing analog to a pseudorange processing. A fixing of the integer ambiguities is only possible if corrections from a DGPS base station are available, which is not the case for most unmanned aerial vehicles. This problem is overcome by forming time differences of carrier phase measurements, so that the constant integer ambiguities are eliminated. Additionally, a method for processing the time differenced carrier phase measurements in a Kalman filter is described. Test drive results illustrate the usefulness of this approach. In order to verify the approach in a missile-typical scenario where the INS is exposed to severe vibrations, hardware-in-theloop tests were performed. In all cases, an improvement of performance was observed, as expected. 2. GPS/INS integration architectures Kalman filters are widely used in integrated navigation systems to merge the data of the navigation sensors. The Kalman filter estimates the errors of the INS navigation solution. The subsequent correction of these errors assures the long-term accuracy of the system. Additionally, the inertial measurement unit (IMU) is calibrated. In the following, two integration architectures are discussed which differ mainly in the type of GPS information that is processed in the navigation Kalman filter Loosely coupled vs. tightly coupled Today, most of the integrated navigation systems are loosely coupled systems: The position and velocity of the vehicle estimated by the GPS receiver Kalman filter is processed in the navigation Kalman filter to aid the INS, which is known as decentralized or cascaded filtering, too. This design option is often chosen because of its simplicity, as the GPS receiver outputs are directly comparable with the INS outputs. Unfortunately, the errors in the position and velocity information provided by the GPS receiver Kalman filter are time-correlated, which can cause a degradation in performance or even instability of the navigation Kalman filter, if these correlations are not considered by some means. In the case of incomplete constellations, i.e. less than four satellites in view, the output of the GPS receiver has to be ignored completely, leaving the INS unaided [6]. A tightly coupled GPS/INS system is characterized by the fact that GPS pseudorange and delta-range measurements are processed directly in the navigation Kalman filter [7]. For some authors, the aiding of the receiver tracking loops using velocity information provided by the INS is an essential characteristic of a tightly coupled system, too [9]. However, as this receiver aiding is possible in a loosely coupled system, too, this topic is not addressed here any further. The main advantage of a tightly coupled system is that in the case of less than four visible satellites, a limited aiding of the INS with the raw GPS measurements to the remaining satellites is still possible. This is of special benefit in a missile navigation system, which often has to operate in a hostile environment where the reception of the satellite signals is difficult due to jamming. Besides that, tightly coupled systems offer increased integrity monitoring possibilities. On the other hand, the need to handle raw GPS data, e.g. the calculation of satellite clock corrections or satellite positions and velocity from ephemeris data, complicates the design process of a tightly coupled system. Furthermore, at least two additional Kalman filter states are required in order to estimate the GPS receiver clock error cδt and clock error drift cδf. Another solution is to process the differences of the raw measurements to different space vehicles. This causes the building up crosscorrelations, which have to be considered in the data fusion algorithm, see [3] Hardware-in-the-loop test Hardware-in-the-loop (HIL) tests were performed in order to compare the performance of two GPS/INS systems based on loosely and tightly coupled architectures, respectively. A GPS space segment simulator was used to generate RF signals according to a predefined trajectory, which were transferred to a GPS receiver via an antenna cable. This GPS receiver was interfaced with a PC used as navigation computer, hosting the navigation Kalman filters. The data of a tactical grade IMU was simulated according to the prede-

3 J. Wendel, G.F. Trommer / Aerospace Science and Technology 8 (2004) Carrier phase measurements Fig. 1. Comparison of the overall position errors of a loosely and a tightly coupled GPS/INS system, obtained in a HIL test. fined trajectory, too. Additionally, the vibration environment a missile is exposed to was taken into account by adding time correlated noise to the inertial sensor data, using noise process models that were obtained from the analysis of missile flight test data [10]. This vibration induced noise was modeled in the navigation Kalman filters by a technique given in [11], which avoids the usually required additional shaping filter states and therefore keeping the computational load reasonable. Fig. 1 shows the position errors of the navigation solutions of a loosely and a tightly coupled system obtained in this HIL test. With four or more satellites available, both systems show a comparable performance as the positions errors are essentially defined by the GPS position accuracy. During periods with less than four satellites available, the growth of the position errors is significantly slower for the tightly coupled system. The rapid growth of the loosely coupled system position errors has two reasons: First, the vibration induced noise affects the inertial navigation performance of the INS. Second, the time until the first incomplete constellation at t = 500 s was not sufficient to achieve an accurate calibration of the IMU, so that the inertial sensor biases contributed significantly to the growth of the position error. This also explains why during the second and the third period with purely inertial navigation of the loosely coupled system, starting at t = 800 s and t = 1100 s, respectively, the growth of position error is slower. 