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Digital filter structures having low errors and simple hardware implementation

Sensitivity and roundoff errors can seriously limit the application of recursive digital filters in practice, particularly when the filters have poles near z = + 1. A filter structure, based on digital incremental computers is proposed, which has low sensitivity, good error characteristics, and simple hardware implementation for pole locations close to z = + 1. Expressions for the roundoff errors are derived and compared to those for conventional structures. A design procedure is suggested to implement the new filter structure given the transfer function. Simulation results are presented.

Abu-El-haija, A. I.↗

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.↗

A median filter approach for correcting errors in a vector field

Techniques are presented for detecting and correcting errors in a vector field. These methods employ median filters which are frequently used in image processing to enhance edges and remove noise. A detailed example is given for wind field maps produced by a spaceborne scatterometer. The error detection and replacement algorithm was tested with simulation data from the NASA Scatterometer (NSCAT) project.

Schultz, H.↗

Attitude Error Representations for Kalman Filtering

The quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation. The quaternion must obey a unit norm constraint, though, which has led to the development of an extended Kalman filter using a quaternion for the global attitude estimate and a three-component representation for attitude errors. We consider various attitude error representations for this Multiplicative Extended Kalman Filter and its second-order extension.

Markley, F. Landis↗

Correction of magnetooptic device phase errors in optical correlators through filter design modifications

We address the problem of optical phase errors in an optical correlator introduced by the input and filter plane spatial light modulators. Specifically, we study a laboratory correlator with magnetooptic spatial light modulator (MOSLM) devices. We measure and characterize the phase errors, analyze their effects on the correlation process, and discuss a means of correction through a design modification of the binary phase-only optical filter function. The phase correction technique is found to produce correlation results close to those of an error-free correlator.

Downie, John D.↗

Combating speckle in SAR images - Vector filtering and sequential classification based on a multiplicative noise model

An adaptive vector linear minimum mean-squared error (LMMSE) filter for multichannel images with multiplicative noise is presented. It is shown theoretically that the mean-squared error in the filter output is reduced by making use of the correlation between image bands. The vector and conventional scalar LMMSE filters are applied to a three-band SIR-B SAR, and their performance is compared. Based on a mutliplicative noise model, the per-pel maximum likelihood classifier was derived. The authors extend this to the design of sequential and robust classifiers. These classifiers are also applied to the three-band SIR-B SAR image.

Lin, Qian↗

A Nonlinear Adaptive Filter for Gyro Thermal Bias Error Cancellation

Deterministic errors in angular rate gyros, such as thermal biases, can have a significant impact on spacecraft attitude knowledge. In particular, thermal biases are often the dominant error source in MEMS gyros after calibration. Filters, such as J\,fEKFs, are commonly used to mitigate the impact of gyro errors and gyro noise on spacecraft closed loop pointing accuracy, but often have difficulty in rapidly changing thermal environments and can be computationally expensive. In this report an existing nonlinear adaptive filter is used as the basis for a new nonlinear adaptive filter designed to estimate and cancel thermal bias effects. A description of the filter is presented along with an implementation suitable for discrete-time applications. A simulation analysis demonstrates the performance of the filter in the presence of noisy measurements and provides a comparison with existing techniques.

Galante, Joseph M.↗

Design of Ternary Correlation Filters to Reduce Probability of Error

The problem of designing ternary phase and amplitude filters (TPAF's) that reduce the probability of image misclassification for a two-class image set is studied. The Fisher ratio is used as a measure of the correct classification rate, and an attempt is made to maximize this quantity in the filter designs. Given the nonanalytical nature of the design problem, a simulated annealing optimization technique is employed. Computer simulation results are presented for several cases including single in-class and out-of-class image sets and multiple image sets corresponding to the design of synthetic discriminant function filters. Significant improvements are found in expected rates of correct classification in comparison to binary phase-only filters and other TPAF designs. Approaches to accelerate the filter design process are also discussed.

Downie, John D.↗

A structure for digital notch filters

Narrow-band digital notch filters have their poles near the unit circle. As the sampling rate is increased, the poles move towards Z = +1. Implementing such filters requires long registers to overcome the sensitivity and roundoff errors. A filter structure based on digital incremental computers is proposed which has low sensitivity and round-off errors, and simple hardware implementation. The filter structure can be directly used on differentially pulse-code modulated signals. Hardware multipliers are not required as the poles approach z = +1, and excellent results can be obtained using multipliers with very short word lengths, or with small size read-only memories.

