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

AIAA Guidance, Navigation, and Control Conference

Gross

et al. 2012

Self Cite

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). NomenclatureA = state prediction Jacobian matrix a x , a y , a z = acceleration in aircraft body frame (m/s 2 ) f = state prediction function g = acceleration due to gravity (m/s 2 ) H = observation matrix I = identity matrix K = Kalman gain matrix k = discrete time index P = state covariance matrix p = roll rate (deg/s) Q = process noise covariance matrix q = pitch rate (deg/s) R = measurement noise covariance matrix r = yaw rate (deg/s) T = averaging time (s) T s = sampling time (s) u = input vector v = measurement noise vector V x , V y , V z = local components of velocity (m/s) W = random walk coefficient w = process noise vector x = state vector y = output vector z = measurement vector 2 θ = pitch angle (deg) σ A = root Allan variance ϕ = roll angle (deg) ψ = yaw angle (deg)

Section: Introductionmentioning

confidence: 99%

Fusion of GPS and Redundant IMU Data for Attitude Estimation

AIAA Guidance, Navigation, and Control Conference

Gross

et al. 2012

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“…Therefore, the input vector is given by (11) where û is the measured input vector, and b is a vector of sensor biases which follow a first order Gauss-Markov noise model as determined in [32].…”

Section: Optical Flow and Ins Integrationmentioning

confidence: 99%

“…The parameters of the Gauss-Markov noise model for the bias states were determined in [32] for the considered research platform.…”

Section: B Determination Of Noise Assumptionsmentioning

confidence: 99%

Wide-field optical flow aided inertial navigation for unmanned aerial vehicles

2014 IEEE/RSJ International Conference on Intelligent Robots and Systems

Huo

2014

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Low-cost navigation can be performed for aircraft using the integration of Inertial Navigation System (INS) information in conjunction with a regulatory information source, such as Global Position System (GPS). For situations where GPS is unavailable, it is desirable to have an alternative information source in order to regulate the known drifting phenomenon experienced by INS. In this paper, the use of wide-field optical flow is explored to regulate INS drift for the purpose of GPS-denied navigation. An Unscented Information Filter (UIF) algorithm for Unmanned Aerial Vehicle (UAV) velocity and attitude estimation is proposed and evaluated with experimental flight data. The results demonstrate that the new filtering algorithm is capable of estimating the vehicle speed with approximately 1.4 m/s of error and regulating attitude errors to within 1.5 degrees standard deviation of error for both roll and pitch angles.

“…The use of diverse flight data, along with the availability of independent "truth" measurements, provides a realistic and quantifiable evaluation of estimation algorithms. This paper presents a continuation of previous GPS/INS sensor fusion research conducted at WVU [24][25][26][27][28]. Early work on this topic involved a baseline comparison of a single GPS/INS formulation using an EKF, an UKF, and a particle filter on a single set of flight data [24].…”

Section: Introductionmentioning

confidence: 97%

“…Using this same data set, different methods of computing the matrix square root were compared for the UKF [27]. The calibration and error modeling of low-cost navigation sensors was also studied for use within GPS/INS sensor fusion applications [28]. The present study further investigates the differences between the EKF and UKF for attitude state estimation using three GPS/INS sensor fusion formulations, two of which had not been previously considered by the authors.…”

Section: Introductionmentioning

confidence: 98%

Sensitivity Analysis of Extended and Unscented Kalman Filters for Attitude Estimation

Journal of Aerospace Information Systems

Gross

et al. 2013

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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 compared with independent measurements from a mechanical 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.