To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure no-reply@cambridge.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Chapter 9 explores many interesting phenomena that arise in the physics of continuous quantum measurement. We discuss measurement reversal (or “quantum uncollapse”), the most likely path of continuous quantum measurements, the joint simultaneous measurements of noncommuting observables, and entanglement of distant quantum systems by continuous measurement.
Unmanned aerial vehicles (UAVs) have recently been widely applied in a comprehensive realm. By enhancing computer photography and artificial intelligence, UAVs can automatically discriminate against environmental objectives and detect events that occur in the real scene. The application of collaborative UAVs will offer diverse interpretations which support a multiperspective view of the scene. Due to the diverse interpretations of UAVs usually deviating, UAVs require a consensus interpretation for the scenario. This study presents an original consensus-based method to pilot multi-UAV systems for achieving consensus on their observation as well as constructing a group situation-based depiction of the scenario. Taylor series are used to describe the fuzzy nonlinear plant and derive the stability analysis using polynomial functions, which have the representations $V(x )={m_{\textrm{1} \le l \le N}}({{V_\textrm{l}}(x )} )$ and ${V_l}(x )={x^T}{P_l}(x )x$. Due to the fact that the ${\dot{P}_l}(x )$ in ${\dot{V}_l}(x )={\dot{x}^T}{P_l}(x )x + {x^T}{\dot{P}_l}(x )x + {x^T}{P_l}(x )\dot{x}$ will yield intricate terms to ensure a stability criterion, we aim to avoid these kinds of issues by proposing a polynomial homogeneous framework and using Euler's functions for homogeneous systems. First, this method permits each UAV to establish high-level conditions from the probed events via a fuzzy-based aggregation event. The evaluated consensus indicates how suitable is the scenario collective interpretation for every UAV perspective.
We present a deep learning approach for near real-time detection of Global Navigation Satellite System (GNSS) radio frequency interference (RFI) based on a large amount of aircraft data collected onboard from the Global Positioning System (GPS) and Attitude and Heading Reference System (AHRS). Our approach enables detection of GNSS RFI in the absence of total GPS failure, i.e. while the receiver is still able to estimate a position, which means RFI sources with low power or at larger distance can be detected. We demonstrate how deep one-class classification can be used to detect GNSS RFI. Furthermore, thanks to a unique dataset from the Swiss Air Force and Swiss Air-Rescue (Rega), preprocessed by Swiss Air Navigation Services Ltd. (Skyguide), we demonstrate application of deep learning for GNSS RFI detection on real-world large scale aircraft data containing flight recordings impacted by real jamming. The approach we present is highly general and can be used as a foundation for solving various automated decision-making problems based on different types of Communications, Navigation and Surveillance (CNS) and Air Traffic Management (ATM) streaming data. The experimental results indicate that our system successfully detects GNSS RFI with 83$\,\cdot\,$5% accuracy. Extensive empirical studies demonstrate that the proposed method outperforms strong machine learning and rule-based baselines.
Accidents are a prevalent feature of working in the maritime industry. While studies have shown to what extent accidents and fatalities have occurred, the current research has generally been limited to commercial shipping. There is nearly no academic research focusing on the safety issues in the superyacht industry. This paper analyses the importance of promoting safety culture in the superyacht industry, the role of maritime legislation in maintaining safety and the role of Port State Control in ensuring all legislation is implemented. It aims to provide a critical examination of safety culture in the superyacht industry and evaluate the appropriateness for further measures to ensure safe working practices. It found out that while some superyachts do maintain an effective safety system, there remains almost 50% of the investigated fleet that do not promote the desired safety culture. It becomes evident that complacency and poor education contribute to the reduced and limited safety culture. The lack of education and awareness is demonstrated when the study shows individuals believing they maintain good safety practices but still admitting to taking various life-threatening risks.
This research boarded on a novel initiative to replace the error-prone and labour-intensive process of converting Paper Nautical Chart (PNC) symbols to Electronic Navigational Chart (ENC) symbols with a more efficient and automated manner using Artificial Intelligence (AI). The proposed method applies the Convolutional Neural Network and YOLOv5 model to recognise and convert symbols from PNC into their corresponding ENC formats. The model's competence was evaluated with performance metrics including Precision, Recall, Average Precision, and mean Average Precision. Among the different variations of the YOLOv5 models tested, the YOLOv5m version revealed the best performance achieving a mean Average Precision of 0 ⋅ 837 for all features. A confusion matrix was used to visualise the model's classification accuracy for various chart symbols, underlining strengths and identifying areas for improvements. While the model has demonstrated high ability in identifying symbols like ‘Obstruction’ and ‘Major/Minor Lights’, it exhibited lesser accuracy with ‘Visible Wreck’ and ‘Background’ categories. Further, the developed graphical user interface (GUI) allowed users to interact with the artificial neural network model without demanding detailed knowledge of the underlying programming or model architecture.
