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At least 109 records · Page 6

Stratospheric Assimilation of Chemical Tracer Observations Using a Kalman Filter: Chi-Square Validated Results and Analysis of Variance and Correlation Dynamics - Pt. 2

A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I (Menard et al. 1998) The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board of the Upper Atmosphere Research Satellite are described in this paper. A robust (chi)(sup 2) criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only three days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. We further found that the model error due to numerical discretization as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave-breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, we have conducted an analysis of the variance and correlation dynamics to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.

Menard, Richard↗

On the performance of digital phase locked loops in the threshold region

Extended Kalman filter algorithms are used to obtain a digital phase lock loop structure for demodulation of angle modulated signals. It is shown that the error variance equations obtained directly from this structure enable one to predict threshold if one retains higher frequency terms. This is in sharp contrast to the similar analysis of the analog phase lock loop, where the higher frequency terms are filtered out because of the low pass filter in the loop. Results are compared to actual simulation results and threshold region results obtained previously.

Hurst, G. T.↗

The behavior of forecast error covariances for a Kalman filter in two dimensions

The behavior of forecast error covariances in a fairly realistic setting is demonstrated via a Kalman filter algorithm. It is used to assimilate simulated data from the existing radiosonde network, from the demonstration network of 31 Doppler wind profilers in the central U.S., and from hypothetical radiometers located at five of the profiler sites. Some theoretical justification of the hypothesis advanced by Phillips (1982), and the hypothesis is used to formulate the model error covariance matrix required by the Kalman filter. The results show that assimilating the profiler wind data leads to a large reduction of forecast/analysis error in heights as well as in winds, over the profiler region and also downstream, when compared with the results of assimilating the radiosonde data alone. The forecast error covariance matrices that the Kalman filter calculates to obtain this error reduction differ considerably from those prescribed by the optimal interpolation schemes that are employed for data assimilation at operational centers.

Cohn, Stephen E.↗

Robotic Vision-Based Localization in an Urban Environment

A system of electronic hardware and software, now undergoing development, automatically estimates the location of a robotic land vehicle in an urban environment using a somewhat imprecise map, which has been generated in advance from aerial imagery. This system does not utilize the Global Positioning System and does not include any odometry, inertial measurement units, or any other sensors except a stereoscopic pair of black-and-white digital video cameras mounted on the vehicle. Of course, the system also includes a computer running software that processes the video image data. The software consists mostly of three components corresponding to the three major image-data-processing functions: Visual Odometry This component automatically tracks point features in the imagery and computes the relative motion of the cameras between sequential image frames. This component incorporates a modified version of a visual-odometry algorithm originally published in 1989. The algorithm selects point features, performs multiresolution area-correlation computations to match the features in stereoscopic images, tracks the features through the sequence of images, and uses the tracking results to estimate the six-degree-of-freedom motion of the camera between consecutive stereoscopic pairs of images (see figure). Urban Feature Detection and Ranging Using the same data as those processed by the visual-odometry component, this component strives to determine the three-dimensional (3D) coordinates of vertical and horizontal lines that are likely to be parts of, or close to, the exterior surfaces of buildings. The basic sequence of processes performed by this component is the following: 1. An edge-detection algorithm is applied, yielding a set of linked lists of edge pixels, a horizontal-gradient image, and a vertical-gradient image. 2. Straight-line segments of edges are extracted from the linked lists generated in step 1. Any straight-line segments longer than an arbitrary threshold (e.g., 30 pixels) are assumed to belong to buildings or other artificial objects. 3. A gradient-filter algorithm is used to test straight-line segments longer than the threshold to determine whether they represent edges of natural or artificial objects. In somewhat oversimplified terms, the test is based on the assumption that the gradient of image intensity varies little along a segment that represents the edge of an artificial object.

Mchenry, Michael↗

Description of data on the Nimbus 7 LIMS map archive tape: Ozone and nitric acid

The Nimbus 7 Limb Infrared Monitor of the Stratosphere (LIMS) data set has been processed into a Fourier coefficient representation with a Kalman filter algorithm applied to profile data at individual latitudes and pressure levels. The algorithm produces synoptic data at noon Greenwich Mean Time (GMT) from the asynoptic orbital profiles. This form of the data set is easy to use and is appropriate for time series analysis and further data manipulation and display. Ozone and nitric acid results are grouped together in this report because the LIMS vertical field of views (FOV's) and analysis characteristics for these species are similar. A comparison of the orbital input data with mixing ratios derived from Kalman filter coefficients indicates errors in mixing ratio of generally less than 5 percent, with 15 percent being a maximum error. The high quality of the mapped data was indicated by coherence of both the phases and the amplitudes of waves with latitude and pressure. Examples of the mapped fields are presented, and details are given concerning the importance of diurnal variations, the removal of polar stratospheric cloud signatures, and the interpretation of bias effects in the data near the tops of profiles.

