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INS-GPS-GLONASS navigation fusion scheme for high dynamics guided projectiles

Aug 2012 | No Comment
This paper presents a comprehensive study on the combining of GPS and GLONASS for receivers and the advantages of either system in case of restricted visibility of satellites and degraded performance of geometric Dilution of Precision

G Satheesh Reddy

Outstanding Scientist, Research Center Imarat,
Defence Research and Development Organisation (DRDO),
Hyderabad, India

Manjit Kumar

Scientist, Research Center Imarat,
Defence Research and Development Organisation (DRDO),
Hyderabad, India

The Satellite Navigation solution is the most preferable, effective and economic aid to various Low and Medium Grade Inertial Sensors in order to get better Navigation accuracy for medium and long duration of navigation solutions. The navigation data from INS and Sat. Receiver at different intervals is synchronized and fused together by using Kalman Filter algorithm so as to obtain precise Navigation solution as long as Sat. Receiver tracks healthy and suffi cient number of Satellites constellation. The major limiting factor with the mostly used/popular GPS system performance is the availability of Satellites and the geometry of Satellites in view at any particular point in space and time. In order to alleviate this restriction for single constellation (i.e. GPS), it stands to reason that more observations to be introduced to provide increased levels of positioning continuity and higher levels of data redundancy. The recent enhancement of GLONASS satellite system suggests combined use with GPS, in order to increase the satellites availability as well as Navigation Solution continuity and accuracy. Taking the advantage of combined GPSGLONASS systems, the new Hybrid Navigation scheme has been developed to fuse the data from INS, GPS and GLONASS systems by using the raw measurements ( Pseudo ranges and Delta Pseudo-ranges) of GG Receiver and which are Synchronized to INS clock (Real-Time algorithms are adopted). The INS system is implemented in the strap down confi guration and the Extended Kalman fi lter is used to fuse the Inertial and GPS-GLONASS Raw measurements data in tightly coupled architecture.

Integration of GPSGLONASS systems

The GPS and GLONASS satellites transmit ranging signal and the ephemeris data at two different frequencies in the L-band. To our interest, L1 transmitting frequencies for both the systems are shown below. We can also state the transmitted C/A code signal on L1 frequencies from GPS and GLONASS satellites by following equations:


The power transmitted by the GPS and GLONASS satellites are almost similar, where the minimum received power level at the earth’s surface is approximately -130 dBm for the C/A code signal. This implies that the signal is merged in thermal noise and is detected using de-spreading the signal.

A combined GPS-GLONASS receiver can dramatically improve the reliability, visibility and productivity of positioning. However, the basic design differences of these system results in signifi cant complexity in terms of modeling and ambiguity resolution for integrated GPS and GLONASS positioning system. Two major differences between GPS and GLONASS that affect the combined positioning are given below.

System time

GLONASS system Time is closely coupled to Moscow time UTC SU (ICDGLONASS –2000). GLONASS system time is permanently monitored and adjusted in a way that the difference to UTC-SU does not exceed 100ns. It is closely coupled to UTC, but with a constant offset of three hours along with some leap seconds. Since there exist two different master clocks there is difference, which need to be accounted. GLONASS user is informed about the difference to UTC with parameter τc, as a part of GLONASS ephemeris .In order to combine GLONASS and GPS the different system time scales must be taken into consideration such that we obtain a unique time for all observation. Transformation from GLONASS time to GPS time can be done with the help of following equation.



Since the data from the local timing centers are not compared and combined to UTC in real-time, the difference between UTC(USNO) and UTC(SU), therefore the difference between GPS and GLONASS system time neither is directly (a-priori) available in real-time. This is the crucial problem to be solved when combining GPS – GLONASS data in navigation or in other near Real-Time Operation.

Co-ordinate frames

In GLONASS only solutions, satellite positions in PZ-90 are obtained from the ephemeris data, thus the user position is in PZ-90. In GPS only positioning solutions, the satellite positions are given in WGS84 and thus the user position is in WGS84. Since GPS navigation has become the standard in Western countries and WGS84 therefore is more widely spread and better known than PZ-90, it is considered best to transform GLONASS satellite positions from PZ-90 to WGS84, thus obtaining the user position also in WGS84. There are several transform available, fi gure below shows one of the most commonly used transform.

