METHODS, ALGORITHMS AND TOOLS FOR ...

METHODS, ALGORITHMS AND TOOLS FOR PRECISE TERRESTRIAL NAVIGATION Eduard Angelats, M. Eulàlia Parés and Ismael Colomina Institute of Geomatics Generalitat de Catalunya & Universitat Politècnica de Catalunya Av. Carl Friedrich Gauss 11, Parc Mediterrani de la Tecnologia 08860 Castelldefels, Spain

Key words: kinematic surveying, corridor mapping, terrestrial navigation, INS/GNSS, nonholonomic constraints

Abstract Modern corridor mapping applications are nowadays growing, in number and relevance. Within this field, vehicle trajectory determination, i.e. navigation, is a major component. Classical and well-known strategies widely used for many years in INS/GNSS based navigation are no more valid to achieve required position and attitude. Moreover, navigation suffers from a non-friendly environment with weak GNSS signals and very low dynamics. Therefore, new strategies, not only in processing but also in mission planning, should be developed to achieve the necessary requirements. In this context, and based on previous experience in terrestrial navigation, this paper seeks to explore, develop and test several methods, algorithms and tools to obtain a precise navigation to be used in such applications.

1. Introduction and motivation Mobile mapping or, more to the point, terrestrial mobile mapping is consolidating itself as the third mapping paradigm, after airborne and satellite mapping –both of them “mobile” as well. It seems that the two business success ingredients, market needs and technology availability, have met there: complete, turnkey mobile mapping systems can be ordered and put to work; the demand of 3D high-resolution cartographic information is growing. Many traditional mapping and surveying companies are complementing their airborne acquisition systems with terrestrial ones. And they are learning the lessons, namely, that, to start with, georeferencing may not be as easy and straightforward as expected or, even more, that getting precise and accurate trajectories for a terrestrial vehicle can be far more difficult than for an airplane. Of course, terrestrial mobile mapping platforms include one or more GNSS receivers, IMUs and a few other navigation aids. This paper deals with precise navigation and positioning with INS/GNSS-based multisensor systems in the context of terrestrial applications such as corridor mapping and kinematic surveying. As said, in contrast to airborne navigation, terrestrial navigation, particularly in urban environments, faces additional challenges such as GNSS signal obstruction, GNSS signal multipath and low dynamics motion. Moreover, while in airborne missions well defined standard procedures are applied, terrestrial missions suffer from a lack of them. Due to the environment constraints, airborne procedures can not be directly applied for land missions. The main goal of the paper is to illustrate the necessary balance between the quality of the sensor system and an appropriate mission design. We will show that with an appropriate mission design and data processing we can improve the quality of our terrestrial trajectory. The proposed strategy includes a favourable IMU mounting geometry, innovative IMU calibration sequences, control points, velocity updates (VUPTS and odometer based velocities), and an appropriate processing algorithm (based on the use of trajectory and low dynamics constraints). The new procedure will be evaluated using different IMU performances, from navigation-grade to tactical-grade IMU. With this new approach the productivity of terrestrial corridor mapping and the terrestrial kinematic surveying can be improved. This paper is organized as follows: first theoretical approach is presented. After that, the performed tests are detailed and then the preliminary results are shown.

2. Proposed approach An INS/GNSS system mainly consists of an Inertial Measurement Unit (IMU) and a GNSS receiver, with fully operational capabilities. An IMU is an assembly of three gyroscopes, that measure angular velocities, and three accelerometers, that measure linear accelerations along the same axis. GNSS data have high long-term stability but are noisy in the low frequencies; IMU data show the opposite behavior, hence, putting them together retains the best of each one [2]. In order to correct the IMU sensors’ drifts and biases with the help of GNSS measurements, the classical approaches apply a Kalman filter [1,3,9]. For airborne navigation this solution has been proved efficient enough. But in land environments where GNSS may suffer from errors due to multipath or even worst can suffer from outages an extension of the algorithm is needed. Nonholonomous constrains has been proved to be useful [8]. The opportunity to use control points for positioning updates has also to be considered, as well as the use of magnetometers or multi-antenna GNSS receivers [7]. In section 2.1 the user will find a brief review of these algorithmic improvements. But, the same way that in avionics a well-known procedure is defined in order to help the system calibration in groundvehicles a procedure should be defined. In section 2.2 a ground procedure is proposed. 2.1 Processing algorithm •

Position updates

In specific environments as rail tracks, coordinates of defined points can be used as an update. This update can be very useful in high multipath environments or outages paths. The update equations are the same of the GNSS position measurements but taking into account the specific lever arm between the system and the control point and the error in the measurement of this lever arm. •

Velocity updates

A nonholonomic system is characterized by the fact that the total degrees of freedom are more than the controllable degrees of freedom. For example, although theoretically a rail-trolley could be moved in all three orthogonal axes, the fact is that it only can be moved in the X body-frame direction. Hence, it has sense to define two nonholonomic constraints on the Y and Z body-frame directions [4,8]. Due to the small uncertainty of this affirmation, instead of implementing the constraint we implement it as pseudo-observations [5] with very slow related noise. In order to bounder the errors related to vbx GNSS speed measurements, or odometer measurements can be used. In static acquisition periods ZUPTS (Zero Velocity Update Points) are highly recommended.

