This paper studies the role of stochastic volatility in a setting where housing serves as an important propagation mechanism. After showing time-varying volatility in US house prices, we estimate a dynamic stochastic general equilibrium model with housing, financial frictions, and stochastic volatility using a nonlinear approximation and Bayesian econometric techniques. Incorporating stochastic volatility into the model greatly improves model fit and accounts for approximately half of the increased volatility in house prices observed during the Great Recession. Increased stochastic volatility escalates uncertainty which has significant effects on macroeconomic variables. While uncertainty in most sectors has negative effects on the economy, uncertainty on collateral constraints has the largest role. Unlike other uncertainty shocks, the housing demand uncertainty creates positive spillovers in the economy. Credit conditions, adjustment costs of capital and housing, and monetary policy are important transmission mechanisms for the stochastic volatility shocks.

In this paper we develop the nonlinear motion equations in terms of the true anomaly varying Tschauner–Hempel equations relative to a notional orbiting particle in a Keplerian orbit, relatively close to an orbiting primary satellite to estimate the position of a spacecraft. A second orbiting body in Earth orbit relatively close to the first is similarly modelled. The dynamic relative motion models of the satellite and the second orbiting body, both of which are modelled in terms of independent relative motion equations, include several perturbing effects, such as the asymmetry of the Earth gravitational field resulting in the Earth's oblateness effect and the third body accelerations due to the Moon and the Sun. Linear control laws are synthesised for the primary satellite using the transition matrix so it can rendezvous with the second orbiting body. The control laws are then implemented using the state estimates obtained earlier to validate the feedback controller. Thus, we demonstrate the application of a Linear Quadratic Nonlinear Gaussian (LQNG) design methodology to the satellite rendezvous control design problem and validate it.