Extended Kalman Filter vs. Error State Kalman Filter for Aircraft Attitude Estimation

Madyastha, Venkatesh; Ravindra, Vishal Cholapadi; Mallikarjunan, Srinath; Goyal, Anup

doi:10.2514/6.2011-6615

Cited by 92 publications

(61 citation statements)

References 41 publications

(51 reference statements)

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“…In this work, we focus on the Error-State Kalman Filter (ESKF), also found under the name of Indirect Kalman Filter [23,25]. [32,37] reviews the application of ESKF for AD and highlights its advantages as: i) the error-state uses a minimal parametrization, in form of rotation vector, for the rotation. Thus, redundancy issues related to the unit-norm constraint is avoided, preventing also possible singularity risks during the covariance matrix estimation.…”

Section: Eskf -Float Estimationmentioning

confidence: 99%

Attitude Determination via GNSS Carrier Phase and Inertial Aiding

Medina¹,

Centrone²,

Ziebold³

et al. 2019

Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 201

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Attitude Determination (AD) constitutes an important navigation component for vehicles that require orientation information, such as spacecraft or ships. Global Navigation Satellite Systems (GNSS) enable resolving the orientation of a vehicle in a precise and absolute manner, by employing a setup of multiple GNSS antennas rigidly mounted onboard the tracked vehicle. To achieve high-precision attitude estimation based on GNSS, the use of carrier phase observations becomes indispensable, with the consequent added complexity of resolving the integer ambiguities. The use of inertial aiding has been extensively exploited for AD, since it enables tracking fast rotation variations and bridging short periods of GNSS outage. In this work, the fusion of inertial and GNSS information is exploited within the recursive Bayesian estimation framework, applying an Error State Kalman Filter (ESKF). Unlike common Kalman Filters, ESKF tracks the error or variations in the state estimate, posing meaningful advantages for AD. On the one hand, ESKF represents attitude using a minimal state representation, in form of rotation vector, avoiding attitude constraints and singularity risks on the covariance matrix estimates. On the other hand, second-order products on the derivation of the Jacobian matrices can be neglected, since the errorstate operates always close to zero. This work details the procedure of recursively estimating the attitude based on the fusion of GNSS and inertial sensing. The GNSS attitude model is parametrized in terms of quaternion rotation, and the overall three-steps AD procedure (float estimation, ambiguity resolution and solution fixing) is presented. The method performance is assessed on a Monte Carlo simulation, where different noise levels, number of satellites and baseline lengths are tested. The results show that the inertial aiding, along with a constrained attitude model for the float estimation, significantly improve the performance of attitude determination compared to classical unaided baseline tracking.Traditionally, the GNSS compass model relates the double difference observations to the baseline vectors relating the antennas, expressed in the global frame. The use of this model in combination with the standard LAMBDA method has been often applied for AD [6][7][8][9]. However, classical LAMBDA is not designed for AD, due to the nonlinear constraints related to the prior knowledge of the distance and relative orientation between the antennas [10]. Aiming to improve LAMBDA for GNSS carrier phase-based AD, Teunissen and Giorgi introduced the Constrained-LAMBDA (C-LAMBDA) and the Multivariate Constrained-LAMBDA (MC-LAMBDA) methods. First, C-LAMBDA modifies the original LAMBDA method introducing the information on the baseline length as a constraint, exploited during the process of AR and solution fixing [11][12][13]. Although C-LAMBDA is shown to provide significant improvement against classical LAMBDA, additional information on the relative orientation between antennas is not included. In MC-LAMBDA, the...

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Section: Eskf -Float Estimationmentioning

confidence: 99%

Attitude Determination via GNSS Carrier Phase and Inertial Aiding

Medina¹,

Centrone²,

Ziebold³

et al. 2019

Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 201

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“…Error-state Kalman filter a) Nominal-state propagation: The nominal state is propagated according to (16) with all perturbation impulses {v i , θ i , a i , ω i } set to zero. b) Error-state KF prediction: The error-state system (14) can be posed as…”

Section: A Extended Kalman Filtermentioning

confidence: 99%

“…They are summarized hereafter. First, we implement extended (EKF) and error-state (ESKF) Kalman filters [16]. Second, we express the orientation errors of ESKF both in local (LE) and global (GE) frames [17].…”

Section: Introductionmentioning

confidence: 99%

High-frequency MAV state estimation using low-cost inertial and optical flow measurement units

Santamaria-Navarro

Solà

Andrade‐Cetto

2015

2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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Abstract-This paper develops a simple and low-cost method for 3D, high-rate vehicle state estimation, specially designed for free-flying Micro Aerial Vehicles (MAVs). We fuse observations from inertial measurement units and the recently appeared lowcost optical flow smart cameras. These smart cameras integrate a sonar altimeter, a triaxial gyrometer and an optical flow sensor, and directly provide metric ego-motion information in the form of body velocities and altitude. Compared to stateof-the-art visual-inertial odometry methods, we are able to drastically reduce the computational load in the main processor unit, and obtain an accurate estimation of the vehicle state at a high update rate of 100Hz. We thus extend the current use of these smart cameras from hovering purposes to odometry estimation. In order to propose a simple algorithmic solution, we investigate the performances of two Kalman filters, in the extended and error-state flavors, alongside a large number of algorithm variations, using simulations and real experiments with precise ground-truth. We observe that the marginal performance gain attained with these algorithm improvements does not pay for the effort of implementing them. We conclude that a classical EKF in its simplest form is sufficient for providing motion estimates that coherently exploit the available measurements.

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“…In effect, the Kalman filter uses a model of the system to filter measurements of states that are measured and to observe states that are not measured. 3,7,10,14 The input to the system is typically modeled as a combination of an unknown stochastic signal and a known deterministic signal. When the Kalman filter is used within the context of LQG control, the deterministic signal is injected numerically into the Kalman filter in order to take advantage of the separation principle.…”

Section: Introductionmentioning

confidence: 99%

Retrospective-Cost-Based Adaptive State Estimation and Input Reconstruction for a Maneuvering Aircraft with Unknown Acceleration

Gupta

D’Amato

Ali

et al. 2012

AIAA Guidance, Navigation, and Control Conference

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A method is presented to obtain state estimates for a possibly nonminimum-phase system in the presence of unknown harmonic inputs. The method estimates the states and reconstructs the unknown harmonic input. An adaptive feedback model injects an input into the estimator such that the error between the estimator output and the actual output converges to zero despite the presence of the unknown harmonic input. Using input reconstruction based on a retrospective cost, the unknown harmonic input is reconstructed. Using the reconstructed input, the parameters of the adaptive feedback system are updated using recursive least squares. Results are presented for a rigid body, a damped rigid body, and a 2D missile with a three-loop autopilot topology.

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Extended Kalman Filter vs. Error State Kalman Filter for Aircraft Attitude Estimation

Cited by 92 publications

References 41 publications

Attitude Determination via GNSS Carrier Phase and Inertial Aiding

Attitude Determination via GNSS Carrier Phase and Inertial Aiding

High-frequency MAV state estimation using low-cost inertial and optical flow measurement units

Retrospective-Cost-Based Adaptive State Estimation and Input Reconstruction for a Maneuvering Aircraft with Unknown Acceleration

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