Identification Theory for Time Varying Models

The identification of time-varying coefficient regression models is investigated using an analysis of the classical information matrix. The variable coefficients are characterized by autoregressive stochastic processes, allowing the entire model to be case in state space form. Thus the unknown stochastic specification parameters and priors can be interpreted in terms of the coefficient matrices and initial state vector. Concentration of the likelihood function on these quantities allows the identification of each to be considered separately. Suitable restriction of the form of the state space model, coupled with the concept of controllability, lead to sufficient conditions for the identification of the coefficient transition parameters. Partial identification of the variance-covariance matrix for the random disturbances on the coefficients is established in a like manner. Introducing the additional concept of observability then provides for necessary and sufficient conditions for identification of the unknown priors. The results so obtained are completely analogous to those already established in the econometric literature, namely, that the coefficients of the reduced form are always identified subject to the absence of multicollinearity. Some consistency results are also presented which derive from the above approach.

On the Identification of Time Varying Structures

The identifiability of reduced form econometric models with variable coefficients is investigated using the control theoretic concepts of uniform complete observability and uniform complete controllability. First, a variant of the state space representation of the traditional reduced form is introduced which transcribes the underlying non-stationary estimation problem into one particularly suited to a Kalman filtering solution. Using such a formulation, observability and controllability can be called upon to obtain a necessary and sufficient condition for identification of the specific parameterization. The results so obtained are completely analogous to those already established in the econometric literature, namely, that the parameters of the reduced form are always identified subject to the absence of multicollinearity(referred to as "persistent excitation" in the control literature). How-ever, now the multicollinearity condition is seen to depend on the structure of the parameter variations as well as the statistical nature of the explanatory variables. The verification of identifiability thus reduces to a check for uniform complete observability which can always be affected in econometric applications. Some consistency results are also presented which derive from the above approach.

A Note on Optimal Smoothing for Time Varying Coefficient Problems

An algorithm is presented which provides a complete solution to the optimal estimation problem for time-varying parameters when no proper prior distribution is specified. The key ideas involve a combination of the information-form Kalman filter with the two-filter interpretation of the optimal smoother. The algorithm produces efficient estimates of the parameter trajectories over the entire sample, arid is equally applicable when a proper prior distribution has been specified.

An investigation of the facsimile camera response to object motion

A general analytical model of the facsimile camera response to object motion is derived as an initial step toward characterizing the resulting image degradation. This model expresses the spatial convolution of a time-varying object radiance distribution and camera point-spread function for each picture element in the image. Time variations and these two functions during each convolution account for blurring of small image detail, and variations between, as well as during, successive convolutions account for geometric image distortions. If the object moves beyond the angular extent of several picture elements while it is being imaged, then geometric distortion tends to dominate blurring as the primary cause of image degradation. The extent of distortion depends not only on object size and velocity but also on the direction of object motion, and is therefore difficult to classify in a general sense

Optical analysis of a compound quasi-microscope for planetary landers

A quasi-microscope concept, consisting of facsimile camera augmented with an auxiliary lens as a magnifier, was introduced and analyzed. The performance achievable with this concept was primarily limited by a trade-off between resolution and object field; this approach leads to a limiting resolution of 20 microns when used with the Viking lander camera (which has an angular resolution of 0.04 deg). An optical system is analyzed which includes a field lens between camera and auxiliary lens to overcome this limitation. It is found that this system, referred to as a compound quasi-microscope, can provide improved resolution (to about 2 microns ) and a larger object field. However, this improvement is at the expense of increased complexity, special camera design requirements, and tighter tolerances on the distances between optical components

Prediction of Viking lander camera image quality

Formulations are presented that permit prediction of image quality as a function of camera performance, surface radiance properties, and lighting and viewing geometry. Predictions made for a wide range of surface radiance properties reveal that image quality depends strongly on proper camera dynamic range command and on favorable lighting and viewing geometry. Proper camera dynamic range commands depend mostly on the surface albedo that will be encountered. Favorable lighting and viewing geometries depend mostly on lander orientation with respect to the diurnal sun path over the landing site, and tend to be independent of surface albedo and illumination scattering function. Side lighting with low sun elevation angles (10 to 30 deg) is generally favorable for imaging spatial details and slopes, whereas high sun elevation angles are favorable for measuring spectral reflectances

Molecular gas temperature and density in spiral galaxies

We combine beam-matched CO-13, CO-12 J = 3 yields 2 and J = 2 yields 1 line data to infer the molecular gas excitation conditions in the central 500 to 1600 pc diameters of a small sample of infrared-bright external galaxies: NGC253, IC342, M 83, Maffei 2, and NGC6946. Additional observations of the J = 1 yields 0 lines of C-18O and CO-13 set limits on the opacity of the CO-13 J = 1 yields 0 line averaged over the central kiloparsec of these spiral galaxies

Performance evaluation of a quasi-microscope for planetary landers

Spatial resolutions achieved with cameras on lunar and planetary landers have been limited to about 1 mm, whereas microscopes of the type proposed for such landers could have obtained resolutions of about 1 um but were never accepted because of their complexity and weight. The quasi-microscope evaluated in this paper could provide intermediate resolutions of about 10 um with relatively simple optics that would augment a camera, such as the Viking lander camera, without imposing special design requirements on the camera of limiting its field of view of the terrain. Images of natural particulate samples taken in black and white and in color show that grain size, shape, and texture are made visible for unconsolidated materials in a 50- to 500-um size range. Such information may provide broad outlines of planetary surface mineralogy and allow inferences to be made of grain origin and evolution. The mineralogical descriptions of single grains would be aided by the reflectance spectra that could, for example, be estimated from the six-channel multispectral data of the Viking lander camera