Typically, the trackin and estimation community has been concerned with the girect problem of tra... more Typically, the trackin and estimation community has been concerned with the girect problem of tracking a threat in a near optimal fashion. The usage of secondary quantities or derived quantities from state estimates that can be used for other purposes than tracking have been i nored. An example of a derived quantity that is useful irectly for tracking and classification is the energy associated with the threat. We discuss a number of such informative priors that can be useful to pure tracking applications as well as how dissipation of energy and ballistic coefficients can be estimated indirectly.
IEEE Transactions on Electromagnetic Compatibility, 1987
In this paper, array beamforming based on nonsinusoidal waveforms has been extended to account fo... more In this paper, array beamforming based on nonsinusoidal waveforms has been extended to account for the effects of band-limited Gaussian noise. To account for the statistical nature of noise, the resolution angle of the array beam is expressed in terms of statistical quantities; i.e., given a signal-to-noise ratio (SNR), the resolution angle is bounded in a confidence interval. For large SNR, such a representation leads to the noise-free case when the resolution angle reaches a minimum. For small SNR's on the other hand, beam instability occurs, signifying either angular ambiguity or the total loss of angular information.
Parks introduced a formulation of time dependent weak values in 2008, which is the formalism we u... more Parks introduced a formulation of time dependent weak values in 2008, which is the formalism we use in this paper. In this paper we extend notions from time dependent weak values to show that Hamiltonians associated with weak value measurements can be shown to exhibit even or odd symmetric properties. They exhibit PT or anti-PT symmetry, respectively. These symmetries are manifested during the measurement process as pointer translations, which have vanishing imaginary or vanishing real parts. The consequence of this that one can characterize some of the aspects of these symmetries of the time dependent Hamiltonians that arise from time dependent weak values. This allows one to generalize some work on non-Hermitian variables in quantum mechanics (QM) due to Bender related to weak values and weak measurement. We also speculate how these symmetries might apply to distinguishing between the various two-time interpretations of QM in the Conclusions of this paper.
Record of the IEEE 2000 International Radar Conference [Cat. No. 00CH37037]
A formalism to determine the probability density function (PDF) resulting from a coordinate trans... more A formalism to determine the probability density function (PDF) resulting from a coordinate transformation applied to an arbitrary PDF is developed. The results are applied to the coordinate transformation used in target tracking, specifically the transformation from spherical to Cartesian coordinates. This result is then applied to the specific example of a Gaussian random variable transformed by sine and cosine
Since the inception of coherent waveforms, it has been realized that the effect of non-uniform mo... more Since the inception of coherent waveforms, it has been realized that the effect of non-uniform motion of a non-point like object can induce structure in the return spectrum of the waveform that can be exploited. The non-uniform Doppler spectrum has useful information that can be found in the spreading of the Doppler spectrum for the motion models: acceleration, jerk, quadric, and exponential slowdown as examples well as a characteristic of periodic motion. We illustrate this with examples relevant to automotive radar, tracking meteors with ambient sources, characterizing moving sources and other relevant examples.
We present an axiomatic approach to the mean and discuss generalizations of the mean, including o... more We present an axiomatic approach to the mean and discuss generalizations of the mean, including one due to Kolmogorov based on the Weak Law of Large Numbers. We offer examples and counterexamples, describe conventional and unconventional uses of the mean in statistical mechanics, and resolve an anomaly in quantum theory concerning apparent simultaneous coexistence of means and variances of observables. These issues all arise from the familiar definition of the mean.
Division, that responds to the need for improved techniques in dealing with the situation where m... more Division, that responds to the need for improved techniques in dealing with the situation where many threats are attacking battle group. In such a situation, each threat has a large number of potential targets fi which to choose. Prioritization of the threats within a raid that involves a large number of Anti-Ship Cruise Missiles (ASCMs) presents a problem to a global scheduler in terms of both selection of shooting platforms and determining the queue for engagement scheduling. This problem becomes particularly challenging when placed in the context of the network centric paradigm envisioned for the future of the surface navy, and represents a significant potential problem that needs to be addressed. This work not only addresses the problem by discussing its formulation and occurrence, it also proposes a solution. Threats targeting high valued assets such as a carrier would be ranked above those targeting a destroyer. Similarly, a threat arriving earher would be ranked above one arriving later. But what makes this problem not straightforward is such concerns as: How does one rank a threat arriving at a destroyer earher than one arriving later at a carrier? The ranking scheme proposed here is b^ed on the "Loss Threshold Time" (LTT), which is defined as the time at which the expected destructive potential of a threat exceeds a specified value. Then, threats with earlier LTTs are ranked higher. An algorithm is proposed that estimates the probabihty of each defended ship becoming the target of a given threat. The r^ult is a matrix of "Objective Probabihties", which is used to calculate the "Expected Loss" (EL) function of each threat. The objective probabilities are higher for ships that can be reached earlier and more easily. The combination of these two concepts represents a conceptual shift in how warfare planning is considered in algorithm design and implementation. This work represents a significant conceptual breakthrough that may have practical consequences in fiiture combat systems.
