Organizations: School of Surveying and Geo-Informatics, Tongji University, Shanghai 200092, China · School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, Shanghai 200240, China · School of Robotics, Wuhan University, Wuhan 430072, China
Geometric filters have recently been introduced to improve the accuracy and consistency of inertial-based integrated navigation systems. Error states were defined through specific group operations, introducing state correlations in error definition, which were lacked in the additive error used by a conventional indirect Kalman filter. The desirable consistent filtering models can be obtained based on specific geometric errors. For zero-velocity measurements expressed in the reference frame, this paper derives left-error process and measurement models from invariant filtering, two-frame-group filtering, and equivariant filtering. Importantly, a new group operation is introduced for the left tangent-group equivariant error. The analysis shows that the two-frame-group invariant extended Kalman filter (TFG-IEKF) and the tangent-group equivariant filter (TG-EqF) do not offer a significant consistency advantage over the invariant extended Kalman filter (IEKF). Experiments with an INS/ZUPT measurement system show that, under small initial attitude errors, the conventional indirect extended Kalman filter (EKF) achieves loop-closure position errors below 0.1% of the traveled distance, while the three geometric filters achieve comparable positioning accuracy.
Figures & tables
Figure 1: Data-acquisition system and total-station point measurements.
Specification
Gyroscope
Accelerometer
Noise random walk
0.015deg/h
0.017(m/s)/h
Bias instability
0.5deg/h
10μg
Measurement range
500deg/s
8g
Table 1: Specifications of the MEMS IMU.
Figure 2: Indoor experiment and positioning result.
Segment
1
2
3
4
5
6
7
8
9
10
11
12
13
Reference
2.145
3.117
3.071
3.115
3.088
3.586
3.581
3.116
3.124
3.074
3.067
2.040
10.872
Measured
2.154
3.138
3.085
3.136
3.104
3.603
3.580
3.124
3.137
3.075
3.091
2.031
10.884
Absolute error
0.009
0.021
0.014
0.021
0.016
0.017
0.001
0.008
0.013
0.001
0.024
0.009
0.009
Table 2: Errors in distances between adjacent indoor control points (m).
Figure 3: Positioning results for the six outdoor experiments.
Data
EKF
IEKF
TFG-IEKF
TG-EqF
m
%D
m
%D
m
%D
m
%D
1
0.047
0.023
0.071
0.035
0.072
0.035
0.070
0.034
2
0.190
0.065
0.205
0.070
0.215
0.073
0.241
0.082
3
0.173
0.060
0.097
0.034
0.096
0.033
0.097
0.034
4
0.077
0.031
0.083
0.033
0.078
0.031
0.088
0.035
5
0.052
0.027
0.031
0.016
0.033
0.018
0.031
0.017
Table 3: Loop-closure position errors for the outdoor experiments.
Data
Length (m)
Speed (m/s)
Airborne (s)
Stationary (s)
ZUPTs
1
205.50
1.27
10.52
4.00
16
2
293.72
1.26
8.46
2.36
28
3
290.23
1.22
8.95
2.34
27
4
254.31
1.22
8.68
2.44
24
5
188.89
0.90
5.97
2.88
33
6
183.52
1.02
6.16
2.86
29
Table 4: Statistics of the outdoor experimental datasets.
Error (m)
EKF
IEKF
TFG-IEKF
TG-EqF
Horizontal position
5.88
5.71
4.83
5.60
Height
6.13
0.48
0.27
0.63
Table 5: Loop-closure results for Data 1 with an initial roll error of 60\SIUnitSymbolDegree .
Figure 4: Trajectories of the four filters with an initial roll error of 60\SIUnitSymbolDegree .
Airbus Central Research and Technology, Taufkirchen, Germany · Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway