Carrier Tracking using Extended Kalman Filters for GNSS Synthetic Aperture Processing with a Rotating Antenna

A single GNSS antenna moving along a known trajectory can be used to synthesize a virtual array in order to apply spatial diversity techniques, e.g. beamforming. With these techniques, referred as synthetic aperture (SA) techniques, the receiver can mitigate interfering signals, including multipath. The use of a single antenna element, instead of an antenna array, significantly reduces the hardware complexity, and there is no longer need for precise calibration and system synchronization. Before SA techniques can be used to process the GNSS signal, a critical practical issue must be addressed: the carrier Doppler frequency caused by the antenna motion only, that we have called “relative” Doppler, must be isolated from any other carrier frequency contribution. We have called the sum of all these possible contributions “reference” Doppler. In this paper, we propose two new techniques making use of the so-called extended Kalman filter (EKF), in order to compensate the reference Doppler at the correlation output. The first method, named EKF1, tracks the carrier frequency using a conventional FLL, and then uses its output to feed an EKF responsible for the reference Doppler estimation. The second method, named EKF2, is an ultra-tight integration solution in charge of the carrier tracking, while simultaneously estimating the reference Doppler component from the correlators output. A comparison of these new methods with two previously existing techniques, in terms of their impact on direction-of-arrival estimation techniques, is presented. Synthetic and real GPS L1 C/A signals are used in this comparison.Real signal measurements were obtained using a GPS antenna mounted on a mechanical rotating arm –built in-house– to implement an approximately uniform circular movement.

Parameter Estimation with GNSS-Reflectometry and GNSS Synthetic Aperture Techniques

Miguel Angel Ribot Sanfelix

Aside from intentional interference, multipath is the most significant error source for Global Navigation Satellite Systems (GNSS) receivers in many operational scenarios. In this thesis, we study the multipath estimation from two different perspectives: to retrieve useful information from it using GNSS-Reflectometry (GNSS-R) techniques; and to mitigate its effects or to estimate its direction-of-arrival (DOA) as well as the line-of-sight (LOS) signal¿s using synthetic aperture (SA) processing. The first part of the thesis focuses on precision bounds for GNSS-R techniques for ground-based receivers, in scenarios where a single antenna simultaneously receives the LOS signal and a specular reflection. First, we derive the Cramér-Rao bound (CRB) of the receiver¿s height and the reflection coefficient, with the latter depending on the surface¿s electrical properties. More specifically, we propose a CRB derivation applicable to GNSS-R techniques that make use of the phase information and long observation times, such as the interference pattern technique (IPT). The derivation is based on the parameter transformation of the Fisher information matrix. We study the dependence of the computed CRB on the scenario and the receiver bandwidth. The CRB results for the simulated scenarios are consistent with the precision reported for many GNSS-R techniques used in these scenarios. The proposed CRB is meant to benchmark and compare new and existing techniques. Besides the derived CRB, we propose an algorithm to obtain the maximum-likelihood (ML) estimator of the parameters of interest with the IPT: the segmented ML estimator (SML). The SML transforms a complex multivariate optimization problem into multiple simpler ones by dividing the parameter search space taking advantage of the cost function¿s particular structure. The SML is validated with simulated signal and asymptotically cross-validates the CRB results. The second part of the thesis is devoted to the study of the SA processing of GNSS signals. The goal is to estimate the DOA of the signals received, and mitigate errors in the navigation solution caused by interfering signals, such as multipath. We start by deriving the CRB for the SA context, as a function of the antenna trajectory. This CRB considers the effect of the antenna complex gain, and we show in simulations that it is possible to achieve meaningful DOA estimation only by changing the antenna¿s orientation. We continue by proposing a development framework built upon a signal tracking architecture integrating SA processing. Before any SA processing, it is necessary to estimate and compensate any carrier phase contribution not related to the antenna motion. To do so, we propose two new sequential techniques based on the extended Kalman filter (EKF): EKF1 and EKF2. Also, we develop an open-loop version of the proposed SA tracking architecture, more robust than its closed-loop counterpart. Finally, we validate the proposed architecture and SA-based techniques with synthetic GPS signals at first, and then with real signals, recorded using an antenna mounted on a mechanical rotating arm. The obtained results validate the implemented techniques and show how the proposed SA architecture can ultimately mitigate the position bias error observed in environments with severe multipath interference.

EPFL2018

Estimation Bounds for GNSS Synthetic Aperture Techniques

Cyril Botteron, Joaquin Cabeza de Pablo, Pierre-André Farine, Miguel Angel Ribot Sanfelix

This paper characterizes the estimation performance of synthetic aperture (SA) techniques in the context of moving GNSS receivers. Under the assumption of a stationary channel, SA techniques transform a single antenna into a virtual array. We first introduce a model for the GNSS signal received by a single moving antenna. Leveraging this model, SA processing enables direction-of-arrival (DOA) and beamforming on a single antenna. The model does not make use of the narrowband assumption, which makes it suitable for relatively large trajectories. In addition, it includes the effects of the polarization mismatch between the received signal and the receiving antenna. Then, the proposed model is used to derive the Cram´er-Rao lower bound (CRB) for the joint estimation of the received signal amplitudes, synchronization and DOA parameters. We compute the CRB for two different antenna motions, with results depending on the antenna trajectory as well as on the scenario geometry. Results highlight how SA processing profits from spatial and polarization diversities, pointing out its potential for DOA estimation and beamforming applications in moving GNSS platforms, such as unmanned air vehicles or smartphones.

2017

Position+Attitude from GPS+INS for RTK Airborne Sensoring

Telmo Cunha, Phillip Tomé

This is a presentation of the techniques used to process inertial and GPS data collected during an airborne gravimetric and altimetric survey in order to obtain absolute position and attitude estimates of the sensors mounted on board the aircraft. For high precision gravimetry and altimetry, these navigational parameters are required, in the order of a decimeter for position and better than one arc-minute for attitude. The survey took place in the Portuguese Azorean area in October 1997. It consisted of flying a series of profiles with a set of instruments mounted in a military aircraft, covering a large area around the islands, mainly over the mid-Atlantic ridge. The instruments whose position and attitude had to be determined were a gravimeter and two altimeters (one laser and another radar). For this purpose, three GPS receivers and an Inertial Measurement Unit (IMU) were used. The basic idea was to have a relatively low cost system that would be able to supply position and attitude with a level of accuracy and reliability similar to other more expensive systems, like gimbaled and ring laser gyro based inertial systems. One other requirement was that it should be able to work in real time. This feature could be useful for repeating flight tracks and for many other applications. For this purpose, a radio link was established with the aircraft to supply GPS data from a ground reference station. The methodology for processing GPS and IMU raw data was implemented with an integrated feedback loop. The position determination is based on real time DGPS with L1 and L2 carrier phase ambiguity fixing, using online IMU processed data to validate and increase the positions reliability, especially during GPS outages and when the aircraft is far away from the nearest GPS reference station. For the attitude angles, the IMU raw data is processed using the absolute GPS position measurements for continuous alignment. The baseline between a pair of GPS antennas is also computed (without resorting to a reference station data), using L1 and L2 carrier phase and doppler measurements. This baseline is very helpful for the continuous alignment of the strapdown analytical platform in heading, since this angle estimate is weakly coupled to position updates, especially in the absence of high horizontal accelerations. The position and attitude values were obtained from all the measurements using an Extended Kalman filter. Besides the normal navigation states, the filter also includes extra states to account for the inertial sensor errors and the vertical gravity anomaly.