Thirty-Sixth Southeastern Symposium on System Theory, 2004. Proceedings of the, 2004
Abstract There are three commonly used relationships between alpha and beta that are reported in ... more Abstract There are three commonly used relationships between alpha and beta that are reported in the literature: Kalata, Benedict-Bordner, and continuous white noise. The Kalata relation is obtained from steady state Kalman filter theory assuming zero mean white ...
2006 Proceeding of the Thrity-Eighth Southeastern Symposium on System Theory, 2006
A brief introduction to the history of chaos and chaotic encryption is provided. Simple circuits ... more A brief introduction to the history of chaos and chaotic encryption is provided. Simple circuits that oscillate chaotically are reviewed. Methods of removing the masking produced by a single chaotic oscillator are reviewed. Methods that have been proposed to produce a secure encryption scheme using chaotic oscillators are described and evaluated. Based on the knowledge that only circuits with a single nonlinear element synchronize quickly enough to allow the encryption decryption of realtime communications, and that such schemes are inherently vulnerable to return map reconstruction, it appears that chaotic encryption will not be deployed in communications systems. However, systems with multiple nonlinearities continue to show some promise.
Calculation of the mean of an observable in quantum mechanics is typically assumed to require tha... more Calculation of the mean of an observable in quantum mechanics is typically assumed to require that the state vector be in the domain of the corresponding selfadjoint operator or for a mixed state that the operator times the density matrix be in the trace class. We remind the reader that these assumptions are unnecessary. We state what is actually needed to calculate the mean of an observable as well as its variance.
The problem of prediction of target location and the role that this problem plays in the design a... more The problem of prediction of target location and the role that this problem plays in the design and evolution of a modern combat system is analyzed. Connected with this problem is the task of choosing one set of hypotheses from among many viable sets. The functional dependence of the ability to make a prediction is discussed with particular attention paid to efficiencies and deficiencies. A general principle is proposed that helps bound the prediction problem from a weapons system perspective. A technique due to Jaynes called the transformation group method is applied to understand some of the problems of prediction
We discuss the principle of superposition relative to the definition of extensivity in thermodyna... more We discuss the principle of superposition relative to the definition of extensivity in thermodynamics and discuss how it can be extended to systems that do not obey the linear principle of superposition. This leads to the concept of generalized superposition, of which, there are multiple types defined in the paper. Generalized superposition can be used to explore the breakdown of linearity at the nano-scale, which leads to deeper understanding of nano-materials and nano-thermodynamics.
Typically, the trackin and estimation community has been concerned with the girect problem of tra... more Typically, the trackin and estimation community has been concerned with the girect problem of tracking a threat in a near optimal fashion. The usage of secondary quantities or derived quantities from state estimates that can be used for other purposes than tracking have been i nored. An example of a derived quantity that is useful irectly for tracking and classification is the energy associated with the threat. We discuss a number of such informative priors that can be useful to pure tracking applications as well as how dissipation of energy and ballistic coefficients can be estimated indirectly.
IEEE Transactions on Electromagnetic Compatibility, 1987
In this paper, array beamforming based on nonsinusoidal waveforms has been extended to account fo... more In this paper, array beamforming based on nonsinusoidal waveforms has been extended to account for the effects of band-limited Gaussian noise. To account for the statistical nature of noise, the resolution angle of the array beam is expressed in terms of statistical quantities; i.e., given a signal-to-noise ratio (SNR), the resolution angle is bounded in a confidence interval. For large SNR, such a representation leads to the noise-free case when the resolution angle reaches a minimum. For small SNR's on the other hand, beam instability occurs, signifying either angular ambiguity or the total loss of angular information.
Parks introduced a formulation of time dependent weak values in 2008, which is the formalism we u... more Parks introduced a formulation of time dependent weak values in 2008, which is the formalism we use in this paper. In this paper we extend notions from time dependent weak values to show that Hamiltonians associated with weak value measurements can be shown to exhibit even or odd symmetric properties. They exhibit PT or anti-PT symmetry, respectively. These symmetries are manifested during the measurement process as pointer translations, which have vanishing imaginary or vanishing real parts. The consequence of this that one can characterize some of the aspects of these symmetries of the time dependent Hamiltonians that arise from time dependent weak values. This allows one to generalize some work on non-Hermitian variables in quantum mechanics (QM) due to Bender related to weak values and weak measurement. We also speculate how these symmetries might apply to distinguishing between the various two-time interpretations of QM in the Conclusions of this paper.
Record of the IEEE 2000 International Radar Conference [Cat. No. 00CH37037]
A formalism to determine the probability density function (PDF) resulting from a coordinate trans... more A formalism to determine the probability density function (PDF) resulting from a coordinate transformation applied to an arbitrary PDF is developed. The results are applied to the coordinate transformation used in target tracking, specifically the transformation from spherical to Cartesian coordinates. This result is then applied to the specific example of a Gaussian random variable transformed by sine and cosine
Since the inception of coherent waveforms, it has been realized that the effect of non-uniform mo... more Since the inception of coherent waveforms, it has been realized that the effect of non-uniform motion of a non-point like object can induce structure in the return spectrum of the waveform that can be exploited. The non-uniform Doppler spectrum has useful information that can be found in the spreading of the Doppler spectrum for the motion models: acceleration, jerk, quadric, and exponential slowdown as examples well as a characteristic of periodic motion. We illustrate this with examples relevant to automotive radar, tracking meteors with ambient sources, characterizing moving sources and other relevant examples.
