Novel quaternion Kalman filter

This paper presents a novel Kalman filter (KF) for estimating the attitude-quaternion as well as gyro random drifts from vector measurements. Employing a special manipulation on the measurement equation results in a linear pseudo-measurement equation whose error is state-dependent. Because the quaternion kinematics equation is linear, the combination of the two yields a linear KF that eliminates the usual linearization procedure and is less sensitive to initial estimation errors. General accurate expressions for the covariance matrices of the system state-dependent noises are developed. In addition, an analysis shows how to compute these covariance matrices efficiently. An adaptive version of the filter is also developed to handle modeling errors of the dynamic system noise statistics. Monte-Carlo simulations are carried out that demonstrate the efficiency of both versions of the filter. In the particular case of high initial estimation errors, a typical extended Kalman filter (EKF) fails to converge whereas the proposed filter succeeds.     

Subsurface Water Oceans on Icy Satellites: Chemical Composition and Exchange Processes

The state of knowledge about the structure and composition of icy satellite interiors has been significantly extended by combining direct measurements from spacecraft, laboratory experiments, and theoretical modeling. The existence of potentially habitable liquid water reservoirs on icy satellites is dependent on the radiogenic heating of the rock component, additional contributions such as the dissipation of tidal energy, the efficiency of heat transfer to the surface, and the presence of substances that deplete the freezing point of liquid water. This review summarizes the chemical evolution of subsurface liquid water oceans, taking into account a number of chemical processes occuring in aqueous environments and partly related to material exchange with the deep interior. Of interest are processes occuring at the transitions from the liquid water layer to the ice layers above and below, involving the possible formation of clathrate hydrates and high-pressure ices on large icy satellites. In contrast, water-rock exchange is important for the chemical evolution of the liquid water layer if the latter is in contact with ocean floor rock on small satellites. The composition of oceanic floor deposits depends on ambient physical conditions and ocean chemistry, and their evolutions through time. In turn, physical properties of the ocean floor affect the circulation of oceanic water and related thermal effects due to tidally-induced porous flow and aqueous alteration of ocean floor rock.     

Kalman filtering for matrix estimation

A general discrete-time Kalman filter (KF) for state matrix estimation using matrix measurements is presented. The new algorithm evaluates the state matrix estimate and the estimation error covariance matrix in terms of the original system matrices. The proposed algorithm naturally fits systems which are most conveniently described by matrix process and measurement equations. Its formulation uses a compact notation for aiding both intuition and mathematical manipulation. It is a straightforward extension of the classical KF, and includes as special cases other matrix filters that were developed in the past. Beyond the analytical value of the matrix filter, it is shown through various examples arising in engineering problems that this filter can be computationally more efficient than its vectorized version.     

Phase Behaviour of Ices and Hydrates

The primary volatile ‘rock-forming’ minerals in the icy satellites of the outer solar system include water-ice and various hydrated crystals of methane and ammonia. The rich polymorphism of these substances as a function of pressure and temperature are described in this chapter. This polymorphism has a fundamental influence on the exchange of mass and energy between the core and the surface of icy satellites. We describe the current state-of-the-art in our understanding of the high pressure phase behaviour and the measurements of thermoelastic and transport properties of these substances. In addition we describe the structures and properties of hydrated phases of methanol, sulfuric acid, and various sulfate salts.