satellite navigation system
inertial navigation system
A.Yu. Shatilov, I.A. Nagin
It’s not a secret that complementary properties of GNSS receiver and INS allow to get more reliable and precise navigation solutions. Tightly-coupled GNSS/INS integration scheme implies that INS data is fed to receiver’s tracking loops to compensate line-of-sight dynamics and tighten their bandwidths. It increases the receiver’s sensitivity and antijam capability under high dynamic movement. From the other hand, GNSS navigation data allows to estimate and compensate INS errors at the IMU sensors level. It results in more precise INS standalone navigation solution during GNSS outages. Moreover, the compensation of IMU errors also results in more precise inertial aiding data for receiver’s tracking loops that even more increases their sensitivity and antijam capability.
The development of proposed tightly-coupled algorithm is aimed towards: (1) achievement of maximum receiver’s antijam capability by using tracking loops aiding with precise data from compensated IMU, and (2) reducing the INS error growth in standalone navigation mode (when GNSS data is not available) by estimation and compensation of IMU errors in periods of GNSS availability. The algorithm is intended to work with multi-purpose GNSS/INS integrated system and it should not depend on user’s specific properties.
The proposed tightly-coupled algorithm was tested on simulation model. The following preliminary simulation results are obtained for tactical-grade IMU with 0.1 deg/hr gyro drift, 0.0001g accelerometer bias, 5 arcmin axes misalignment. The best antijam results obtained for new GLONASS L3OC / GPS L5 signals that comprise pilot component. User dynamic had been chosen highest possible for today: 50g acceleration and 50 g/s jerk. Algorithm simulation resulted in velocity error of ±0.02 m/s, whereas GNSS receiver provides only ±0.8 m/s precision under such a high dynamic. During GNSS outage the positioning error at INS output growed to ~25 m over first 10 minutes that is 32 times better than that for INS with same uncompensated IMU. The velocity error growed only to ±0.15 m/s over first 10 minutes that is ~33 times better than that for uncompensated IMU. Attitude errors were at the level of ±0.5 angular minutes that is approximately 8 times lower that these of standalone INS with uncompensated IMU. We have to note that positioning error in integrated mode could not be reduced significantly in compare to standalone GNSS receiver. This is because of long-term pseudorange error components, such as multipath, ionospheric, ephemeris and SV clock errors. Antijam capability (J/S) of developed system is 67…70 dB - this is 17 dB higher than J/S of standalone receiver without aiding. The convergence time of integration algorithm is about 250-300 seconds to best precision. Presented results show that proposed algorithm efficiently achieves the declared objectives.
It would be fair to mention the bottlenecks of simulation model. The model does not account for (1) processing delay and (2) lever-arm between GNSS antenna and IMU sensitivity center. Nevertheless, known compensation techniques allow to minimize these effects in real system.
The navigational part of algorithm is built around EKF which state vector includes user velocity, user attitude in quaternion form and IMU sensor errors (27 states overall). Key feature of this EKF is that the user velocity dynamic model is expressed via IMU outputs: acceleration and rotation rate vector measurements in body frame. It lead to seamless filter design that implements INS mechanization algorithm within EKF extrapolation step. Filter update step is issued only in the moment of GNSS data availability. Such an approach results in more robust working during GNSS outages, good estimation of EKF covariance and convenient software/hardware implementation of the algorithm.
In EKF design the generic IMU error model is used. The biases, scale factors and axes misalignments both for accelerometers and gyros are included in state vector. It allows using most types of IMU: from navigation-grade to low-grade ones. Switching from IMU to IMU is just a question of constant parameters tuning. To avoid used attitude uncertainty problem caused by mutual accelerometer/gyro axes misalignment, the ‘pivot axis’ technique is suggested. It requires that one of the accelerometer and one of the gyro axes must be aligned to each other precisely. Hence the axes misalignment matrices are reduced from 9-element to 7-element ones - it shortens state vector and therefore computational cost.
No user specific information was used in filter’s design. I.e. there’s no built-in movement equations, connecting specific forces and rotation rates with navigation parameters of certain object (car or plane, for example). It makes the proposed system really independant from carrier’s properties.
The loops aiding part of algorithm takes user acceleration vector in ECEF frame from INS mechanization routine. Based on these data, the line-of-sight (LOS) jerks are evaluated. It is the LOS jerk data used to aid receiver’s PLLs. Jerk aiding allows PLL to keep the 3-rd order during switching from unaided mode to the aided one - that must be resulted in more smooth tracking. Due to jerk aiding in high dynamic conditions, the PLL bandwidth is reduced from 42 Hz to 0.7…1 Hz that increases antijam capability by 17 dB. The DLL with bandwidth of 0.1 Hz is always aided from PLL and does not affect overall antijam performance.
User position estimation and GNSS measurements integrity control are implemented in another part of proposed algorithm. Position estimation is implemented in rather straightforward way of INS correction with GNSS data. Integrity control is based on GNSS position and velocity measurements analysis with respect to their predicted covariances.
Proposed algorithm is designed to be put into hardware of multi-purpose INS consisting of 3 separate hardware units: GNSS receiver, IMU and navigation computer. The division of the algorithm into several parts suggests the hardware structure flexibility. So it can be practically used in variety of INS’es for aerospace and military applications as well as in low-cost civil applications with MEMS-based IMU’s.