Gianluca Falco

A Comparison between Different Error Modeling of MEMS Applied to GPS/INS Integrated Systems

Advances in the development of micro-electromechanical systems (MEMS) have made possible the fabrication of cheap and small dimension accelerometers and gyroscopes, which are being used in many applications where the global positioning system (GPS) and the inertial navigation system (INS) integration is carried out, i.e., identifying track defects, terrestrial and pedestrian navigation, unmanned aerial vehicles (UAVs), stabilization of many platforms, etc. Although these MEMS sensors are low-cost, they present different errors, which degrade the accuracy of the navigation systems in a short period of time. Therefore, a suitable modeling of these errors is necessary in order to minimize them and, consequently, improve the system performance. In this work, the most used techniques currently to analyze the stochastic errors that affect these sensors are shown and compared: we examine in detail the autocorrelation, the Allan variance (AV) and the power spectral density (PSD) techniques. Subsequently, an analysis and modeling of the inertial sensors, which combines autoregressive (AR) filters and wavelet de-noising, is also achieved. Since a low-cost INS (MEMS grade) presents error sources with short-term (high-frequency) and long-term (low-frequency) components, we introduce a method that compensates for these error terms by doing a complete analysis of Allan variance, wavelet de-nosing and the selection of the level of decomposition for a suitable combination between these techniques. Eventually, in order to assess the stochastic models obtained with these techniques, the Extended Kalman Filter (EKF) of a loosely-coupled GPS/INS integration strategy is augmented with different states. Results show a comparison between the proposed method and the traditional sensor error models under GPS signal blockages using real data collected in urban roadways.

Performance Analysis of Constrained Loosely Coupled GPS/INS Integration Solutions

The paper investigates approaches for loosely coupled GPS/INS integration. Error performance is calculated using a reference trajectory. A performance improvement can be obtained by exploiting additional map information (for example, a road boundary). A constrained solution has been developed and its performance compared with an unconstrained one. The case of GPS outages is also investigated showing how a Kalman filter that operates on the last received GPS position and velocity measurements provides a performance benefit. Results are obtained by means of simulation studies and real data.

Theoretical analysis and tuning criteria of the Kalman filter-based tracking loop

AbstractIn recent years, Kalman filter (KF)-based tracking loop architectures have gained much attention in the Global Navigation Satellite System field and have been widely investigated due to its robust and better performance compared with traditional architectures. However, less attention has been paid to the in-depth theoretical analysis of the tracking structure and to the effects of Kalman tuning. A new approach is proposed to analyze the KF-based tracking loop. A control system model is derived according to the mathematical expression of the Kalman system. Based on this model, the influence of the choice of the setting parameters on the temporal evolution of the system response is discussed from the perspective of a control system. As a result, a reasoned and complete suite of criteria to tune the initial error covariance as well as the process and measurements noise covariances is demonstrated. Furthermore, a strategy is presented to make the system more robust in higher order dynamics without degrading the accuracy of carrier phase and Doppler frequency estimates.

Analysis and modelling of MEMS inertial measurement unit

Thanks to advances in the development of Micro-Electromechanical Systems (MEMS), it has been possible to fabricate small dimension and cheap accelerometers and gyros, which are being used in many applications where the GPS/INS integration is carried out, as for example to identify track defects, navigation, geo-referencing, agriculture, etc. Although these MEMS devices have a low-cost, they present different errors which degrade the accuracy of the navigation systems in a short period of time. Therefore, a suitable modelling of these errors is necessary in order to improve the system performance. In this work, Allan Variance and Power Spectral Density techniques are used to identify the random processes that affect the inertial sensor data. Once the random components are identified, they are modelled using first-order Gauss-Markov and random walk processes. Two models are assessed augmenting the states of the Extended Kalman Filter (EKF) to 6 and 9. Subsequently, another analysis and modelling of the inertial sensors which combines Autoregressive Filters and Wavelet De-noising is implemented and in this case the EKF of the loosely coupled GPS/INS integration strategy is augmented with 6, 12 and 18 states. Finally, the results show a comparison between these sensor error models with real data under GPS outage conditions.