3. Performance improvement by carrier phase processing In the following a method is proposed, which allows to further increase the performance of tightly coupled systems by using carrier phase measurements instead of delta-range measurements to aid the INS. The measurement model of a GPS carrier phase measurement can be expressed as (φ + N)λ= r SU + cδt + δ cm + δ mp + v rcvr, (1) where φ denotes the measured carrier phase in cycles, N is the integer phase ambiguity, λ is the carrier wavelength, r SU is the distance between GPS antenna and satellite, cδt is the GPS receiver clock error in meters, δ cm are the common mode errors, e.g. ionosphere and ephemeris, δ mp is the carrier-signal multipath and v rcvr is white receiver noise. Except for the sign of the ionospheric error, the common mode errors on a carrier phase measurement and on a pseudorange measurement are essentially the same, whereas multipath and receiver noise are much smaller for the carrier phase measurement. Usually, the common mode errors are removed by using corrections from a DGPS base station. Then, if a fixing of the integer phase ambiguities was successful, the carrier phase measurements can be processed in the navigation Kalman filter in the same way as a pseudorange measurement, see [4,7]. However, for missile applications the usage of a DGPS base station in sufficient proximity is not possible. Instead, in the following it is exploited that the common mode errors are slowly time-varying. Therefore it is possible to remove these common mode errors almost completely by forming time differences of carrier phase measurements from two successive epochs Time-differenced carrier phase Triple differenced carrier phase measurements (TDCP) are already used in a variety of applications, mostly for the detection of cycle slips. TDCP measurements are obtained by first forming differences between the measurements of a base station and a rover, second between different satellites and finally between two successive epochs. With the approach described here, only differences between two successive carrier phase measurements valid at t k and,respectively, are formed. A DGPS base station is not used. Such a time differenced carrier phase measurement can be formulated as follows: (φ k φ k 1 )λ = r SU,k r SU,k 1 + cδt k cδ + v k. (2) The remaining measurement error that is not removed by forming time differences is denoted with v k. The constant integer phase ambiguity is removed completely, and therefore an estimation of this quantity like in other approaches is not necessary. In order to be able to derive a measurement equation that is suitable to process the measurement (φ k φ k 1 )λ in the navigation Kalman filter, its relations to the quantities of which the errors are estimated by the filter have to be identified. These quantities are the three dimensional position, velocity and attitude, the six inertial sensor biases as well as receiver clock error and clock error drift. From Fig. 2, following relation is obtained:

4 630 J. Wendel, G.F. Trommer / Aerospace Science and Technology 8 (2004) Inserting the differential equation describing the propagation of the attitude errors with time, ψ ω in n ψ + Ĉb nδ ωb ib, see [8], and exploiting that L n k 1 ωn in,k δ L n k gives (C n b,k Cn b,k 1 ) L b δ L n k + δ L n k ψ k + t [ L n k 1 ] Ĉ n b,k δ ωb ib,k. (7) So, the desired measurement equation for a time-differenced carrier phase measurement is given by Fig. 2. Position of a GPS satellite and the GPS antenna at two successive epochs with carrier phase measurements available. r SU,k r SU,k 1 = e T k r SU,k e T k 1 r SU,k 1 e T k ( r SU,k r SU,k 1 ) = e T k ( S k b k ). (3) Hereby e k denotes the unit vector pointing from the GPS antenna to the satellite, S k is the displacement of the satellite in the time interval t = t k and b k is the displacement of the GPS-antenna in the same time interval. Combining Eqs. (2) and (3) leads to (Φ k Φ k 1 )λ e T k S k = e T k b k + cδt k cδ + v k = = e T k vn eu dt + cδf dt + v k e T k vn eb dt et k (Cn b,k Cn b,k 1 ) L b + cδf dt + v k (4) where v eu n is the velocity of the GPS antenna with respect to the Earth in navigation frame coordinates, v eb n is the velocity of the vehicle body frame, L b is the lever arm between IMU and GPS antenna in body frame coordinates, and Cb n is the direction cosine matrix (DCM) describing the transformation from body to navigation coordinates. With the skew symmetric matrix Ψ k of the misorientation vector ψ k and the relation between true and estimated ( ) DCM C n b,k = (I Ψ κ)ĉ n b,k (5) the lever arm term can be reformulated: (C n b,k Cn b,k 1 ) L b = (I Ψ k ) ( L n k L n k 1) (Ψk Ψ k 1 ) L n k 1 = (I Ψ k )δ L n k t Ψ k L n k 1. (6) (φ k φ k 1 )λ e k T ( S k δ L n ) k = ( e k T vn eb + cδf )dt e T k ( δ L n k ψ k + t [ L n k 1 ] Ĉ n b,k δ ωb ib,k) + v k. (8) On the right hand side of this measurement equation, the integral term including GPS antenna velocity and receiver clock error drift is usually dominant. However, ignoring the lever arm terms when deriving a Kalman filter measurement matrix can lead to poor estimation results e.g. in case of vehicle rotations. Additionally, considering the lever arm speeds up the estimation of the gyroscope biases δ ω b ib,k. The problem in the processing of this type of measurement is, that in Eq. (8) a time integral occurs containing quantities of which the errors are estimated by the filter. The usual form of a Kalman filter measurement equation is given by y k = H k x k + v k (9) where the measurement matrix H describes the linear mapping between the system state x k at time t k and the current measurement vector y k Kalman filter design In principle it is possible to process the carrier phase differences equation (8) by using a delayed state Kalman filter [1]. However, this would be connected with several disadvantages: For the problem considered here, the covariance matrix of the measurement noise of all carrier phase differences available at the current epoch has diagonal form. Using a delayed state Kalman filter, this diagonal form is lost. Therefore, a sequential, scalar processing of these measurements which is desirable because of numerical reasons is not possible without an additional decorrelation procedure. This results in a further increase in computational load, besides the already increased computational load due to the usage of a delayed state Kalman filter itself. Therefore a different approach was chosen, which originates from the processing of TDCP measurements in [2,5].

5 J. Wendel, G.F. Trommer / Aerospace Science and Technology 8 (2004) A general formulation of a measurement equation involving a time integral is given by y k = H x(t)dt + v k. (10) Considering the problem of processing time differenced carrier phase measurements, the measurement matrix H in Eq. (10) selects from the system state vector the velocity states weighted with the unit vector to the satellite, and the clock drift state. This can be seen by comparison with Eq. (8). With the transition matrices Φ t,tk 1 and Φt 1 k,,thestate vector x(t) can be expressed as x(t) = Φ t,tk 1 Φt 1 k, x k. (11) Inserting Eq. (11) in Eq. (10) and moving the time constant terms outside of the integral allows to rewrite Eq. (10) in the form of the typical Kalman filter measurement equation (9): y k = H Φ t,tk 1 dt Φt 1 k, x k + v k. (12) }{{} H k Most GPS receivers provide measurements at a data rate of 1 Hz, while the navigation system state vector is updated at a higher rate 1/δt, e.g. the rate with which inertial sensor measurements are available. In each subinterval i in between two successive GPS receiver measurements, a transition matrix Φ iδt+tk 1,(i 1)δt+ is calculated which is used to propagate the navigation Kalman filter state vector covariance matrix forward in time. These transition matrices can be used to construct the measurement matrix H k. The matrix Φ 1 t k, is calculated starting from an identity matrix at i = 0 from Φ 1 iδt+, = Φ 1 (i 1)δt+, Φ 1 iδt+,(i 1)δt+. (13) Starting from a zero-matrix, the integral term in Eq. (12) is constructed: iδt+t k 1 HΦ t,tk 1 dt = (i 1)δt+ HΦ t,tk 1 dt + H iδt+tk 1 Φ iδt+tk 1,(i 1)δt+ δt. (14) The resulting measurement matrix H k allows to process the time differenced carrier phase measurements equation (8) directly in the navigation Kalman filter. With this approach, which is perfectly general and can be applied to any measurement equation involving a time integral of state vector components, the diagonal form of the measurement noise covariance matrix is maintained, a scalar sequential measurement processing is therefore possible without a previous decorrelation required. Theperformanceof thisapproachcomparedto the aiding with delta-range measurements was investigated in a HIL test. Fig. 3 shows the velocity accuracy achieved by both filters. Obviously, the velocity accuracy is increased by using time differenced carrier phase measurements instead of delta-range measurements. It can also be seen that a delayed state Kalman filter in combination with a decorrelation procedure and the time differenced carrier phase processing achieves comparable results. The increase in velocity accuracy has a positive effect on attitude accuracy, too, as shown in Fig. 4. During the first part of the simulated trajectory, no movement was assumed. Without horizontal accelerations, the yaw angle is not observable, drifting around its initialized value. This explains the rapid decrease in attitude error in the acceleration phase starting at t = 200 s. Fig. 3. Overall velocity errors of tightly coupled systems processing delta-range or time differenced carrier phase measurements, obtained in a HIL test.

