Novel quaternion Kalman filter

Choukroun, Daniel; Bar-Itzhack, Itzhack Y.; Oshman, Yaakov

doi:10.1109/taes.2006.1603413

Cited by 290 publications

(115 citation statements)

References 10 publications

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“…Cohen 1996;Crassidis and Markley 1997;Bar-Itzhach et al 1998;Li et al 2002) and (2) stochastic filtering algorithms (e.g. Ward and Axelrad 1996;Chun and Park 2001;Choukroun 2002). There are two types of point estimation algorithms.…”

Section: Introductionmentioning

confidence: 99%

On-the-fly GPS-based attitude determination using single- and double-differenced carrier phase measurements

Zhang

Roberts

et al. 2004

GPS Solutions

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Carrier phase measurements are primary observations for GPS attitude determination. Although the satellite-related errors can be virtually eliminated by forming single differences, the baseline-related errors such as line biases are still present in the single-differenced carrier phase measurements. It is, therefore, difficult to resolve the single-differenced integer ambiguities due to the line biases. By forming double differences, the line biases of the single-differenced carrier phase measurements can be effectively removed. However, the main disadvantages of this method lie in the fact that the double-differenced measurements are mathematically correlated and consequently the attitude obtained from the double differences is noisy. This paper presents a new algorithm through which both single and double differences are used simultaneously to resolve these problems in realtime. The solution of the integer ambiguities can be obtained by searching for the most likely grid point in the attitude domain that is independent of the correlation with the double differences. Next, the line biases and corresponding single difference integer ambiguities can be resolved on the fly by using the noisy attitude solution obtained from the previous double difference procedure. In addition, the relationship between the physical signal path difference and the line bias is formed. A new method is also applied to derive the attitude angles through finding the optimal solution of the attitude matrix element. The proposed new procedure is validated using ground and flight tests. Results have demonstrated that the new algorithm is effective and can satisfy the requirement of real-time applications.

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Section: Introductionmentioning

confidence: 99%

On-the-fly GPS-based attitude determination using single- and double-differenced carrier phase measurements

Zhang

Roberts

et al. 2004

GPS Solutions

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“…, (3) normalizing the state vector at the end of each update step [5]. The first two methods result in non-linear measurement models, which defeats our purpose of developing equations for a truly linear filter.…”

Section: Kalman Filter Equationsmentioning

confidence: 99%

“…As a result in this work, we focus on deriving a linear update model to estimate SE(3) elements. Chaukron et al [5] come closest to our work in terms of formulating a linear update model, but they only estimate the SO(3) element. In this work, we start with a non-linear update model, and using multiple sensor measurements simultaneously, we rearrange the update model into a linear form.…”

Section: Introductionmentioning

confidence: 97%

“…State dependent measurement uncertainties have been used in systems for satellite tracking [27] and robot navigation [28]. We use an approach similar to [27], [5] to formulate the expressions for the state dependent measurement uncertainties. It should be noted that the measurement uncertainties have a linear dependence on their state vector, which allows for derivation of exact expressions of uncertainties [14].…”

Section: Introductionmentioning

confidence: 99%

“…The extended Kalman filter (EKF) and unscented Kalman filter (UKF) have been used to estimate SE(3) elements for satellite orientation [27], manipulation [18], registration [24,21] and sensor calibration [9]. EKF based filters perform first-order linear approximations of the non-linear update models and produce estimates which are known to diverge in the presence of high initial estimation errors [5]. UKF based methods do not linearize the models but instead require evaluation at multiple specially chosen points (called sigma points), which can be expensive for a high-dimensional system such as SE(3).…”

Section: Introductionmentioning

confidence: 99%

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Estimating SE(3) elements using a dual quaternion based linear Kalman filter

Srivatsan¹,

Rosen²,

Mohamed³

et al.

Robotics: Science and Systems XII

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Abstract-Many applications in robotics such as registration, object tracking, sensor calibration, etc. use Kalman filters to estimate a time invariant SE(3) element by locally linearizing a non-linear measurement model. Linearization-based filters tend to suffer from inaccurate estimates, and in some cases divergence, in the presence of large initialization errors. In this work, we use a dual quaternion to represent the SE(3) element and use multiple measurements simultaneously to rewrite the measurement model in a truly linear form with state dependent measurement noise. Use of the linear measurement model bypasses the need for any linearization in prescribing the Kalman filter, resulting in accurate estimates while being less sensitive to initial estimation error. To show the broad applicability of this approach, we derive linear measurement models for applications that use either position measurements or pose measurements. A procedure to estimate the state dependent measurement uncertainty is also discussed. The efficacy of the formulation is illustrated using simulations and hardware experiments for two applications in robotics: rigid registration and sensor calibration.

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Single and Multiple Sensor Networking for Gait Analysis

2020

Body Sensor Networking, Design and Algorithms

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Novel quaternion Kalman filter

Cited by 290 publications

References 10 publications

On-the-fly GPS-based attitude determination using single- and double-differenced carrier phase measurements

On-the-fly GPS-based attitude determination using single- and double-differenced carrier phase measurements

Estimating SE(3) elements using a dual quaternion based linear Kalman filter

Single and Multiple Sensor Networking for Gait Analysis

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