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All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

An Upper Bound on Orbital Debris Collision Probability When Only One Object has Position Uncertainty Information

Upper bounds on high speed satellite collision probability, P (sub c), have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum P (sub c). If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but useful P (sub c) upper bound. There are various avenues along which an upper bound on the high speed satellite collision probability has been pursued. Typically, for the collision plane representation of the high speed collision probability problem, the predicted miss position in the collision plane is assumed fixed. Then the shape (aspect ratio of ellipse), the size (scaling of standard deviations) or the orientation (rotation of ellipse principal axes) of the combined position error ellipse is varied to obtain a maximum P (sub c). Regardless as to the exact details of the approach, previously presented methods all assume that an individual position error covariance matrix is available for each object and the two are combined into a single, relative position error covariance matrix. This combined position error covariance matrix is then modified according to the chosen scheme to arrive at a maximum P (sub c). But what if error covariance information for one of the two objects is not available? When error covariance information for one of the objects is not available the analyst has commonly defaulted to the situation in which only the relative miss position and velocity are known without any corresponding state error covariance information. The various usual methods of finding a maximum P (sub c) do no good because the analyst defaults to no knowledge of the combined, relative position error covariance matrix. It is reasonable to think, given an assumption of no covariance information, an analyst might still attempt to determine the error covariance matrix that results in an upper bound on the P (sub c). Without some guidance on limits to the shape, size and orientation of the unknown covariance matrix, the limiting case is a degenerate ellipse lying along the relative miss vector in the collision plane. Unless the miss position is exceptionally large or the at-risk object is exceptionally small, this method results in a maximum P (sub c) too large to be of practical use. For example, assuming that the miss distance is equal to the current ISS alert volume along-track (+ or -) distance of 25 kilometers and that the at-risk area has a 70 meter radius. The maximum (degenerate ellipse) P (sub c) is about 0.00136. At 40 kilometers, the maximum P (sub c) would be 0.00085 which is still almost an order of magnitude larger than the ISS maneuver threshold of 0.0001. In fact, a miss distance of almost 340 kilometers is necessary to reduce the maximum P (sub c) associated with this degenerate ellipse to the ISS maneuver threshold value. Such a result is frequently of no practical value to the analyst. Some improvement may be made with respect to this problem by realizing that while the position error covariance matrix of one of the objects (usually the debris object) may not be known the position error covariance matrix of the other object (usually the asset) is almost always available. Making use of the position error covariance information for the one object provides an improvement in finding a maximum P (sub c) which, in some cases, may offer real utility. The equations to be used are presented and their use discussed.

Frisbee, Joseph H., Jr.↗
NASA NTRS1990

General upper bound on single-event upset rate

A technique of predicting an upper bound on the rate at which single-event upsets due to ionizing radiation occur in semiconducting memory cells is described. The upper bound on the upset rate, which depends on the high-energy particle environment in earth orbit and accelerator cross-section data, is given by the product of an upper-bound linear energy-transfer spectrum and the mean cross section of the memory cell. Plots of the spectrum are given for low-inclination and polar orbits. An alternative expression for the exact upset rate is also presented. Both methods rely only on experimentally obtained cross-section data and are valid for sensitive bit regions having arbitrary shape.

Chlouber, Dean↗
NASA NTRS2017

Pre-Test Assessment of the Upper Bound of the Drag Coefficient Repeatability of a Wind Tunnel Model

A new method is presented that computes a pre{test estimate of the upper bound of the drag coefficient repeatability of a wind tunnel model. This upper bound is a conservative estimate of the precision error of the drag coefficient. For clarity, precision error contributions associated with the measurement of the dynamic pressure are analyzed separately from those that are associated with the measurement of the aerodynamic loads. The upper bound is computed by using information about the model, the tunnel conditions, and the balance in combination with an estimate of the expected output variations as input. The model information consists of the reference area and an assumed angle of attack. The tunnel conditions are described by the Mach number and the total pressure or unit Reynolds number. The balance inputs are the partial derivatives of the axial and normal force with respect to all balance outputs. Finally, an empirical output variation of 1.0 microV/V is used to relate both random instrumentation and angle measurement errors to the precision error of the drag coefficient. Results of the analysis are reported by plotting the upper bound of the precision error versus the tunnel conditions. The analysis shows that the influence of the dynamic pressure measurement error on the precision error of the drag coefficient is often small when compared with the influence of errors that are associated with the load measurements. Consequently, the sensitivities of the axial and normal force gages of the balance have a significant influence on the overall magnitude of the drag coefficient's precision error. Therefore, results of the error analysis can be used for balance selection purposes as the drag prediction characteristics of balances of similar size and capacities can objectively be compared. Data from two wind tunnel models and three balances are used to illustrate the assessment of the precision error of the drag coefficient.

drag coefficient measurement↗
NASA NTRS1993

Upper-Bound SEU Rates In Anisotropic Fluxes

Upper bounds on rates of single-event upsets (SEU's) in digital integrated circuits and other electronic devices exposed to anisotropic fluxes of energetic ionizing particles computed by use of improved method. Derived from simplified, worst-case mathematical models of charge-collecting volumes and physical phenomena in electronic devices.

Edmonds, Larry D.↗
NASA NTRS1977

New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities

An upper bound on the rate of a binary code as a function of minimum code distance (using a Hamming code metric) is arrived at from Delsarte-MacWilliams inequalities. The upper bound so found is asymptotically less than Levenshtein's bound, and a fortiori less than Elias' bound. Appendices review properties of Krawtchouk polynomials and Q-polynomials utilized in the rigorous proofs.

Mceliece, R. J.↗
NASA NTRS2003

Upper bounds to error probabilities of coded systems beyond the cutoff rate

A family of upper bounds to error probabilities of coded systems was recently proposed by Divsalar. These bounds are valid for transmission over the additive white Gaussian noise channel, and require only the knowledge of the weight spectrum of the code words. After illustrating these bounds, we extend them to fading channels. Contrary to the union bound, our bounds maintain their effectiveness below the signal-to-noise ratio (SNR)at which the cutoff rate of the channel equals the rate of the code. Some applications are shown. First, we derive upper bounds to the minimum SNR necessary to achieve zero error probability as the code block length increases to infinity. Next, we use our bounds to predict the performance of turbo codes and low-density parity-check codes.

Biglieri, Ezio↗
NASA NTRS1991

Upper bound SEU rate for devices in an isotropic or nonisotropic flux

A method for constructing upper bound estimates for device single event upset (SEU) rates is presented. A directional Heinrich flux, as a function of direction, must be known. A computer code, included, converts the directional Heinrich flux into an 'effective flux'. The effective flux provides a simple way to estimate upper bound SEU rates for devices with a known normal incident cross section versus LET curve.

Edmonds, Larry D.↗
NASA NTRS2015

An Upper Bound on High Speed Satellite Collision Probability When Only One Object has Position Uncertainty Information

Upper bounds on high speed satellite collision probability, PC †, have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum PC. If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but potentially useful Pc upper bound.

Frisbee, Joseph H., Jr.↗
NASA NTRS1974

Upper bounds on sequential decoding performance parameters

This paper presents the best obtainable random coding and expurgated upper bounds on the probabilities of undetectable error, of t-order failure (advance to depth t into an incorrect subset), and of likelihood rise in the incorrect subset, applicable to sequential decoding when the metric bias G is arbitrary. Upper bounds on the Pareto exponent are also presented. The G-values optimizing each of the parameters of interest are determined, and are shown to lie in intervals that in general have nonzero widths. The G-optimal expurgated bound on undetectable error is shown to agree with that for maximum likelihood decoding of convolutional codes, and that on failure agrees with the block code expurgated bound. Included are curves evaluating the bounds for interesting choices of G and SNR for a binary-input quantized-output Gaussian additive noise channel.

Jelinek, F.↗
NASA NTRS2008

Safe Upper-Bounds Inference of Energy Consumption for Java Bytecode Applications

Many space applications such as sensor networks, on-board satellite-based platforms, on-board vehicle monitoring systems, etc. handle large amounts of data and analysis of such data is often critical for the scientific mission. Transmitting such large amounts of data to the remote control station for analysis is usually too expensive for time-critical applications. Instead, modern space applications are increasingly relying on autonomous on-board data analysis. All these applications face many resource constraints. A key requirement is to minimize energy consumption. Several approaches have been developed for estimating the energy consumption of such applications (e.g. [3, 1]) based on measuring actual consumption at run-time for large sets of random inputs. However, this approach has the limitation that it is in general not possible to cover all possible inputs. Using formal techniques offers the potential for inferring safe energy consumption bounds, thus being specially interesting for space exploration and safety-critical systems. We have proposed and implemented a general frame- work for resource usage analysis of Java bytecode [2]. The user defines a set of resource(s) of interest to be tracked and some annotations that describe the cost of some elementary elements of the program for those resources. These values can be constants or, more generally, functions of the input data sizes. The analysis then statically derives an upper bound on the amount of those resources that the program as a whole will consume or provide, also as functions of the input data sizes. This article develops a novel application of the analysis of [2] to inferring safe upper bounds on the energy consumption of Java bytecode applications. We first use a resource model that describes the cost of each bytecode instruction in terms of the joules it consumes. With this resource model, we then generate energy consumption cost relations, which are then used to infer safe upper bounds. How energy consumption for each bytecode instruction is measured is beyond the scope of this paper. Instead, this paper is about how to infer safe energy consumption estimations assuming that those energy consumption costs are provided. For concreteness, we use a simplified version of an existing resource model [1] in which an energy consumption cost for individual Java opcodes is defined.

Navas, Jorge↗
NASA NTRS1976

An improved upper bound on the block coding error exponent for binary input discrete memoryless channels

For coded telemetry systems it is important to know the tradeoff between the error probability and the complexity of implementation. For systems using block codes, the block coding error exponent is a good way to estimate this tradeoff. The new upper bounds on the minimum distance of binary codes result in improved upper bounds on the coding error exponents for binary input memoryless channels.

Mceliece, R. J.↗