6 632 J. Wendel, G.F. Trommer / Aerospace Science and Technology 8 (2004) The experimental integrated navigation system used in the test drives is shown in Fig. 5. It consists of a GPS receiver, several IMUs, additional hardware which allows to time-tag the IMU data with GPS time, and a power supply. A Linux PC was used as navigation computer. This system allows to log the navigation sensor data for an offline processing, but it is also possible to run navigation algorithms in realtime. However, in order to assure identical conditions for the comparison of delta-range and carrier-phase processing, an offline processing of logged data was chosen Test drive results Fig. 4. Overall attitude errors of tightly coupled systems processing delta-range or time differenced carrier phase measurements, obtained in a HIL test. 4. Experimental verification The practical value of the proposed aiding with time differenced carrier phase measurements was proven in a test drive with an experimental integrated GPS/INS system. This system and the achieved results are described in the following Navigation system hardware An experimental verification is necessary to prove that simulation and HIL test provide realistic results, because simulated data can only approximate the environment in which the navigation system operates. Especially, realistic GPS multipath errors are hard to simulate. The problem with the analysis of the estimated navigation solutions is in opposite to HIL test and simulation the lack of an ideal reference, which would be needed to calculate the navigation errors directly. Therefore, indirect measures of performance have to be used. A test drive trajectory was chosen were the vehicle returned in the end to its initial position. After a short period of time for northseeking and initialization, delta-ranges or time differenced carrier phase measurements, respectively, were used to aid the INS, while the pseudorange data was ignored. The growth of position error, that can be assessed from the comparison of initial and final position, is then a measure for the velocity accuracy of the navigation solution. The position solutions obtained in this test are shown in Fig. 6. It can be seen that starting point and final point are in better agreement for the aiding with time differenced carrier phase measurements, therefore at least the velocity accuracy of this approach is superior to the delta-range processing. Fig. 5. Experimental integrated navigation system used in the test drive.

7 J. Wendel, G.F. Trommer / Aerospace Science and Technology 8 (2004) this point in time, the drive actually started. This is of course connected to vibrations, while during the first 200 seconds the car was at rest. Finally, the velocity errors can be calculated during periods were the vehicle is at rest. This was the case in the beginning of the test drive, the corresponding velocity errors are shown in Fig. 8. Again, the aiding with time differenced carrier phase measurements produces superior results, as expected. Fig. 6. Test drive position solution by processing delta-range or time differenced carrier phase measurements, without processing pseudorange measurements. 5. Application to missile navigation systems The possibility to improve the performance of missile navigation systems by using the proposed method was investigated in HIL-Tests Influence of vibrations and dynamics Fig. 7. Test drive filter residuals by processing delta-range or time differenced carrier phase measurements. Fig. 8. Test drive overall velocity errors of the delta-range and the time differenced carrier phase processing while the vehicle was at rest. A further measure of performance are the filter residuals shown in Fig. 7, i.e. the difference between the available measurements and predicted measurements, with the prediction based on the a posteriori navigation solution. In the case of delta-range measurements and time differenced carrier phase measurements, the residuals are directly comparable. Obviously, the aiding by means of the carrier phase produces the smaller residuals. The increase in filter residual magnitude after 200 seconds can be explained by the fact that at The processing of time differenced carrier phase measurements instead of delta-range measurements allows to increase the velocity accuracy of the navigation solution. The improvement in position accuracy is negligible, as the position accuracy is determined mainly by the pseudorange measurements. However, the increase in velocity accuracy leads to in increase in attitude accuracy, too. Velocity and attitude accuracy in the beginning of a period with purely inertial navigation, e.g. when GPS is lost because of jamming, has a significant influence on the growth of navigation errors with time, and is therefore of major importance. The influence of a velocity error on the position error growth is obvious; an attitude error results in an inaccurate elimination of the gravity sensed by the accelerometers in the strapdown calculations. This leads to an apparent acceleration of the vehicle, which causes an additional growth in position error. Of course, the advantage of the time differenced carrier phase processing concerning the inertial navigation performance is lost, if the growth in position error is caused mainly by the vibrations entering the inertial sensor data, so that the increased velocity and attitude accuracy has no influence. Additionally, an increase in velocity accuracy is only possible if the vibration environment is not too severe, otherwise carrier phase and delta-range aiding provide a comparable velocity accuracy. Finally, the trajectory dynamics has an influence on the possible increase in attitude accuracy, too: In the presence of aggressive maneuvers the attitude errors can be estimated easily, so that the aiding with delta-ranges is sufficient to obtain very accurate attitude estimates HIL test results In order to assess the performance of the proposed carrier phase aiding for missile applications, HIL tests with a benign missile trajectory were performed. For the missile INS, a tactical grade IMU with 5 /h-1sigma gyroscope biases was simulated. In the beginning, a one-shot alignment