The update equations can be deduced from: z = (speed ,0,0) h( xˆ , vˆ e , Rˆ e , bˆ b ) = Rˆ b vˆ e e

b

e

With related measurement noise matrix: 2  σ speed  R = 0  0 

0 2 σ NHC

0

0   0  2  σ NHC 

•

Attitude updates

In addition to the classical transfer alignment, recently the use of multi-antenna GNSS receivers has been proved as an effective solution for aiding in the heading determination. Several algorithms has been presented [7] with similar results. The most extended one is based in the following equations:

z = ( x1e ; x2e )  I 0  e  Rˆ be h( xˆ e , vˆ e , Rˆ be , bˆ b ) =   xˆ +  0 I   0

0  o1b    Rˆ be  o 2b 

With related measurement noise matrix:

 σ x2 R =  1  0

0   σ x22 

2.2 Data acquisition strategy In low dynamics missions, the signal-to-noise ratio for tactical grade IMUs uses to be low both for gyros and for horizontal sensing accelerometers. In order to increase this ratio two ideas are proposed: •

IMU pose

Given an IMU, the only way to increase the signal-to-noise ratio of the accelerometers is to increase the signal magnitude. In order to increase this signal for all the accelerometers even in static acquisition missions we can take advantage of the gravity force. In classical terrestrial missions the IMU is mounted in the vehicle with the x and y axis perpendicular to the vehicle floor (that corresponds to the ground). Thus, z is generally sensing almost all the gravity force while x and y axes do not sense almost anything unless severe pitch or roll. Changing the pose of the IMU in a way that the gravity is sensed equally by the three axis would reduce the noise ratio of the z axis but would increase the noise ratio of the x and y axis.

Figure 2: Detail of IMU pose. IMU is rotated 56º along y axis •

Calibration sequences

As said in previous subsection the actual movement of a terrestrial vehicle is quite limited. But even short movements if sudden and fast enough will increase the signal-to-noise ration and will help the sensor calibration. Thus, fast FW and BW movements covering a distance larger than GNSS precision will help mainly the horizontal axis accelerometer calibration and repeated mini “infinite-loops” [6] will help the calibration of the vertical gyro and of the horizontal accelerometers.

3. Experimental tests In order to explore the capabilities of INS, together with GNSS, for doing kinematic surveying and corridor mapping, two kinds of test areas were considered. First, a rail environment, typical for these applications, was selected as the candidate for the first test. Then, after this initial test, extra tests were carried out in a University Campus where the Institute of Geomatics is located. All tests have in common a slow motion of the vehicle. The aim of this first rail test (Figure 3), was to validate the feasibility of doing these applications using INS/GNSS. To do that, a navigation-grade IMU (IG’s iMAR FJI) and a tactical-grade IMU (IG’s Northrop Grumman LN200) were used together with DGNSS. Several stripes (a rail-track distance of 200 m), was carried out and acquired data was processed in real-time using a loosely-coupled INS/GNSS (Figure 4a). The test results have shown us that we had achieved the required precision in positioning determination as well as pitch and roll determination. However, a good heading determination was not achieved. These results motivated us to re-define our test strategy taken into account the proposed improvements that we have presented in the previous section.

Figure 3: Railway test system configuration

41.3436

Path 1 rail Path 2 rail

Lat (º)

41.3436

41.2755

Path 1 Path 2

Lat (º)

41.2754

41.3435

41.2753

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41.3434 41.2751

41.3434 41.275

41.3433 41.2749

41.3433 Lon (º) 41.3432 2.1216 2.1218 2.122 2.1222 2.1224 2.1226 2.1228 2.123

a)

Lon (º)

41.2748 1.98585 1.9859 1.98595 1.986 1.98605 1.9861 1.98615

b)

Figure 4: a) Railway test trolley path. b) Campus test trolley path

A new campaign of four tests was carried out to evaluate the proposed improvements (Figure 5). In this campaign, only IG’s LN200 IMU (enough to achieve the attitude requirements) was used and 2 high-performance GNSS receivers. The acquired data was also processed in real-time using the same hybridisation technique.