The combination of GLONASS and GPS nearly doubles the number of available satellites. This will increase the effectiveness of some applications, e.g., Real-time Kinematics’ (RTK) and troposphere estimates. The usage of two autonomous systems should also improve the reliability. As we saw above that in order to combine GLONASS and GPS

• a unique time scale for all observations and satellite ephemerides and

• a unique reference system for all satellite and receiver positions are required.

Combined positioning

In GPS or GLONASS system, as you know there are four unknowns and more than four observables available. The measurement can be mathematically represented as,

We know that with increased number of measurements the user position accuracy improves. In order to have more number of measurements we can use satellites from both GPS and GLONASS constellation. It also improves the reliability and integrity of the solution. However, the GPS and GLONASS clocks are not exactly synchronized. So, when computing the combined position solution, we need to solve for this additional unknown. We require a minimum of total 5 satellites from GPS-GLONASS (GG) to get a position fi x. A similar least squares approach as defi ned above can be used for integrated GPS and GLONASS position computation. The Direction Cosines Matrix gets modifi ed as, α11 to αi1 rows are for GPS, and the remaining are that of GLONASS.

High dynamics signal tracking

Two tracking loops are needed to track Navigation Satellites signal. One tracking loop is for Carrier Doppler removal and another is Code tracking loop for phase error elimination. Doppler frequency from carrier tracking loop can be aided to the code tracking loop. The loop consists of prediction integrators, a discriminator and a loop fi lter. Prediction integrator reduces the noise by integrating the correlation value for a given time. As the integration time increases, the noise performance improves, but the dynamics performance becomes weak. Beyond certain high dynamics the single mode FLL is the preferred carrier tracking loop to track the Satellites signal than FLL assisted PLL Loop. Single mode leads to a marginal tradeoff between accuracy and tracking of the signal beyond certain high dynamics. In our receiver design third order FLL loop has been adopted in order to successfully track the GPS-GLONASS Satellites signal for High Dynamics Projectiles applications.

Tightly coupled INS-GPSGLONASS fusion scheme

A system diagram representing the integrated INS-GG navigation scheme is shown in fi gure 1. The diagram contains the major elements like INS sensors, GG Receiver and 19-states Extended Kalman Filter in tightly coupled confi guration. The complexity of the tightly coupled fi lter is that the raw measurements are added to the INS-GG filter. At least four more states are be added to the Filter to estimate GG receiver clock bias and clock drift rate w.r.t GPS and GLONASS frames of measurement. The INS process and models (as shown in Table.1) measurements from inertial sensors and reconstruct the equation of motions in the ECEF frame for the Vehicle.

The tightly coupled filter requires line of sight information to the satellites as well as potential information on GG signal strength or elevation angle to improve the measurement noise estimates while incorporating the GPS and GLONASS updates. Apart from characterizing the measurement errors to design the measurements matrix R (for Pr & DPr) the KF does Estimates Clock Bias and Clock Drift errors of Receiver clock in order to correct the Clock Bias and Clock Drift Models (as shown in Table 2) so as to compute true Range and Delta-Range. Before processing the pseudo-range measurement update, an estimate of range to the satellite from the INS i.e. is computed with INS position estimate and the Line-of-Sight vectors to the satellites as shown below:

where, Rsv is the satellite position, and e is the satellite Line-of-Sight unit vector. The Kalman fi lter measurement is now defi ned in terms of the pseudo-range estimate and the GG measured pseudo-range.
The delta-range measurements are formulated by fi rst differencing the pseudo-range estimated at the epoch from the current.

The delta-range measurement update is then defi ned by:

with Δt the time from the last epoch to the current.

In the observation matrixes the fi rst two elements represent the GPS clock bias and clock drift observations. The next two elements are the GLONASS clock bias and clock drift observations. The Measurement noise values for Pr & Dpr are 2 m and 0.02 m/s respectively. Voting for multiple GG navigation solutions and receiver data validation for KF

The fusion Filter is driven by number of Navigation solutions available with GG receiver. Therefore it becomes obvious to take best decision in Real time to get optimized Hybrid Navigation solution so as to guide the Vehicle in the desired basket of accuracy.