8 634 J. Wendel, G.F. Trommer / Aerospace Science and Technology 8 (2004) Fig. 9. Overall velocity errors of tightly coupled systems processing delta-range or time differenced carrier phase measurements obtained in a HIL test, missile-typical scenario. satellites allow to prevent or slow down the increase in position error a stand-alone INS shows. Additionally, the velocity and attitude accuracy of a tightly coupled system was increased by processing time differenced carrier phase measurements instead of delta-range measurements, which has been shown in HIL tests and in a test drive. This is of great importance in the beginning of a time interval with purely inertial navigation. The time integral contained in the measurement equation relating the time differenced carrier phase measurements to the navigation filter state vector could be rewritten in the form of a usual Kalman filter measurement equation, and therefore allowing to process this type of measurement in the navigation Kalman filter directly. Additionally, due to the time differencing, a DGPS base station is not required. Therefore, any tightly coupled system that uses a GPS receiver providing carrier phase measurements can be upgraded with the proposed method by a pure software change. Finally, advantages of the proposed method were found for a missile-typical scenario, where significant vibrations corrupt the inertial sensor data. As the increase in performance is depending on the strength of these vibrations, the gain in performance is dependent on the application. References Fig. 10. Overall velocity errors of tightly coupled systems processing delta-range or time differenced carrier phase measurements obtained in a HIL test, missile-typical scenario. of the missile navigation system was assumed. The vibration induced inertial sensor noise was generated according to noise process models that were identified from the analysis of missile flight test data during free flight. Details concerning the vibration induced noise can be found in [10]. Fig 9 shows that in this scenario, the processing of time differenced carrier phase measurements offers an increase in velocity accuracy compared to a delta-range aiding. Compared to the HIL test result shown in Fig. 3 were only sensor inherent noise according to a tactical grade IMU was assumed, the gain in performance is smaller. Nevertheless, the increased velocity accuracy leads to an increased attitude accuracy, shown in Fig. 10. Again, compared to Fig. 4 the gain in performance is reduced because of the vibrations. 6. Conclusion In this contribution, the advantage of tightly coupled systems processing GPS pseudorange and delta-range measurements compared to loosely coupled systems processing GPS position and velocity information was illustrated: In situations with limited GPS availability, e.g. in missile applications due to jamming, the measurements to the remaining [1] R.G. Brown, P.Y.C. Hwang, Introduction to Random Signals and Applied Kalman Filtering, Wiley, New York, [2] J.L. Farrell, Carrier phase processing without integers, in: Proceedings of the Institute of Navigation 57th Annual Meeting, June 2001, Albuquerque, NM, USA, 2001, pp [3] J.L. Farrel, GPS/INS streamlined, Navigation: J. Institute of Navigation 49 (4) (2002) [4] J.A. Farrell, T.D. Givargis, M.J. Barth, Real-time differential carrier phase GPS-aided INS, IEEE Trans. Control Syst. Technol. 8 (4) (2000) [5] F. van Graas, J.L. Farrell, GPS/INS a very different way, in: Proceedings of the Institute of Navigation 57th Annual Meeting, June 2001, Albuquerque, NM, USA, 2001, pp [6] Z.H. Lewantowicz, Architectures and GPS/INS integration: impact on mission accomplishment, IEEE Aerospace and Electronics Systems Magazine 7 (6) (1992) [7] B.M. Scherzinger, Precise robust positioning with Inertial/GPS RTK, in: Proceedings of the ION GPS, September 2000, Salt Lake City, UT, USA, 2000, pp [8] D.H. Titterton, J.L. Weston, Strapdown Inertial Navigation Technology, Peter Peregrinus Ltd., on Behalf of the Institution of Electrical Engineers, London, England, [9] B. Vik, Nonlinear design and analysis of Integrated GPS and inertial Navigation systems, PhD thesis, Norwegian University of Science and Technology, Trondheim, Norway, [10] J. Wendel, G.F. Trommer, IMU performance requirement assessments for GPS/INS missile navigation systems, in: The Institute of Navigation 58th Annual Meeting, June 24 26, Albuquerque, NM, USA, [11] J. Wendel, G.F. Trommer, An efficient method for considering time correlated noise in GPS/INS integration, in: The Institute of Navigation National Technical Meeting, January 24 26, San Diego, CA, USA, 2004.