This paper provides a survey of modern nonlinear filtering methods for attitude estimation. Early applications relied mostly on the extended Kalman filter for attitude estimation. Since these applications, several new approaches have been developed that have proven to be superior to the extended Kalman filter. Several of these approaches maintain the basic structure of the extended Kalman filter, but employ various modifications in order to provide better convergence or improve other performance characteristics. Examples of such approaches include: filter QUEST, extended QUEST and the backwards-smoothing extended Kalman filter. Filters that propagate and update a discrete set of sigma points rather than using linearized equations for the mean and covariance are also reviewed. A twostep approach is discussed with a first-step state that linearizes the measurement model and an iterative second step to recover the desired attitude states. These approaches are all based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance. Other approaches that do not require this assumption are reviewed, Associate Professor, Department of Mechanical & Aerospace Engineering. Email: johnc@eng.buffalo.edu. Associate Fellow AIAA. Aerospace Engineer, Guidance, Navigation and Control Systems Engineering Branch. Email: Landis.Markley@nasa.gov. Fellow AIAA. Postdoctoral Research Fellow, Department of Mechanical & Aerospace Engineering. Email: cheng3@eng.buffalo.edu. Member AIAA.

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Survey of nonlinear attitude estimation methods

The quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation. The quaternion must obey a unit norm constraint, though, which has led to the development of an extended Kalman filter using a quaternion for the global attitude estimate and a three-component representation for attitude errors. We consider various attitude error representations for this Multiplicative Extended Kalman Filter and its second-order extension.

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Attitude Error Representations for Kalman Filtering

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This article develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter truncates the probability density function (PDF) of the Kalman filter estimate at the known constraints and then computes the constrained filter estimate as the mean of the truncated PDF. The incorporation of state variable constraints increases the computational effort of the filter but also improves its estimation accuracy. The improvement is demonstrated via simulation results obtained from a turbofan engine model. It is also shown that the truncated Kalman filter may provide a more accurate way of incorporating inequality constraints than other constrained filters (e.g. the projection approach to constrained filtering).

/pdf/constrained-kalman-filtering-via-density-function-truncation-253hoh34a8.pdf

Constrained Kalman filtering via density function truncation for turbofan engine health estimation

A method and system senses the attitude of an accelerating object by measuring acceleration with accelerometers in three orthogonal axes and measuring angular rate with angular rate sensors disposed about each such axis to compute attitude of the object accurately relative to a vertical axis. A processor updates a quaternion representation of attitude based upon the angular rate of the object, and a corrective rate signal is determined from level frame acceleration as a reference for a Kalman filter in calculating the attitude of the object. When velocity or airspeed is available from an external source, an aiding algorithm is employed to provide accurate attitude representations throughout all flight regimes.

Dynamic attitude measurement method and apparatus

Adetailed survey ispresentedoftheliteratureonattituderepresentationdatingfromtheearlyworkofEulerand Hamilton to recent publications in e elds such as navigation and control. The scope is limited to the development of the aircraft kinematic transformation equations in terms of four different attitude representations, including the well-known Euler angles, the Euler-axis rotation parameters, the direction cosines, and the Euler ‐Rodrigues quaternion.Theemphasisisdirectedattheapplicationofthequaternionformulationtoaircraftkinematics.Results are presented that reinforce observations that the quaternion formulation, typically implemented to eliminate singularities associated with the Euler angle formulation, is far superior to the other commonly used formulations based on computational efe ciency alone. A development of quaternion constraints necessary to independently constrain roll, pitch, yaw, bank angle, elevation angle, and/or azimuth angle is presented. For verie cation of simulation codes, a general closed-form solution to the quaternion formulation, for the case of constant rotation, is also presented. Additionally, a discussion is provided of numerical integration methods and numerical errors for the quaternion formulation. This discussion is especially important for simulations that may still utilize a common error reduction scheme originally developed for analog computers.

Review of Attitude Representations Used for Aircraft Kinematics

The stringent attitude determination accuracy and faster slew maneuver requirements demanded by present-day spacecraft control systems motivate the development of recursive nonlinear filters for attitude estimation. This paper presents the second-order filter development for the estimation of attitude quaternion using three-axis gyro and star tracker measurement data. Performance comparisons have been made by computer simulation of system models and filter mechanization. It is shown that the second-order filter consistently performs better than the extended Kalman filter when the performance index of the root sum square estimation error of the quaternion vector is compared. The second-order filter identifies the gyro drift rates faster than the extended Kalman filter. The uniqueness of this algorithm is the online generation of the time-varying process and measurement noise covariance matrices, derived as a function or the process and measurement nonlinearity, respectively.

