Jason N. Gross

Flight-Test Evaluation of Sensor Fusion Algorithms for Attitude Estimation

In this paper, several Global Positioning System/inertial navigation system (GPS/INS) algorithms are presented using both extended Kalman filter (EKF) and unscented Kalman filter (UKF), and evaluated with respect to performance and complexity. The contributions of this study are that attitude estimates are compared with independent measurements provided by a mechanical vertical gyroscope using 23 diverse sets of flight data, and that a fundamental difference between EKF and UKF with respect to linearization is evaluated.

Evaluation of Matrix Square Root Operations for UKF within a UAV GPS/INS Sensor Fusion Application

Using an Unscented Kalman Filter (UKF) as the nonlinear estimator within a Global Positioning System/Inertial Navigation System (GPS/INS) sensor fusion algorithm for attitude estimation, various methods of calculating the matrix square root were discussed and compared. Specifically, the diagonalization method, Schur method, Cholesky method, and five different iterative methods were compared. Additionally, a different method of handling the matrix square root requirement, the square-root UKF (SR-UKF), was evaluated. The different matrix square root calculations were compared based on computational requirements and the sensor fusion attitude estimation performance, which was evaluated using flight data from an Unmanned Aerial Vehicle (UAV). The roll and pitch angle estimates were compared with independently measured values from a high quality mechanical vertical gyroscope. This manuscript represents the first comprehensive analysis of the matrix square root calculations in the context of UKF. From this analysis, it was determined that the best overall matrix square root calculation for UKF applications in terms of performance and execution time is the Cholesky method.

Sensitivity Analysis of Extended and Unscented Kalman Filters for Attitude Estimation

The extended Kalman filter (EKF) and unscented Kalman filter (UKF) for nonlinear state estimation with both additive and nonadditive noise structures are presented and compared. Three different Global Positioning System (GPS)/inertial navigation system (INS) sensor fusion formulations for attitude estimation are used as case studies for the nonlinear state estimation problem. A diverse set of actual flight data collected from research unmanned aerial vehicles was used as empirical data for this study. Roll and pitch estimation results were comparedwith independent measurements from amechanical vertical gyroscope to evaluate the performance. The performance of the EKF and UKF is compared in terms of noise assumptions, covariance matrix tuning, sampling rate, initialization error, GPS outages, robustness to inertial measurement unit bias and scale factors, and linearization. Similar sensitivity for this GPS/INS attitude estimation problem was found between the EKF and UKF for most cases. Small differences were seen between EKF and UKF for initialization error and GPS outages: the UKF was found to be more robust to inertial measurement unit calibration errors, and the EKF was determined to be more computationally efficient.

A comparative study of optical flow and traditional sensors in UAV navigation

Optical flows have great potential for navigation of small or micro unmanned aerial vehicles (UAVs) in GPS-degraded or GPS-denied environments, inspired by the study of the flight of several insects. This paper focuses on a comparative study between optical flow and traditional navigation sensors with validation provided through UAV flight tests. More specifically, optical flow calculated from videos is compared side-by-side with the corresponding combination of GPS velocity, range, and IMU measurements. Scale invariant feature transform (SIFT) algorithm is used to convert camera videos into optical flows due to its stability and robustness for feature extraction purposes. Four basic motions are analyzed through ground tests including two rotational and two translational motions, with rotation axis parallel/orthogonal to optical axis. The UAV flight data are used for comparisons of more general motions. The flight results show that the measured optical flow has a mean error of 1.10/1.16 pixel per frame and a standard deviation of 1.05/1.18 pixel per frame in the longitudinal/lateral direction for a 33.4 millisecond interval (29.97 Hz), using the corresponding combination of GPS/INS/range data as the ground truth.

On-line Modeling and Calibration of Low-Cost Navigation Sensors

In this paper, calibration modeling of a low-cost Inertial Measurement Unit (IMU) sensor for Small Unmanned Aerial Vehicle (SUAV) attitude estimation is considered. First, an Allan variance analysis method is used to determine stochastic noise model parameters for each sensor of a Micro-Electro-Mechanical-System (MEMS) IMU. Next, these models are included in a Global Positioning System/Inertial Navigation System (GPS/INS) sensor fusion algorithm for on-line calibration. In addition, an off-line magnetometer calibration is considered that uses a set of GPS/INS sensor fusion attitude estimates to derive a calibration model. This off-line magnetometer calibration model is then augmented on-line with sensor fusion estimates of the residual sensor biases. Finally, using the calibrated magnetometers, attitude estimation is considered that uses only a low-cost IMU with magnetometers. Each sensor fusion algorithm is formulated using an Unscented Kalman Filter (UKF). For performance validation, attitude estimates are calculated with data collected on-board a SUAV and are compared with high-quality vertical gyroscope measurements.