Remsberg, E. E.↗

Low-Cost Telemetry System for Small/Micro Satellites

A Software Defined Radio (SDR) concept uses a minimum amount of analog/radio frequency components to up/downconvert the RF signal to/from a digital format. Once in the digital domain, all other processing (filtering, modulation, demodulation, etc.) is done in software. The project will leverage existing designs and enhance capabilities in the commercial sector to provide a path to a radiation-hardened SDR transponder. The SDR transponder would incorporate baseline technologies dealing with improved Forward Error Correcting (FEC) codes to be deployed to all Near Earth Network (NEN) ground stations. By incorporating this FEC, at least a tenfold increase in data throughput can be achieved. A family of transponder products can be implemented using common platform architecture, allowing new products to be more quickly introduced into the market. Software can be reused across products, reducing software/hardware costs dramatically. New features and capabilities, such as encoding and decoding algorithms, filters, and bit synchronizers, can be added to the existing infrastructure without requiring major new capital expenditures, allowing implementation of advanced features in the communication systems. As new telecommunication technologies emerge, incorporating them into the SDR fabric will be easily accomplished with little or no requirements for new hardware. There are no preferred flight platforms for the SDR technology, so it can be used on any type of orbital or sub-orbital platform, all within a fully radiation hardened design.

Sims, William↗

Development and Operation of a Material Identification and Discrimination Imaging Spectroradiometer

Many imaging applications require quantitative determination of a scene's spectral radiance. This paper describes a new system capable of real-time spectroradiometric imagery. Operating at a full-spectrum update rate of 30Hz, this imager is capable of collecting a 30 point spectrum from each of three imaging heads: the first operates from 400 nm to 950 nm, with a 2% bandwidth; the second operates from 1.5 micro-m to 5.5 micro-m with a 1.5% bandwidth; the third operates from 5 micro-m to 12 micro-m, also at a 1.5% bandwidth. Standard image format is 256 x 256, with 512 x 512 possible in the VIS/NIR head. Spectra of up to 256 points are available at proportionately lower frame rates. In order to make such a tremendous amount of data more manageable, internal processing electronics perform four important operations on the spectral imagery data in real-time. First, all data in the spatial/spectral cube of data is spectro-radiometrically calibrated as it is collected. Second, to allow the imager to simulate sensors with arbitrary spectral response, any set of three spectral response functions may be loaded into the imager including delta functions to allow single wavelength viewing; the instrument then evaluates the integral of the product of the scene spectral radiances and the response function. Third, more powerful exploitation of the gathered spectral radiances can be effected by application of various spectral-matched filtering algorithms to identify pixels whose relative spectral radiance distribution matches a sought-after spectral radiance distribution, allowing materials-based identification and discrimination. Fourth, the instrument allows determination of spectral reflectance, surface temperature, and spectral emissivity, also in real-time. The spectral imaging technique used in the instrument allows tailoring of the frame rate and/or the spectral bandwidth to suit the scene radiance levels, i.e., frame rate can be reduced, or bandwidth increased to improve SNR when viewing low radiance scenes. The unique challenges of design and calibration are described. Pixel readout rates of 160 MHz, for full frame readout rates of 1000 Hz (512 x 512 image) present the first challenge; processing rates of nearly 600 million integer operations per second for sensor emulation, or over 2 billion per second for matched filtering, present the second. Spatial and spectral calibration of 66,536 pixels (262,144 for the 512 x 512 version) and up to 1,000 spectral positions mandate novel decoupling methods to keep the required calibration memory to a reasonable size. Large radiometric dynamic range also requires care to maintain precision operation with minimum memory size.

Dombrowski, Mark↗

Convective Weather Forecast Quality Metrics for Air Traffic Management Decision-Making