Spacecraft attitude determination using a second-order nonlinear filter

Denoising the CT images removes noise from the CT images and so makes the disease diagnosis procedure more efficient. The denoised images have a notable level of raise in its PSNR values, ensuring a smoother image for diagnosis purpose. In the previous work, a CT image denoising technique using window-based Multi-wavelet transformation and thresholding has been proposed. The performance of the technique has been improved by Genetic Algorithm (GA)-based window selection methodology. However, in the perspective of diagnosis, the PSNR values have not much significance; instead they rely on the quality of the images in the perspective of medical diagnosis. In this paper, a quality enhancement methodology is proposed to include in the CT image denoising technique using window-based multi-wavelet transformation and thresholding. The methodology is comprised of an edge detection technique based on canny algorithm that is performed on the gradient images so that the images are visualized better for diagnosis. A pair of micro block set is generated from the edge detected image and it is subjected to unsharp filter to obtain a sharper image. The smoothness of the image is improved by applying Gaussian filter to the sharper image. Implementation results are given to demonstrate the superior performance of the proposed quality enhancement technique over various CT images in terms of medical perspective.

CT Image Denoising Technique using GA aided Window-based Multiwavelet Transformation and Thresholding with the Incorporation of an Effective Quality Enhancement Method

Image denoising is one of the most significant tasks in image processing, analysis and image processing applications. Medical Imaging is one among the emerging application areas where the image denoising plays a vital role. In medical imaging, the acquisition techniques and systems introduce noises and artifacts in the medical image that leads to poor quality image. In this occasion, image denoising is an essential pre-requisite, especially in Computed Tomography, which is an important and most common modality in medical imaging. The significance of the denoising is mainly due to that the effectiveness of clinical diagnosis using CT image depends upon the quality of the image. In this paper, we propose an efficient noise reduction technique for CT images using window-based Multi-wavelet transformation and thresholding. The technique removes Additive white Gaussian noise from the CT images as well as it enhances the quality of the images. The proposed technique consists of three different stages of processing, namely, window-based multi-wavelet transformation and thresholding, reconstruction and quality enhancement. In the first two processes, the AWGN is effectively removed from CT images and the images are reconstructed. In the third process, the quality of the images is enhanced by means of filtering techniques. Hence, denoised and quality enhanced CT images can be obtained using the proposed multi-wavelet based denoising technique.

An Efficient Denoising Technique for CT Images using Window- based Multi-Wavelet Transformation and Thresholding

The problem of tactical missile guidance is very challenging and has been treated using several basic metlfodologies in the past four decades. Major techniques can be grouped under classical guidance laws, modern guidance laws, l'aws for manoeuvring targets, predictive guidance for endgame scenario, and guidance laws based on intelligent control methods. Each technique has some advantages and disadvantages while implementing in a practical system. Guidance law selection is dictated by nature of flight profile like boost, midcourse, terminal homing, etc, and also miss-distance and a single-shot kill probability. This paper presents a brief survey of the existing techniques and current trends in tactical missile guidance.

http://publications.drdo.gov.in/ojs/index.php/dsj/article/download/1991/1028

Current Trends in Tactical Missile Guidance

Image denoising is getting more significance, especially in Computed Tomography (CT), which is an important and most common modality in medical imaging. This is mainly due to that the effectiveness of clinical diagnosis using CT image lies on the image quality. The denoising technique for CT images using window-based Multi-wavelet transformation and thresholding shows the effectiveness in denoising, however, a drawback exists in selecting the closer windows in the process of window-based multi-wavelet transformation and thresholding. Generally, the windows of the duplicate noisy image that are closer to each window of original noisy image are obtained by the checking them sequentially. This leads to the possibility of missing out very closer windows and so enhancement is required in the aforesaid process of the denoising technique. In this paper, we propose a GA-based window selection methodology to include the denoising technique. With the aid of the GA-based window selection methodology, the windows of the duplicate noisy image that are very closer to every window of the original noisy image are extracted in an effective manner. By incorporating the proposed GA-based window selection methodology, the denoising the CT image is performed effectively. Eventually, a comparison is made between the denoising technique with and without the proposed GA-based window selection methodology.

S. Vathsal

Papers

Spacecraft attitude determination using a second-order nonlinear filter

CT Image Denoising Technique using GA aided Window-based Multiwavelet Transformation and Thresholding with the Incorporation of an Effective Quality Enhancement Method

An Efficient Denoising Technique for CT Images using Window- based Multi-Wavelet Transformation and Thresholding

Current Trends in Tactical Missile Guidance

A GA based Window Selection Methodology to Enhance Window based Multi wavelet transformation and thresholding aided CT image denoising technique