As shown in the fig2, for the available multiple GG navigation solutions, the voting is done to select the best available solution among all and w.r.t that the Data validation is carried out for valid channels before its transferred to the KF (as shown in fi g 3). The KF processes the valid data form Inertial Sensors as well as from GG Receiver and generates second level of errors compensation for all designed states as shown in fig 1.

We can conclude that the redundancy of GG Navigation solution ensures high level of reliability to the GG aided inertially guided vehicles in the entire range of flight.

INS-GPS-GLONASS Scheme Performance

The performance of the GPS-GLONASS aided Inertial Navigation systems are evaluated for Real Time in the Lab as well as for the simulated Flight trajectories of various High Dynamics Projectiles. This study has been carried out using different class of Inertial Sensors ranging from Medium Grade to High Grade accuracy. The Navigation fi lter was tuned for different application by adjusting noise spectral densities in order to achieve acceptable fi lter performance for Low and High Dynamics applications. Figure 4 & 6 shows the Medium Grade Dynamically Tuned Gyros based INS-GG System performance ( for static and Low Dynamics). As analyzed, where the INS is aided by single ( GPS/GLO ) constellation, the position error of Hybrid Navigation is driven down to less than 15m (1-σ) after about 50 sec, whereas the position error of combined aided GPS-GLONASS constellations is better than 7m (1-σ) after 50 sec as shown in fi gure 5. It has been observed that for weak GPS constellation the concurrent healthy GLONASS measurements provides better accuracy, high redundancy and more reliable combined GG solution. This also results in improved GDOP and Hybrid Navigation Performance. Further the Real Time Simulation studies are carried to analyze the performance of this scheme for High Velocity Projectile applications. The scheme has been simulated for medium range guided Projectile and post simulation results were analyzed as shown in fi g 7 & fi g 8. The Projectile travelled with forward velocity 800m/s and beyond covers the short (< 100 Km) to medium down range (< 250 Km) in the fl ight time of 371 sec. As it’s analyzed, the Vehicle in the entire Thrust Phase and beyond is guided through either by GPS or GG aided Navigation by correcting all the propagated Navigation errors in all phases, which resulted in achieving the desired accuracy for Hybrid Navigation (< 25 m, 1-σ) of the Vehicle as shown in fig 8.

Summary

In degraded signal environments the accuracy and availability of the GPS are affected for Kinematic applications. To address this issue, combined GPSGLONASS systems are studied for various Low and High Dynamics applications using tightly coupled GG aided INS solutions to overcome the problem of using single constellation when we desire to achieve reliable high terminal accuracy for Inertial Guided Vehicles. In tightly coupled integration scheme the raw receiver measurements are directly used to update the Kalman Filter. Some of the benefi ts are : more direct exploitation of fundamental measurement data, more direct aiding of the receiver tracking loop by the fi lter and INS, better resiliency to poor satellite geometry, high vehicle dynamics and data dropouts etc. Work to further improve the tightly coupled TTFF (Time to First Fix) GG aided Low Grade INS performance for short range is currently underway. In addition, studies which will asses Hybrid Navigation performance under Ultra Tightly Coupled TTFF GG-INS scheme are also planned.

References

George M.Siouris, An Engg. Approach to Optimal Control and Estimation Theory,Air force Institue of Tecnology, Wright-Patterson AFB,Ohio.

G.Satheesh Reddy, Manjit Kumar “Integrated INS & GPS Navigation approach using Kalman Filter ” GNSS- 2007,NERTU, Osmania University, Hyderabad, October 25-26, 2007.

Brown, Robert Grover, Hwang,Patrick Y.C, Introduction to Random Signals and Applied Kalman Filtering.

Kaplan,Elliott D,Ed., Understanding GPS Principles and Applications, Artech House, Norwood,MA,1996.

Seok Bo Son, II Kyu Kim, Sang Heon Oh, Se Hwan Kim , Young Baek Kim, Commercial GPS Receiver Design for High Dynamics Launching Vehicles , The 2004 International Symposium on GNSS/GPS ,6-8 Dec, Sydney Australia.

P.W.Ward (1998) Performance Comparisons between FLL , PLL, and a Novel FLL – assisted – PLL Carrier Tracking Loop under RF interference Conditions, Proceeding of ION GPS 1998, Nashville, Tennessee.

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