Attitude Accuracy Improvement of Ultra Low-Grade MEMS INS
using Alignment of GPS Antenna
(The University of Tokyo,
Department of Aeronautics and Astronautics,
Graduate Student)
Masaru Naruoka
Introduction
Abstract
This study proposes a method to improve the accuracy of attitude estimation of an
ultra low-grade inertial navigation system (INS) by integration of a GPS receiver
and smart placement of the GPS antenna. The proposed method utilizes the "lever
arm effect" originating from the difference in the locations of the inertial
measurement unit (IMU) of the INS and the GPS antenna. The method enhances
the observabilty of the attitude, which can neither be correctly estimated by such a
low-grade IMU nor be obtained directly from the GPS receiver's measurement
values, and its advantage is shown experimentally with a prototype system.
Furthermore, analysis of covariances matrices reveals further hints to use the
method effectively.
1
Paper ID is 483.
Navigation instruments should be smaller, lighter, and more cost-effective.
Not only for conventional aerospace field, but also for applications such as small unmanned
aerial vehicles, and car navigation.
The integration of an ultra low-grade INS which consists of micro-electromechanical system (MEMS) inertial sensors and civil-use GPS receiver is one of
the best solution.
Kalman filtering compensates for the low accuracy of MEMS inertial sensors.
2
Lever arm effect
However, the accuracy in attitude, especially heading, is not sufficient, and should
be improved.
According to the author's previous study, the error in heading is about 10 degrees.
Experiment with a prototype system
If the GPS antenna is fixed at the location different from the IMU, the linealized
observation equation of Kalman filtering is derived like:
To evaluate the effectiveness of the proposed method, experiments to compare
the flight log obtained by a prototype system with that of a high-precision INS/GPS
device, GAIA, are performed.
Specification of prototype
Item
where x, x, a, and b stand for velocity, position, attitude, and sensor biases
respectively, and 0, and v indicate a non-zero value and the error of observed
value. This equation shows that the outputs of a GPS receiver include clues of the
attitude indirectly, and can be used to help the estimation. This is "lever arm effect".
an
Antenna #1 Antenna #2
Attitude
MEMS
Gyro
GPS
Velocity
GPS
Position
Due to the "Lever Arm Effect", the outputs of the
GPS receiver is not equal to those of the INS.
Attitude
Kinematics
Prototype IMU
civil-use
measurement
update
GPS
Improved INS/GPS algorithm
3
4
Experiment results (1)
36.2
5
35.9
35.8
35.7
35.6
139
139.2
139.4
139.6
139.8
Longitude [deg]
80
60
40
20
0
-20
-40
-60
-80
3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71
5
5
3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71
GPS Time [×10 sec]
20
15
10
5
0
-5
-10
-15
-20
Heading [deg]
Down speed [m/s]
3000
2500
2000
1500
1000
500
0
180
120
60
0
-60
-120
-180
3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71
5
3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71
GPS Time [×105 sec]
5
GPS Time [×10 sec]
GPS Time [×10 sec]
Comparison of the time history between the case (C) of the prototype and GAIA
(Prototype:
, GAIA:
)
5
6
Covariance matrix analysis
10-5
Case (A) σ22 (7, 7)
Case (B) σ (7, 7)
Case (C) σ2 (7, 7)
10-6
10-7
3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71
GPS Time [×105 sec]
Dependency [deg]
10-4
45
40
35
30
25
20
15
10
5
0
-10
15
Test cases and horizontal view of the component placement
10
5
0
-5
Front [m]
3.51
-2.97
-0.01
0.01
-0.03
-3.51
-2.73
0.37
Case (B)
Standard
Deviation
1.37
3.05
0.21
0.25
0.22
0.64
0.68
4.60
Mean
2.39
-1.55
-0.01
0.01
-0.03
-3.50
-2.83
0.72
Standard
Deviation
1.93
3.03
0.24
0.27
0.21
0.65
0.53
3.72
Case (C)
Mean
2.41
-1.70
-0.01
0.01
-0.03
-3.53
-2.66
2.94
Standard
Deviation
1.83
3.05
0.18
0.21
0.16
0.54
0.52
2.99
The standard deviation of the attitude error in cases (B) and (C) are smaller than
in case (A) shows that the proposed method improves the attitude accuracy,
10
10
especially in heading. The
results also show that the
5
5
position outputs obtained by the
0
0
GPS receiver does not strongly
-5
-5
contribute to the improvement,
because they are not accurate
-10
-10
15 10
5
0
-5
15 10
5
0
-5
enough.