We present an axiomatic approach to the mean and discuss generalizations of the mean, including o... more We present an axiomatic approach to the mean and discuss generalizations of the mean, including one due to Kolmogorov based on the Weak Law of Large Numbers. We offer examples and counterexamples, describe conventional and unconventional uses of the mean in statistical mechanics, and resolve an anomaly in quantum theory concerning apparent simultaneous coexistence of means and variances of observables. These issues all arise from the familiar definition of the mean.
Division, that responds to the need for improved techniques in dealing with the situation where m... more Division, that responds to the need for improved techniques in dealing with the situation where many threats are attacking battle group. In such a situation, each threat has a large number of potential targets fi which to choose. Prioritization of the threats within a raid that involves a large number of Anti-Ship Cruise Missiles (ASCMs) presents a problem to a global scheduler in terms of both selection of shooting platforms and determining the queue for engagement scheduling. This problem becomes particularly challenging when placed in the context of the network centric paradigm envisioned for the future of the surface navy, and represents a significant potential problem that needs to be addressed. This work not only addresses the problem by discussing its formulation and occurrence, it also proposes a solution. Threats targeting high valued assets such as a carrier would be ranked above those targeting a destroyer. Similarly, a threat arriving earher would be ranked above one arriving later. But what makes this problem not straightforward is such concerns as: How does one rank a threat arriving at a destroyer earher than one arriving later at a carrier? The ranking scheme proposed here is b^ed on the "Loss Threshold Time" (LTT), which is defined as the time at which the expected destructive potential of a threat exceeds a specified value. Then, threats with earlier LTTs are ranked higher. An algorithm is proposed that estimates the probabihty of each defended ship becoming the target of a given threat. The r^ult is a matrix of "Objective Probabihties", which is used to calculate the "Expected Loss" (EL) function of each threat. The objective probabilities are higher for ships that can be reached earlier and more easily. The combination of these two concepts represents a conceptual shift in how warfare planning is considered in algorithm design and implementation. This work represents a significant conceptual breakthrough that may have practical consequences in fiiture combat systems.
Thirty-Sixth Southeastern Symposium on System Theory, 2004. Proceedings of the, 2004
Abstract There are three commonly used relationships between alpha and beta that are reported in ... more Abstract There are three commonly used relationships between alpha and beta that are reported in the literature: Kalata, Benedict-Bordner, and continuous white noise. The Kalata relation is obtained from steady state Kalman filter theory assuming zero mean white ...
2006 Proceeding of the Thrity-Eighth Southeastern Symposium on System Theory, 2006
A brief introduction to the history of chaos and chaotic encryption is provided. Simple circuits ... more A brief introduction to the history of chaos and chaotic encryption is provided. Simple circuits that oscillate chaotically are reviewed. Methods of removing the masking produced by a single chaotic oscillator are reviewed. Methods that have been proposed to produce a secure encryption scheme using chaotic oscillators are described and evaluated. Based on the knowledge that only circuits with a single nonlinear element synchronize quickly enough to allow the encryption decryption of realtime communications, and that such schemes are inherently vulnerable to return map reconstruction, it appears that chaotic encryption will not be deployed in communications systems. However, systems with multiple nonlinearities continue to show some promise.
Calculation of the mean of an observable in quantum mechanics is typically assumed to require tha... more Calculation of the mean of an observable in quantum mechanics is typically assumed to require that the state vector be in the domain of the corresponding selfadjoint operator or for a mixed state that the operator times the density matrix be in the trace class. We remind the reader that these assumptions are unnecessary. We state what is actually needed to calculate the mean of an observable as well as its variance.
The problem of prediction of target location and the role that this problem plays in the design a... more The problem of prediction of target location and the role that this problem plays in the design and evolution of a modern combat system is analyzed. Connected with this problem is the task of choosing one set of hypotheses from among many viable sets. The functional dependence of the ability to make a prediction is discussed with particular attention paid to efficiencies and deficiencies. A general principle is proposed that helps bound the prediction problem from a weapons system perspective. A technique due to Jaynes called the transformation group method is applied to understand some of the problems of prediction
We discuss the principle of superposition relative to the definition of extensivity in thermodyna... more We discuss the principle of superposition relative to the definition of extensivity in thermodynamics and discuss how it can be extended to systems that do not obey the linear principle of superposition. This leads to the concept of generalized superposition, of which, there are multiple types defined in the paper. Generalized superposition can be used to explore the breakdown of linearity at the nano-scale, which leads to deeper understanding of nano-materials and nano-thermodynamics.
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Papers by John Gray