Vessel trajectories from the Automatic Identification System (AIS) play an important role in maritime traffic management, but a drawback is the huge amount of memory occupation which thus results in a low speed of data acquisition in maritime applications due to a large number of scattered data. This paper proposes a novel online vessel trajectory compression method based on the Improved Open Window (IOPW) algorithm. The proposed method compresses vessel trajectory instantly according to vessel coordinates along with a timestamp driven by the AIS data. In particular, we adopt the weighted Euclidean distance (WED), fusing the perpendicular Euclidean distance (PED) and synchronous Euclidean distance (SED) in IOPW to improve the robustness. The realistic AIS-based vessel trajectories are used to illustrate the proposed model by comparing it with five traditional trajectory compression methods. The experimental results reveal that the proposed method could effectively maintain the important trajectory features and significantly reduce the rate of distance loss during the online compression of vessel trajectories.
During the 1519–1522 Magellan expedition, the astronomer Andrés de San Martín made two remarkably accurate longitude measurements, an order of magnitude better than what was typical for the 16th century. How he managed to do so remained shrouded in mystery for the past 500 years. Using modern ephemerides, we have retraced San Martín's observations and calculated their error signatures, clarifying the method he used (a simplified version of lunar distances) and why two out of his six measurements were accurate (a rather fortuitous cancellation of errors). It would be rash to dismiss San Martín's work as sheer luck though, as he was an exceedingly rare combination of a capable astronomer and a knowledgeable mariner.
In this paper, a complete introduction to the dead reckoning navigation technique is offered after a discussion of the many forms of navigation, and the benefits and drawbacks associated with each of those types of navigation. After that, the dead reckoning navigation solution is used as an option that is both low-cost and makes use of the sophisticated equations that are used by the system. Moreover, to achieve the highest level of accuracy in navigation, an investigation of navigation errors caused by dead reckoning is calculated. Employing the suggested dead reckoning navigation system, the final position of an underwater vehicle can be established with a high degree of accuracy by using experimental data (from sensors) and the uncertainties that are associated with the system. Finally, to illustrate the correctness of the dead reckoning navigation process, the system error analysis as uncertainty that was carried out using experimental data using the dead reckoning navigation technique is compared with GPS data.
The release of GNSS raw data on Android smartphones provides the potential for high-precision smartphone positioning using multi-constellation and multi-frequency signals. However, severe multipath and low observation quality in kinematic environments make double-differenced uncombined ambiguities difficult to resolve reliably. To address this, the paper proposes an improved wide-lane (WL) integer ambiguity resolution (IAR) method that combines integer rounding and the Least-Square AMBiguity Decorrelation Adjustment (LAMBDA) methods. The proposed method achieved fix rates of 57% to 70% in challenging environments, with an average improvement of 7 · 7% in horizontal positioning accuracy compared to the float solution. The traditional partial integer rounding method only improved accuracy by 1 · 1%.
The independence polynomial originates in statistical physics as the partition function of the hard-core model. The location of the complex zeros of the polynomial is related to phase transitions, and plays an important role in the design of efficient algorithms to approximately compute evaluations of the polynomial.
In this paper we directly relate the location of the complex zeros of the independence polynomial to computational hardness of approximating evaluations of the independence polynomial. We do this by moreover relating the location of zeros to chaotic behaviour of a naturally associated family of rational functions; the occupation ratios.
Quantum mechanics originally developed for describing non-relativistic systems. It was a natural question to ask how the formalism can be extended to relativistic systems. Besides, it turned out that some of the properties of nonrelativistic systems can be understood naturally in the light of the relativistic theory. One example is the spin of the electron, which has to be introduced in an ad-hoc manner in non-relativistic theory, but appears naturally in the relativistic theory, as we will explain in this chapter. The aim of this chapter is to indicate, rather than elaborate, the kind of questions that can be asked and answered using hints of relativity. A full-edged relativistic theory takes us beyond quantum mechanics, as we argue in §15.1. We also clarify that when we talk of relativity, we only mean the special theory. The general theory of relativity is not discussed at all.
Conict between relativity and quantum mechanics
The special theory of relativity can be interpreted as a theory of the geometry of the 4D space-time, composed of the three spatial dimensions and time. Thus, time and space are treated on equal footing in special relativity.
