Machine guidance systems have been used for construction, mining and agriculture to improve productivity and safety in operating dozers, motor graders, excavators, scrapers, tractors and harvesters. To guide the machines, robotic total stations, GNSS RTK systems, and other sensors (laser systems, INS) have been used in 3D guidance systems. Among the system components, the RTK system takes a key role in providing positioning and navigation information.The most significant challenge associated with the RTK system is multipath reflection at the operating sites. Careful site selection might not be an option for machine guidance. Most of the guidance systems employ dual antenna systems for positioning/orientation, and even when within a short distance of each other, multipath is not removed after differencing. Interestingly enough, one can use this apparent drawback and capitalize on it in order to build a between-antennas multipath profile. This is explained by the fact that the incoming signal phase will change significantly along the ray trajectories of the plane waves passing through each of the antennas (see [1] and [2] for further discussion). This effect is materialized by the mathematical model

(1)

where the subscripts 0 and 1 represent a master and a slave antenna, respectively; the angle is the relative multipath phase delay between the antennas and an effective reflector; and is the multipath signal amplitude–assumed to be the same in the master and the slave antenna.

MIMICS Strategy

As we try to mimic the effects of multipath caused by effective reflectors under variable dynamics, our approach is named MIMICS (Multipath Profile from Between ReceIvers DynaMICS). The single difference (between receivers m and s for a common satellite prn) carrier-phase observation equation is given by

(2)

As we use a single external oscillator connected to both receivers, the receiver clock offset is removed. To obtain multipath observables, we need to remove the geometric range ρ and the ambiguity N. This can be done in two steps. Firstly, we try to remove the geometric range term using the precise estimates of velocity, acceleration, and jerk experienced at both antennas. These higher-order range dynamic estimates should be immune to low-frequency multipath signatures. To cancel the ambiguity term, , we perform differencing (2) in time sequentially. By integrating the differential observations, we will end up with the following equation:

(3)

where E[ ] is the expectation operator. To isolate the initial epoch multipath, , the first term on the right-hand side of (3), , should be removed. This can be accomplished by mechanical calibration and/or numerical randomization. To summarize the idea, we have to create random multipath physically (or numerically) at the initialization step. When the isolation of the initial multipath epoch is completed, we can recover multipath at every epoch using the differential multipath observations, eventually.

The numerically induced pseudo-random multipath is obtained through an adaptive whitening filter using auto-regressive (AR) models. Since the order of the AR coefficient estimation depends on the multipath spectra (dependent on the platform dynamics and reflector distance), we used a cost function to estimate in real time the proper order. The order is set to vary between one (a Gauss-Markov model) and five. The selection of the model order of the AR whitener is a critical one. An order too low results in a poor whitener of the background coloured noise, while an order too large might affect the embedded original signal, which we are interested in detecting.

Multipath Parameter Estimation

A real live-signal test was designed to evaluate the amount of data necessary to isolate the initial multipath from the differential multipath observations. Also, the test was performed to validate our approach in estimating several multipath parameters just from two-antenna observations at every epoch. With a dual antenna-receiver system connected with an external oscillator in a car, we tried to pick up strong multipath by introducing a close-by reflector (using a building’s facade acting as a specular reflector as illustrated in Figure 1). Figures 2a and 2b show multipath spectra ranging from low-frequency components to high-frequency ones.

Figure 1. Kinematic test setup.

Figure 2a. Spectrum of PRN 5 multipath observables.

Figure 2b. Spectrum of PRN 13 multipath observables.

After employing the MIMICS strategy to obtain multipath observations on a satellite by satellite basis (hence in the measurement domain), it is possible to estimate the parameters ( reflection coefficient, phase-delay, azimuth of reflected signal, elevation angle of reflected signal) of the multipath observable described in (1) for each PRN. An Extended Kalman Filter (EKF) is applied to perform the estimation. When the platform experiences higher dynamics, such as rapid rotations, acceleration is no longer constant and jerk is present. Therefore a Gauss-Markov model may be more suitable and can be implemented through a position-velocity-acceleration (PVA) dynamic model [3].

The results from the multipath parameter estimation are given for two satellites, PRN 5 and PRN 13. As shown in Figure 3a, the distance to the reflector (i.e., the phase delay) for PRN 5 converged to about 10 meters after 40 seconds elapsed time. This phase delay estimate was reasonable under the test set up. On the other hand, PRN 13 converged faster, and the estimate of phase delay was around 20 meters in steady-state. The differences in phase delay estimates and convergence time for the two satellites reflect different multipath geometry.

Figure 3a. PRN 5 multipath parameter estimation.

Figure 3b. PRN 13 multipath parameter estimation.

Concluding Remarks

The MIMICS method is designed for machine guidance applications in multipath-rich environments where the machine platform has random/unpredictable dynamics and is surrounded by strong reflectors (e.g., construction sites, harbours, and airports). The method can be used for single-frequency receivers. Furthermore, it can be easily implemented within the receiver firmware like any other routine such as the positioning module.

Based in part on a paper presented at IEEE/ION PLANS 2008, Monterey, California, 5-8 May 2008 [4].

References

[1] Ray, J.K., M.E. Cannon, and P. Fenton (1998). “Mitigation of Static Carrier Phase Multipath Effects Using Multiple Closely-Spaced Antennas”. Proceedings of ION GPS 1998, Nashville, Tennessee, 15-18 September 1998; pp. 1025-1034.
[2] Serrano, L., D. Kim, and R.B. Langley (2005). “A New Carrier-Phase Multipath Observable for GPS Real-Time Kinematics Based on Between Receiver Dynamics”. Proceedings of the 61st Annual Meeting of The Institute of Navigation, Cambridge, Massachusetts, 27-29 June 2005; pp. 1105-1115.
[3] Brown, R. G. and P. Y. C. Hwang (1996). Introduction to Random Signals and Applied Kalman Filtering: with MATLAB Exercises and Solutions (Third ed.): Wiley & Sons, Inc.; 484 pp.
[4] Serrano, L., D. Kim, and R. B. Langley (2008). “Carrier-phase multipath calibration in GPS-RTK machine-guidance applications.” Proceedings of IEEE/ION PLANS 2008, Monterey, California, 5-8 May 2008 (in press).

Luis Serrano, Ph.D. Student
Dr. Don Kim and Prof. Richard B. Langley
Department of Geodesy and Geomatics Engineering
University of New Brunswick