Bounded Constrained Filtering for GPS/INS Integration

This paper considers estimation problems where inequality constraints are imposed on the outputs of linear systems and can be modeled by nonlinear functions. In this case, censoring functions can be designed to constrain measurements for use by filters and smoothers. It is established that the filter and smoother output estimates are unbiased, provided that the underlying probability density functions are even and the censoring functions are odd. The Bounded Real Lemma is employed to ensure that the output estimates satisfy a performance criterion. A global positioning system (GPS) and inertial navigation system (INS) integration application is discussed in which a developed solution exhibits improved performance during GPS outages when a priori information is used to constrain the altitude and velocity measurements.

EM Algorithm State Matrix Estimation for Navigation

The convergence of an expectation-maximization (EM) algorithm for state matrix estimation is investigated. It is shown for the expectation step that the design and observed error covariances are monotonically dependent on the residual error variances. For the maximization step, it is established that the residual error variances are monotonically dependent on the design and observed error covariances. The state matrix estimates are observed to be unbiased when the measurement noise is negligible. A navigation application is discussed in which the use of estimated parameters improves filtering performance.

Practical implementation and performance assessment of an Extended Kalman Filter-based signal tracking loop

In this paper, the structure of a tracking loop with Extended Kalman Filter (EKF) is analyzed. Particular emphasis is given to the NCO update rule, which is seldom mentioned or studied in previous literature. Furthermore, the structure of an EKF-based software receiver is proposed including the special modules dedicated to the initialization and maintenance of the tracking loop. The EKF-based tracking architecture has been compared with a traditional one based on an FLL/PLL+DLL architecture, and the benefit of the EKF within the tracking stage has been evaluated in terms of final positioning accuracy. Further tests have been carried out to compare the Position-Velocity-Time (PVT) solution of this receiver with the one provided by two commercial receivers: a mass-market GPS module (Ublox LEA-5T) and a professional one (Septentrio PolaRx2e@). The results show that the accuracy in PVT of the software receiver can be remarkably improved if the tracking is designed with a proper EKF architecture and the performance we can achieve is even better than the one obtained by the mass market receiver, even when a simple one-shot least-squares approach is adopted for the computation of the navigation solution.

Loose and Tight GNSS/INS Integrations: Comparison of Performance Assessed in Real Urban Scenarios

Global Navigation Satellite Systems (GNSSs) remain the principal mean of positioning in many applications and systems, but in several types of environment, the performance of standalone receivers is degraded. Although many works show the benefits of the integration between GNSS and Inertial Navigation Systems (INSs), tightly-coupled architectures are mainly implemented in professional devices and are based on high-grade Inertial Measurement Units (IMUs). This paper investigates the performance improvements enabled by the tight integration, using low-cost sensors and a mass-market GNSS receiver. Performance is assessed through a series of tests carried out in real urban scenarios and is compared against commercial modules, operating in standalone mode or featuring loosely-coupled integrations. The paper describes the developed tight-integration algorithms with a terse mathematical model and assesses their efficacy from a practical perspective.

Iterative Smoother-Based Variance Estimation

The minimum-variance smoother solution for input estimation is described and it is shown that the resulting estimates are unbiased. The smoothed input and state estimates are used to iteratively identify unknown process noise variances. The use of smoothed estimates, as opposed to filtered estimates, leads to improved approximate Cramér-Rao lower bounds for the unknown parameters. It is also shown that the sequence of iterates are monotonic and asymptotically approach the actual values under prescribed conditions. A nonlinear mining navigation application is described in which unknown parameters are estimated.

Data decoding of the first Galileo IOV PFM satellite and joint GPS+Galileo positions

On the 20th of October 2011, the first two satellites of the Galileo constellation have been launched successfully. The possibility to have these two satellites in orbit represented a great opportunity for researchers to receive and monitor the first Galileo signals. After the satellite switch-on, we continuously monitored the signal broadcast by both the satellites, using a software radio receiver. This paper shows the analysis on the navigation message that was broadcast by the IOV-PFM Galileo satellite on the E1 bandwidth, starting from December 2011. In particular, we were able to observe a valid ephemeris data on December 21st and December 22nd. The successful interpretation of the navigation message enabled the first GPS+Galileo experimentations using real signals that were performed in static condition, through code-phase measurements.