Since numerical weather prediction models are unable to accurately forecast the severity and the location of the storm cells several hours into the future when compared with observation data, there has been a growing interest in probabilistic description of convective weather. The classical approach for generating uncertainty bounds consists of integrating the state equations and covariance propagation equations forward in time. This step is readily recognized as the process update step of the Kalman Filter algorithm. The second well known method, known as the Monte Carlo method, consists of generating output samples by driving the forecast algorithm with input samples selected from distributions. The statistical properties of the distributions of the output samples are then used for defining the uncertainty bounds of the output variables. This method is computationally expensive for a complex model compared to the covariance propagation method. The main advantage of the Monte Carlo method is that a complex non-linear model can be easily handled. Recently, a few different methods for probabilistic forecasting have appeared in the literature. A method for computing probability of convection in a region using forecast data is described in Ref. 5. Probability at a grid location is computed as the fraction of grid points, within a box of specified dimensions around the grid location, with forecast convection precipitation exceeding a specified threshold. The main limitation of this method is that the results are dependent on the chosen dimensions of the box. The examples presented Ref. 5 show that this process is equivalent to low-pass filtering of the forecast data with a finite support spatial filter. References 6 and 7 describe the technique for computing percentage coverage within a 92 x 92 square-kilometer box and assigning the value to the center 4 x 4 square-kilometer box. This technique is same as that described in Ref. 5. Characterizing the forecast, following the process described in Refs. 5 through 7, in terms of percentage coverage or confidence level is notionally sound compared to characterizing in terms of probabilities because the probability of the forecast being correct can only be determined using actual observations. References 5 through 7 only use the forecast data and not the observations. The method for computing the probability of detection, false alarm ratio and several forecast quality metrics (Skill Scores) using both the forecast and observation data are given in Ref. 2. This paper extends the statistical verification method in Ref. 2 to determine co-occurrence probabilities. The method consists of computing the probability that a severe weather cell (grid location) is detected in the observation data in the neighborhood of the severe weather cell in the forecast data. Probabilities of occurrence at the grid location and in its neighborhood with higher severity, and with lower severity in the observation data compared to that in the forecast data are examined. The method proposed in Refs. 5 through 7 is used for computing the probability that a certain number of cells in the neighborhood of severe weather cells in the forecast data are seen as severe weather cells in the observation data. Finally, the probability of existence of gaps in the observation data in the neighborhood of severe weather cells in forecast data is computed. Gaps are defined as openings between severe weather cells through which an aircraft can safely fly to its intended destination. The rest of the paper is organized as follows. Section II summarizes the statistical verification method described in Ref. 2. The extension of this method for computing the co-occurrence probabilities in discussed in Section HI. Numerical examples using NCWF forecast data and NCWD observation data are presented in Section III to elucidate the characteristics of the co-occurrence probabilities. This section also discusses the procedure for computing throbabilities that the severity of convection in the observation data will be higher or lower in the neighborhood of grid locations compared to that indicated at the grid locations in the forecast data. The probability of coverage of neighborhood grid cells is also described via examples in this section. Section IV discusses the gap detection algorithm and presents a numerical example to illustrate the method. The locations of the detected gaps in the observation data are used along with the locations of convective weather cells in the forecast data to determine the probability of existence of gaps in the neighborhood of these cells. Finally, the paper is concluded in Section V.

Chatterji, Gano B.↗

Navigation for space shuttle approach and landing using an inertial navigation system augmented by data from a precision ranging system or a microwave scan beam landing guidance system

A preliminary study has been made of the navigation performance which might be achieved for the high cross-range space shuttle orbiter during final approach and landing by using an optimally augmented inertial navigation system. Computed navigation accuracies are presented for an on-board inertial navigation system augmented (by means of an optimal filter algorithm) with data from two different ground navigation aids; a precision ranging system and a microwave scanning beam landing guidance system. These results show that augmentation with either type of ground navigation aid is capable of providing a navigation performance at touchdown which should be adequate for the space shuttle. In addition, adequate navigation performance for space shuttle landing is obtainable from the precision ranging system even with a complete dropout of precision range measurements as much as 100 seconds before touchdown.

Mcgee, L. A.↗

Adaptive control of stochastic linear systems with unknown parameters

The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

Ku, R. T.↗

On the adaptive control of linear systems using the open-loop-feedback-optimal approach.

This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal (O.L.F.O.) method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first order systems are presented.

Ku, R.↗

On the adaptive control of linear systems using the open-loop-feedback-optimal approach.

This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with uncertain or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal (OLFO) method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.

Ku, R.↗

Open-loop-feedback-optimal adaptive stochastic control of linear systems

This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.

Ku, R.↗

Flight Mechanics/Estimation Theory Symposium

Onboard and real time image processing to enhance geometric correction of the data is discussed with application to autonomous navigation and attitude and orbit determination. Specific topics covered include: (1) LANDSAT landmark data; (2) star sensing and pattern recognition; (3) filtering algorithms for Global Positioning System; and (4) determining orbital elements for geostationary satellites.

Fuchs, A. J.↗

Filtering and error analysis via the UDU super T covariance factorization

Kalman filter algorithms based on the UDU super T covariance factorization are discussed, with special attention given to algorithm implementation efficiency. A U-D-factored covariance error-analysis algorithm is formulated, and its efficiency and numerical stability are demonstrated in a representative orbit determination problem. The numerical results are compared with those obtained using covariance error-analysis formulas, and the comparison highlights the numerical superiority of the present algorithm. A byproduct of the U-D analysis is a highly efficient algorithm mechanization of the arbitrary gain covariance update formula.

Thornton, C. L.↗