Adaptive Method for Multipath Mitigation and Its Applications for Structural Deflection Monitoring

The authors have previously shown that carrier phase kinematic GPS is a powerful tool for measuring the deflections of structures, such as bridges. Current research work at the University of Nottingham looks at integrating Leica dual frequency GPS receivers with triaxial accelerometers to identify small and high dynamic structural movements. The individual sensor systems have disadvantages, in that the current commercial GPS receivers can only gather data at a rate of 10 Hz, and the accelerometer exhibits drift characteristics. The combined system, however, eliminates these problems and combines their benefits. When analysing the results of such bridge deflections, it is possible for multipath noise to exhibit itself as apparent low frequency movement. This paper investigates the use of an adaptive FIR filter for multipath mitigation. Three filter signal input options for comparison with the deflection data are discussed, and a simple Matlab simulator with real-time data processing function developed for this purpose is introduced. The combination and relationship of the desired and reference signals are explored using a cross-correlation approach. Spectrum analysis is adopted to identify the very low frequency characteristics of multipath. By using a multi-antenna configuration and consecutive days’ measurements, the improvements of data quality and effectiveness of adaptive filtering (AF) are analysed in the context of a suspension bridge deflection monitoring. The technique under investigation has been used upon data gathered on a small suspension bridge. The results show that it is possible to separate the real bridge movement from multipath signal and individual receiver random noise. INTRODUCTION The environment surrounding the antenna of a GPS receiver significantly affects the signal propagation, and as a result, noise is introduced into the measured values of pseudorange and carrier phase observables. Eventually, the GPS positioning is greatly degraded by the inference of these distorted signals. Multipath is one of the main error sources induced by the surveying environment. Because multipath changes its phase and amplitude all the time with the change of GPS satellite constellation and fully depends on the surveying site ambient environment, it is very difficult to use mathematical means to characterise it and reduce its influence. In many engineering applications, multipath becomes a very troublesome factor. Research illustrates that the amplitude of the carrier phase multipath can reach several centimeters in the extreme cases and has typically a period of a few minutes (Langley, 1998). It can become the dominant error source when detecting motion with a period of approximately 1~5 minutes. For mitigating reference station multipath, Calgary University presented a closely setup multiple antenna configuration at the reference station sites to reduce the multipath (Ray, 1999). A day to day repeat signature method is adopted to mitigate multipath by using multipath characteristics and improve accuracy of GPS time series by about 50% (Bock, et al, 2000). Moving averaging (MA) is another method used to reduce multipath effects when there are various frequency band signals from real platform movement. Additionally, new types of antennas can greatly reject multipath. These include chokering antenna and NovAtel L1/L2 GPSAntenna Model 600 (http://www.novatel.com). Through careful reference and observation site selection (not always practically applicable), ambient multipath can be mitigated. Ge et al. (2000a, 2000b) studied the feasibility of adaptive filtering to suppress the multipath in the static GPS positioning. But cost-effective and reliable multipath mitigation techniques are still important research emphases, especially when GPS is chosen for precise engineering applications such as structural deformation/deflection monitoring. In structural deflection monitoring, the complexity of the surveying environment and the surrounding infrastructure as well as the limitation in surveying site selection make multipath an unavoidable error source and even a dominant component in the final output time series when lower frequency bridge movement is the research interest. Very strict requirements upon the measurement accuracy, varying deformation sizes from several millimeters up to several meters, and real-time kinematic surveying mode challenge the application of GPS technology to structural deflection monitoring. Research into effective multipath reduction is of great practical importance. Based on the Least Mean Square (LMS) algorithm, an adaptive filtering system can provide a simple way to estimate and reduce the errors in the GPS coordinate time series. Acting as an interference canceler, an adaptive system can isolate the correlated part from two time series. It is possible to use this method to analyse magnitudes of real structural movements, multipath, receiver random noise, tropospheric delay, and other error sources using their correlation characteristics. Relatively clean bridge deflection data sets can be obtained through such processes. The first part of this paper is a brief review of adaptive filtering and is followed with practical applications and discussion about how to use this method to mitigate receiver random noise and multipath. The second part is an example whereby GPS/accelerometer data are gathered during a three-day period upon a footbridge over the River Trent in Nottingham, UK. Through the appropriate signal input combination and ordering, the third part of the paper gives examples of how the AF method is used in extracting real movement of a monitored structure and details the data processing strategy. A methodology is presented to gradually reduce receiver noise and multipath both on the reference station and surveying sites. Also spectral analysis and cross-correlation are applied to the input and output signals to analyse their long-term vibration characteristics and the statistical relationship between different time series. The final part of the paper presents future research, discussion and conclusions. Since multipath characterizes as a low frequency vibration, this research concentrates on lower frequency identification from a time series, when spectral analysis is applied. ADAPTIVE FILTERING METHOD Digital Signal Processing (DSP) begins with a signal which appears to the computer as sequence of digital values. From a system point of view, there are three basic components in any simple DSP, i.e., input sequence ) (n x , operator {} D and output sequence ) (n y . Their general relationship can be expressed as follows: )} ( { ) ( n x D n y = . (1) The equivalent expression of Equation 1 is