Robust UAV Relative Navigation With DGPS, INS, and Peer-to-Peer Radio Ranging

This paper considers the fusion of carrier-phase differential GPS (CP-DGPS), peer-to-peer ranging radios, and low-cost inertial navigation systems (INS) for the application of relative navigation of small unmanned aerial vehicles (UAVs) in close formation-flight. A novel sensor fusion algorithm is presented that incorporates locally processed tightly coupled GPS/INS-based absolute navigation solutions from each UAV in a relative navigation filter that estimates the baseline separation using integer-fixed relative CP-DGPS and a set of peer-to-peer ranging radios. The robustness of the dynamic baseline estimation performance under conditions that are typically challenging for CP-DGPS alone, such as a high occurrence of phase breaks, poor satellite visibility/geometry due to extreme UAV attitude, and heightened multipath intensity, amongst others, is evaluated using Monte Carlo simulation trials. The simulation environment developed for this work combines a UAV formation flight control simulator with a GPS constellation simulator, stochastic models of the inertial measurement unit (IMU) sensor errors, and measurement noise of the ranging radios. The sensor fusion is shown to offer improved robustness for 3-D relative positioning in terms of 3-D residual sum of squares (RSS) accuracy and increased percentage of correctly fixed phase ambiguities. Moreover, baseline estimation performance is significantly improved during periods in which differential carrier phase ambiguities are unsuccessfully fixed. Note to Practitioners-This paper was motivated by the need to enhance the robustness of CP-DGPS/INS relative navigation. In particular, small UAVs exhibit fast dynamics and are often subjected to large and quickly changing bank angles. This in turn induces missed satellite observations and changes in the phase ambiguity. This paper suggests leveraging the emergence of Ultra Wideband ranging radios to directly observe the baseline separation. In this paper, we outline the details of the algorithm implementation. We then use a simulation to show that adding UWB greatly helps to enhance the robustness of the carrier ambiguity integer-resolving algorithm, which is necessary for improved solution accuracy. This work has extensions to ground vehicles, ocean buoys, and space vehicles. In future work, we will experimentally validate results.

Avionics Design for a Sub-Scale Fault- Tolerant Flight Control Test-Bed

1. For carrying remote sensing or other scientific payloads. Highly publicized examples of such applications include the forest fire detection effort jointly conducted by NASA Ames research centre and the US Forest Service (Ambrosia et al., 2004), and the mission into the eye of hurricane Ophelia by an Aerosonde® UAV (Cione et al., 2008); 2. For evaluating different sensing and decision-making strategies as an autonomous vehicle. For examples, an obstacle and terrain avoidance experiment was performed at Brigham Young University to navigate a small UAV in the Goshen canyon (Griffiths et al., 2006); an autonomous formation flight experiment was performed at West Virginia University (WVU) with three turbine-powered UAVs (Gu et al., 2009); 3. As a sub-scale test bed to help solving known or potential issues facing full-scale manned aircraft. For example, a series of flight test experiments were performed at Rockwell Collins (Jourdan et al., 2010) with a sub-scale F-18 aircraft to control and recover the aircraft after wing damages. Another example is the X-48B blended wing body aircraft (Liebeck, 2004) jointly developed by Boeing and NASA to investigate new design concepts for future-generation transport aircraft.

Fusion of GPS and Redundant IMU Data for Attitude Estimation

Attitude estimation using Global Positioning System/Inertial Navigation System (GPS/INS) was used as an example application to study three different methods of fusing redundant multi-sensor data used in the prediction stage of a nonlinear recursive filter. Experimental flight data were collected with an Unmanned Aerial Vehicle (UAV) containing GPS position and velocity calculations and four redundant Inertial Measurement Unit (IMU) sensors. Additionally, the aircraft roll and pitch angles were measured directly with a high-quality mechanical vertical gyroscope to be used as a ‘truth’ reference for evaluating attitude estimation performance. A simple formulation of GPS/INS sensor fusion using an Extended Kalman Filter (EKF) was used to calculate the results for this study. Each of the three presented fusion methods was shown to be effective in reducing the roll and pitch errors as compared to corresponding results using single IMU GPS/INS sensor fusion. Additionally, the fusion methods were shown to be effective in estimating roll and pitch angles without the aid of GPS (dead reckoning).

Sensitivity Analysis of EKF and UKF in GPS/INS Sensor Fusion

This document presents a sensitivity analysis relative to different algorithm design parameters on the attitude performance of two different Global Positioning System/Inertial Navigation System (GPS/INS) sensor fusion algorithms for estimating aircraft attitude angles, namely the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF). The sensor fusion was performed using flight data acquired with three different WVU YF-22 research aircraft under a variety of flight conditions. The attitude estimates were compared with direct ‘truth’ measurements from an on-board mechanical vertical gyroscope. The sensitivity analysis was conducted on the following parameters: process and measurement noise covariance tuning, IMU and GPS sampling rates, GPS outages, time offset between GPS and IMU measurements, and acceleration due to gravity. Overall, the EKF and UKF performed very similarly in response to the different parameters for this study.

A Systematic Approach for Extended Kalman Filter Tuning and Low-Cost Inertial Sensor Calibration within a GPS/INS Application

*† ** This study presents two methods for enhancing the performance of the low-cost navigation solution based on a GPS and a Micro-Electro-Mechanical System (MEMS) Inertial Navigation System (INS). First, a novel inertial sensor calibration approach to improve dead reckoning performance for handling intermittent GPS coverage is presented. This approach models GPS corrections to the INS solution during the Extended Kalman Filter (EKF) based sensor fusion process, by extracting a stochastic measurement bias model of the rate gyros within a Inertial Measurement Unit (IMU). The calibrated INS is then validated with an independent flight data set, and shows improved dead reckoning performance with no GPS information. The second approach presents a systematic method for tuning the noise characteristics modeled within an EKF based GPS/INS sensor fusion algorithm. This approach uses the calibration model derived within the first approach to fine-tune the process-noise characteristics, along with a simplistic method for tuning GPS noise characteristics that is based on the number of GPS satellites available during the measurement. The results show that both approaches lead to an increase in estimation performance within EKF based GPS/INS sensor fusion.