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,

NASA's two Mars Exploration Rovers ͑MER͒ have successfully demonstrated a robotic Visual Odometry capability on another world for the first time. This provides each rover with accurate knowledge of its position, allowing it to autonomously detect and compensate for any unforeseen slip encountered during a drive. It has enabled the rovers to drive safely and more effectively in highly sloped and sandy terrains and has resulted in increased mission science return by reducing the number of days required to drive into interesting areas. The MER Visual Odometry system comprises onboard software for comparing stereo pairs taken by the pointable mast-mounted 45 deg FOV Navigation cameras ͑NAVCAMs͒. The system computes an update to the 6 degree of freedom rover pose ͑x, y, z, roll, pitch, yaw͒ by tracking the motion of autonomously selected terrain features between two pairs of 256ϫ 256 stereo images. It has demonstrated good performance with high rates of successful convergence ͑97% on Spirit, 95% on Opportunity͒, successfully detected slip ratios as high as 125%, and measured changes as small as 2 mm, even while driving on slopes as high as 31 deg. Visual Odometry was used over 14% of the first 10.7 km driven by both rovers. During the first 2 years of operations, Visual Odometry evolved from an "extra credit" capability into a critical vehicle safety system. In this paper we describe our Visual Odometry algorithm, discuss several driving strategies that rely on it ͑including Slip Checks, Keep-out Zones, and Wheel Dragging͒, and summarize its results from the first 2 years of operations on Mars.

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In this paper a novel approach is developed for relative navigation and attitude estimation of spacecraft flying in formation. The approach uses information from an optical sensor, which employs relatively simple electronic circuits with modest digital signal processing requirements, to provide multiple line-of-sight vectors from spacecraft to another. The sensor mechanism is well suited for both near-Earth and deep space applications since it is fully independent of any external systems. The line-of-sight measurements are coupled with gyro measurements and dynamical models in an extended Kalman filter to determine relative attitude, position and gyro biases. The quaternion is used to describe the relative kinematics and general relative orbital equations are used to describe the positional dynamics. Simulation results indicate that the combined sensor/estimator approach provides accurate relative position and attitude estimates.

[1] The size-frequency distributions of rocks >1.5 m diameter fully resolvable in High Resolution Imaging Science Experiment (HiRISE) images of the northern plains follow exponential models developed from lander measurements of smaller rocks and are continuous with rock distributions measured at the landing sites. Dark pixels at the resolution limit of Mars Orbiter Camera thought to be boulders are shown to be mostly dark shadows of clustered smaller rocks in HiRISE images. An automated rock detector algorithm that fits ellipses to shadows and cylinders to the rocks, accurately measured (within 1-2 pixels) rock diameter and height (by comparison to spacecraft of known size) of $10 million rocks over >1500 km 2 of the northern plains. Rock distributions in these counts parallel models for cumulative fractional area covered by 30-90% rocks in dense rock fields around craters, 10-30% rock coverage in less dense rock fields, and 0-10% rock coverage in background terrain away from craters. Above $1.5 m diameter, HiRISE resolves the same population of rocks seen in lander images, and thus size-frequency distributions can be extrapolated along model curves to estimate the number of rocks at smaller diameters. Extrapolating sparse rock distributions in the Phoenix landing ellipse indicate <1% chance of encountering a potentially hazardous rock during landing or that could impede the opening of the solar arrays. Extrapolations further suggest rocks large enough to depress the ground ice table and small enough to be picked up or pushed by the robotic arm should be present within reach for study after landing.

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