Abu-El-haija, A. I.↗

A spectral filter for ESMR's sidelobe errors

Fourier analysis was used to remove periodic errors from a series of NIMBUS-5 electronically scanned microwave radiometer brightness temperatures. The observations were all taken from the midnight orbits over fixed sites in the Australian grasslands. The angular dependence of the data indicates calibration errors consisted of broad sidelobes and some miscalibration as a function of beam position. Even though an angular recalibration curve cannot be derived from the available data, the systematic errors can be removed with a spectral filter. The 7 day cycle in the drift of the orbit of NIMBUS-5, coupled to the look-angle biases, produces an error pattern with peaks in its power spectrum at the weekly harmonics. About plus or minus 4 K of error is removed by simply blocking the variations near two- and three-cycles-per-week.

Chesters, D.↗

Improved Notch Filter For Synchronous-Response Control

Tracking differential-notch filter (TDNF) developed to retain good synchronous-response performance of notch filter, but with vastly improved stability properties. Measurement error perfectly filtered from feedback signal used to drive compensator. Provides good stability of simple lead/lag compensator combined with good synchronous-response performance gained by addition of notch filter.

Johnson, Bruce G.↗

The Use of Field Programmable Gate Arrays (FPGA) in Small Satellite Communication Systems

This paper will describe the use of digital Field Programmable Gate Arrays (FPGA) to contribute to advancing the state-of-the-art in software defined radio (SDR) transponder design for the emerging SmallSat and CubeSat industry and to provide advances for NASA as described in the TAO5 Communication and Navigation Roadmap (Ref 4). The use of software defined radios (SDR) has been around for a long time. A typical implementation of the SDR is to use a processor and write software to implement all the functions of filtering, carrier recovery, error correction, framing etc. Even with modern high speed and low power digital signal processors, high speed memories, and efficient coding, the compute intensive nature of digital filters, error correcting and other algorithms is too much for modern processors to get efficient use of the available bandwidth to the ground. By using FPGAs, these compute intensive tasks can be done in parallel, pipelined fashion and more efficiently use every clock cycle to significantly increase throughput while maintaining low power. These methods will implement digital radios with significant data rates in the X and Ka bands. Using these state-of-the-art technologies, unprecedented uplink and downlink capabilities can be achieved in a 1/2 U sized telemetry system. Additionally, modern FPGAs have embedded processing systems, such as ARM cores, integrated inside the FPGA allowing mundane tasks such as parameter commanding to occur easily and flexibly. Potential partners include other NASA centers, industry and the DOD. These assets are associated with small satellite demonstration flights, LEO and deep space applications. MSFC currently has an SDR transponder test-bed using Hardware-in-the-Loop techniques to evaluate and improve SDR technologies.

Varnavas, Kosta↗

Spectral and Wavefront Error Performance of WFIRST/AFTA Prototype Filters

The Cycle 5 design baseline for the Wide-Field Infrared Survey Telescope Astrophysics Focused Telescope Assets (WFIRSTAFTA) instrument includes a single wide-field channel (WFC) instrument for both imaging and slit-less spectroscopy. The only routinely moving part during scientific observations for this wide-field channel is the element wheel (EW) assembly. This filter-wheel assembly will have 8 positions that will be populated with 6 bandpass filters, a blank position, and a Grism that will consist of a three-element assembly to disperse the full field with an undeviated central wavelength for galaxy redshift surveys. All filter elements in the EW assembly will be made out of fused silica substrates (110 mm diameter) that will have the appropriate bandpass coatings according to the filter designations (Z087, Y106, J129, H158, F184, W149 and Grism). This paper presents and discusses the performance (including spectral transmission and reflectedtransmitted wavefront error measurements) of a subset of bandpass filter coating prototypes that are based on the WFC instrument filter compliment. The bandpass coating prototypes that are tested in this effort correspond to the Z087, W149, and Grism filter elements. These filter coatings have been procured from three different vendors to assess the most challenging aspects in terms of the in-band throughput, out of band rejection (including the cut-on and cutoff slopes), and the impact the wavefront error distortions of these filter coatings will have on the imaging performance of the de-field channel in the WFIRSTAFTA observatory.

cryogenic temperatures↗