Front [m]
Front [m]
Position outputs of the GPS receiver
Discussion
The system covariance matrix of Kalman filtering contains infomation on how
accurate and correlate the estimated values are, when the optimal estimation is
conducted. If the proposed method is effective, the part of the matrix related to the
attitude should have smaller variances, which means it has the possibility of the
estimation being more accurate. It should also have stronger dependencies to
other parts, which indicates that there are more hints.
Variance
Altitude [m]
GPS Time [×10 sec]
Case (C)
Horizontal distance [m]
Altitude [m]
North Speed [m]
East Speed [m]
Down Speed [m]
Rolling [deg]
Pitching [deg]
Heading [deg]
20
15
10
5
0
-5
-10
-15
-20
3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71
Case (B)
Mean
GPS Time [×105 sec]
Pitch [deg]
36
Prototype IMU
Case (A)
3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71
GPS Time [×10 sec]
-5
Statistical summaries of the error
30
20
10
0
-10
-20
-30
3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71
36.1
Case (A)
Prototype IMU
Right [m]
36.3
East speed [m/s]
Latitude [deg]
36.4
Roll [deg]
North speed [m/s]
36.5
0
Experiment results (2)
In all cases, the outputs of the prototype system do not diverge and are nearly
equal to those of GAIA. A comparison of the time history between the case (C) of
the prototype and GAIA is shown below.
80
60
40
20
0
-20
-40
-60
-80
5
INS
Extended
Kalman Filter
time
update
Antenna #1 Antenna #2
*Not consider
lever arm
Lever arm
effect
wnb / i
wbb / i
Antenna #1 Antenna #2
measurement
update
Bias
estimation
wbb / n
Velocity,
Position
GAIA
*
q~nb
Velocity,
Position
Kinematics
Antenna #2
INS
Coordinate
Transformation
Right [m]
MEMS
Accelerometer a b
In order to clarify the effectiveness of the proposed method, three cases are
10
conducted.
Right [m]
translational
part
Gravity
STMicroelectronic LIS3L02AS4 (MEMS)
Analog Devices ADXRS150 (MEMS)
u-blox LEA-4T (4Hz update, L1-signal)
Analog Devices AD7739 (24bits, 100Hz)
200MHz DSP, 8bits-MCU, FPGA
51 x 51 x 60 mm (W x H x D)
121 g
about US$ 500 per unit
Antenna #2
gn
Prototype System
Antenna #1
rotational
part
Accerlerometer
Gyro
GPS receiver
A/D converter
Processors
Size
Weight
Material cost
Prototype
IMU
GPS Antenna
Description
Antenna #1
P6.13
The proposed method is effective, because the attitude accuracy, especially in
heading, is improved. It is also worth to stress that even though the outputs of the
GPS receiver are not accurate for the attitude determination, the standard
deviation of the attitude error is settled to only 3 degrees in case (C).
The covariance analysis supports the fact that case (C) is the most effective.
However, it cannot explain the difference between cases (A) and (B) clearly. This
would be due to the poor accuracy of the MEMS gyros, because the "lever arm
effect" utilizes the angular velocity sensed by the MEMS gyros. On the other
hand, in case (C), that disadvantage is overcome by its 5 degree of freedom,
which is larger than the 3 of cases (A) and (B).
Case (A) dep(uX)
Case (B) dep(uX)
Case (C) dep(uX)
Without changing the MEMS gyros, the further improvement will be achieved by
1) using the longer arm, and 2) using more gyros.
3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71
GPS Time [×105 sec]
Conclusion
An example result of the analysis of the attitude part
In case (C), the variances are the smallest and the devendencies are the strongest
among all cases. In case (B), those values are smaller and stronger than in case
(A). However, the difference between the two is slight.
7
8
This study proposed a method to improve the attitude accuracy of an ultra lowgrade INS by utilizing GPS antenna placement, and comparison experiments
showed its effectiveness. The covariance analysis revealed that the poor accuracy
of the MEMS gyro degraded the performance of the proposed mehtod.