Figure 5: Campus test system configuration

The main characteristics of each of the test are detailed on table 1. The proposed improvements were applied gradually along the tests. That allowed us to evaluate and analyse the impact of each of the element strategy, in the attitude determination as well as the IMU calibration states. The first test was done, without using any of the proposed improvements, such as a standard mission. Then, in the second, we applied at the beginning a set of calibration sequences. These manoeuvres had duration of 45 seconds and include a series of FW and BW movements as well as mini-infinite loops. After that, in the middle of the mission, we did a static period of 30 seconds (VUPT) followed by previous calibration sequences. In this test also, we have acquired data from 2 GNSS receivers, but by now, we have only used in the processing stage, data from one receiver. The IMU pose contribution was analysed in third and fourth test. We did exactly the same mission as the previous test but taken into account an IMU pitch variation of 56º. The aim of that is to distribute the gravity among the three axes that could help us to improve our trajectory determination.

Test number

Multi-antennas

Maneuvers

VUPTs

IMU pose

1

NO

NO

NO

NO

2

YES

YES

YES

NO

3

NO

NO

NO

YES

4

YES

YES

YES

YES

Table 1: Characteristics of the Campus tests

4. Preliminary Results From the results obtained during the railway test, the required precision for positioning and roll and pitch determination was achieved. However, we were not able to achieve the required heading precision neither to determine correctly the IMU calibration states. These motivate us to introduce the proposed improvements that were tested and evaluated during the Campus test campaign. The preliminary results are presented in this section. The standard deviation for x and z IMU accelerometer bias are shown in Figures 6.a and 6.b while Figures 6.c and 6.d show the x and z IMU gyro bias. The red line represents the standard deviation (1 sigma) without taken into account calibration sequences as well as the velocity updates. In the green line, initial and middle mission calibration sequences are considered. Finally blue line represents standard deviation with calibration sequences and velocity updates. The standard deviation is presented over the longitude of the acquisition path. Looking into the figures, the calibration sequences have a positive impact into accelerometer bias while they help less in the gyro bias calibration. Meanwhile

the velocity updates have a high impact in the determination of the accelerometer but doesn’t help too much with the gyros. In terms of attitude determination, the roll and pitch are slightly better determined (Figure 7.a .and 7.b) when velocity updates and calibration sequences are used. However, both things, has much impact with the heading determination (Figure 7.c). With these preliminary results, although the impact is not so clear in the IMU calibration states, we can conclude that a combination of velocity updates and calibration sequences can highly improve the heading determination. To conclude, we observed with our campaigns that an IMU pose variation, in comparison with velocity updates and calibration manoeuvres, has no relevant and positive impact in the attitude determination.

700

700

Sigma b-ax Sigma b-ax (Maneuvers) Sigma b-ax (Maneuvers + Velocity updates)

690

690

680

680

670

670

660

660

650 1.98585

1.9859

1.98595

1.986

1.98605

1.9861

1.98615

650 1.98585 1.9859 1.98595

a) 2.08 2.06

Sigma b-az Sigma b-az (Maneuvers) Sigma b-az (Maneuvers + Velocity updates)

1.986

1.98605 1.9861 1.98615

b)

Sigma b-gx Sigma b-gx (Maneuvers) Sigma b-gx (Maneuvers + Velocity updates)

2.065

Sigma b-gz Sigma b-gz (Maneuvers) Sigma b-gz (Maneuvers + Velocity updates)

2.06

2.04 2.02

2.055

2 2.05

1.98 1.96

2.045

1.94 1.92 1.98585 1.9859 1.98595

1.986

1.98605 1.9861 1.98615

c) Figure 6: Accelerometers and gyros standard deviation bias.

2.04 1.98585 1.9859 1.98595 1.986 1.98605 1.9861 1.98615

d) a) Accelerometer x (ax) b) az c) Gyro x (gx) d) gz

0.8

0.8

Sigma roll Sigma roll (Maneuvers) Sigma roll (Maneuvers + Velocity updates) 0.7

Sigma pitch Sigma pitch (Maneuvers) Sigma 0.7 pitch (Maneuvers + Velocity updates)

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0 1.985851.98591.98595 1.986 1.986051.98611.98615

0 1.985851.98591.98595 1.986 1.986051.98611.98615

a)

b)

3

Sigma he Sigma he (Maneuvers) Sigma he (Maneuvers + Velocity updates) 2.5 2 1.5 1 0.5 0 1.985851.9859 1.98595 1.986 1.986051.98611.98615

c) Figure 7: a) Roll standard deviation. b) Pitch standard deviation. c) Heading standard deviation

5. Final remarks and further research These preliminary results show us that an improving of the attitude determination is possible by means of calibration sequences and velocity updates. With that, in a terrestrial corridor mapping and kinematic surveying application, a precise INS-based navigation and positioning are possible. This paper tries to validate the concept with short missions. Further research should be done in two ways. First, longer missions should be carried out in order to analyze the impact of these improvements in the trajectory determination. Last but not least, empirical validation of the results should be carried out.

Acknowledgements The research reported on this paper has been partially funded by the Spanish Ministry of Science and Innovation, through the GeoTRAM project of the Spanish TRACE Programme (reference: PET2008_0070). The authors sincerely thank Al-Top Topografia for its collaboration with the GeoTRAM project and to make possible the rail test using its RM3D system.

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