This is what causes a conict with quantum mechanics. We have used time as a parameter with respect to which we study the evolution of systems. On the other hand, the spatial coordinates indicating the position are treated as operators, acting on the vector space of state vectors. There is no way that one can make a truly relativistic quantum theory if one maintains this status for time and space.
There are two ways out of the impasse. First, we might contemplate making time an operator as well, just as the position coordinates are. In §3.8, we have argued that this cannot be done. The second alternative is to make the spatial coordinates parameters, just like time is. In this case, one needs to study the evolution of objects in space and time, and the objects to be studied should therefore be some kind of functions of position and time. In physics, a function of space and time is called a field. Examples are electromagnetic and gravitation fields, which can depend on both position and time. In order to do relativistic quantum mechanics, i.e., do quantum mechanics in a way that is compatible with the special theory of relativity, one must therefore do some kind of field theory.
Classical mechanics is governed by Newton's laws of motion. It has been very successful, for over three centuries, in explaining motions of objects that we see around us. However, around the beginning of the twentieth century, when it came to understanding the properties of small systems like an atom, classical mechanics seemed inadequate. In this chapter, we will review the basic formulas of classical mechanics and indicate why it could not describe small systems.
Classical mechanics
Classical mechanics seeks a description of the motion of a particle, by specifying the path of motion of the particle, i.e., the position and velocity of the particle at any given instant. In the Newtonian formulation, this is done by invoking the idea of forces, and using Newton's second law of motion, which says that the rate of change of momentum of a particle is equal to the force that acts on the particle:
If we know the forces as a function of time, we can in principle solve this equation. It is a second-order differential equation in time, so we will need two initial conditions to solve the position vector r as a function of time. In particular, if we know the position r and velocity c = dr/dt at an initial instant, we can solve for the position and velocity of the particle at any instant, given the knowledge of the force F.
There are alternative ways of formulating classical mechanics. One of these is the Lagrangian formulation. In this formulation, one defines a function L of coordinates and velocities of all particles in the system, called the Lagrangian. The equation of motion is then given by
where the xa's denote different independent coordinates and ẋa's their time derivatives, i.e., the corresponding velocities.
In earlier chapters, we have analyzed the quantum behavior of particles in many different kinds of Hamiltonian. Some of these Hamiltonians are quite contrived and used for exemplary purposes only. Some are realistic cases, like the case of the hydrogen atom in Chapter 9. In this chapter, we continue discussing realistic interactions, viz., interactions of particles with magnetic fields.
The Hamiltonian
Classical electrodynamics is described by Maxwell equations, which connect the derivatives of the electric field E and magnetic field B to the sources of the electromagnetic field, the charge density ρ and the current density J. All the quantities mentioned are in general functions of position and time. The behavior of a particle of charge q in such a field is described by the Lorentz force law. In the SI units, this force is given by
If we want to solve the classical problem of the path of a particle in an electromagnetic field, we can just set up Newton's equation of motion with the force shown above.
Clearly, this method does not help us solve the corresponding quantum mechanical problem, because the concept of force is not used in the formulation of quantum mechanics. We need to set up the Hamiltonian of the particle in an electromagnetic field. This cannot be done by using the field strength vectors E and B. Instead, we need to use the potentials A and ϕ, which are related to the fields by the relations
With these potentials, there is a very simple prescription for finding the Hamiltonian of a charged particle in an electromagnetic field.
We mentioned in Chapter 5 that the wavefunction of a system consisting of several identical particles has some special symmetries, related to the permutation of the particles. In this chapter, we discuss the issue in detail, throwing light on some consequences of the symmetry.
Many problems that we come across in quantum systems cannot be solved exactly. In fact, exactly solvable problems form only a small fraction of quantum problems that one encounters in realistic physical systems. In the absence of such exact solutions of the Schrödinger equation, one needs to resort to several methods providing approximate solutions. In this chapter we shall list some of these methods for time-independent Hamiltonians.
Variational method
The variational method is often used for a quick estimation of the ground state energy of a Hamiltonian whose exact eigenvalue and eigenstates are unknown. We first describe this method in general terms and then follow the discussion up with examples.
The method
To elucidate the technique, we first note that a trial wavefunction ψ trial for any quantum Hamiltonian H always satisfies the inequality
where E0 is the exact ground state energy of H. To see why this holds, first let us expand ψ triali in the eigenbasis of H:
where |n〉 is nth eigenstate of H with energy En. Since the eigenstates of H form a complete basis, this can always be done. The eigenstates |n〉, as well as the coeficients cn that appear in Eq. (11.2), can be determined only if we can solve the Hamiltonian problem exactly.