For high technology companies such as Leonardo engaging in innovative research that might not produce a commercial return on investment for up to 10 years or beyond is vital. Our vision is to enable a paradigm shift in high-value low-volume remote sensing systems from concept to production: this requires a fusion of computational imaging concepts, that blur the traditional boundaries between sensing and signal processing, through-life digital modelling, that places innovative manufacture at the heart of the total system design and finally, individual AI/Robotic support, that multiplies the output of highly skilled production and maintenance personnel. The low volume, highly complex sensor systems produced by Leonardo present complex engineering challenges for design and production. Advances in machine learning, cobotics, novel materials, additive manufacturing, digital twinning and signal & image processing provide new paradigms for the end-to-end design and production processes and requires the development of a fully integrated digital design, assembly and manufacturing capability.

Ultra wideband (UWB) technology is one of the latest radio-frequency (RF) device technologies to hit the news. The new technology is very promising for future wireless communications and imaging radar applications where high-capacity multiple access and ultra high speed transmission up to several hundreds of Mbps can be implemented. UWB has the potential to make a substantial contribution to the UK economy. However, with the expansion of wireless communications and services, the available RF spectrum is growing scarce. The problem of interference with other services is one which must be solved if the great potential of UWB is to be fully exploited. Filtering technologies are key to controlling the spectrum of RF signals and tackling interference issues. This proposal aims at developing advanced UWB filters for future UWB wireless communications and radar systems.System-on-package (SOP) is a very attractive approach for the development of future UWB RF front-ends, where a high-performance module can be implemented while simultaneously achieving cost and size reduction. To this end, the proposed research will deploy liquid crystal polymer (LCP) that has recently emerged as a new microwave substrate and package material. It has a low loss over a very wide frequency range, near hermetic nature, multilayer capability, and is low cost, and so is ideal for SOP integration. In particular, such a low-cost solution is vital if UWB products are to succeed in the personal consumer market.With this new material a great deal of effort is required on the design and implementation. The proposed research will investigate new design philosophies. Innovative UWB filtering structures that exploit multilayer capability of LCP will be implemented in the light of enabling manufacturing technologies such as laser machining. The reconfigurable UWB filtering sub-system integrating both active and passive components in a single LCP package will be developed.

In this proposal we seek to establish a Centre for Doctoral Training in Mathematical Analysis and its Applications. The main purpose of the centre is to train upwards of 60 new PhD students in this area over several years, and in doing so address the proven skills need for highly-trained researchers in this area. The centre will be founded on rigorous mathematical analysis and its applications, with a strong focus on nonlinear partial differential equations, under three broad themes: theoretical, stochastic and numerical. Its scope includes harmonic analysis, mathematical analysis of large-scale discrete structures, applied analysis, dynamical systems, stochastic analysis, financial mathematics, applied probability and computational mathematics. There will be a special emphasis on the connections and interactions between these areas, and their applications, and active collaboration with industry -- in the formulation of student projects, in mentoring PhD students, in developing work placements for the students, and more broadly in two-way knowledge exchange -- will be a key feature of this CDT. The need for mathematicians trained in this centre is manifest in real-world phenomena where cutting-edge differential and/or stochastic models are needed, for example in oil extraction, in power grid renewable energy strategies, in finance processes, in ecological impacts of climate change, and in procceses inside the brain. We shall provide a flow of such PhDs with multiple skill sets and the ability to deal with the sophisticated challenges arising in mathematical modelling: they will be able to both analyse and implement and will be in a position to mount rapid and agile responses to current and future challenges. MIGSAA training will be constructed on two main pillars: outstanding academic provision and early-stage career development. These are underpinned by development of a strong sense of cohort. As a fully integrated joint 4 year PhD programme, it will offer much more than the standard UK Mathematics PhD model. Initial academic training will build upon the firm foundation provided by SMSTC, and will feature a strong taught and assessed component. Students will also complete two assessed projects during their first year. It is intended that the two projects will span the areas of MIGSAA, and will provide a firm basis for choosing the topic for the main PhD dissertation towards the end of Year 1. The main PhD project, which will be challenging and substantial, will lead to original research findings at the cutting edge of mathematical endeavour. A tranche of specially designed, more advanced courses will be available for students in Year 2 and beyond so that students will continue to consolidate the available knowledge and expertise as they continue on their main research project. Students will be further supported by a carefully-planned programme of complementary research activities. There will be a strong focus on early-stage career development in its broadest sense. This will include training in public engagement, effective collaboration, understanding the impact agenda and responsible innovation, leadership, outreach, media training, engagement with industry and networking. Central to our vision for MIGSAA is the sense of cohort which it will foster. Beginning with the annual induction event, the cohort environment already offered by participation in SMSTC will be significantly enhanced by provision of contiguous office accommodation and dedicated common spaces, with Year 1 students collocated at ICMS in central Edinburgh. For the later years cohort activities include: physical attendance at higher level courses, research seminars and generic skills courses; active working groups encouraging peer-to-peer learning; annual residential symposia.

Precision timing is essential for accurate navigation and a large variety of civilian commercial and military infrastructure services including both small and large fixed and mobile platforms. These include: space, air, ground and marine vehicles, RADAR, reliable energy supply, safe transport links for air traffic control, network servers for data networks and electronic financial transactions. All of these are critical to the security and stability of the nation as many systems currently rely on large atomic clocks and the Global Navigation Satellite Systems (GNSS) for the timing signal. The aim of this project is to develop new types of atomic clock which offer enhanced timing in a compact and autonomous form-factor. This work will produce simplified Physics packages which when combined with state-of-the-arts flywheel oscillators produce highly accurate and stable compact atomic clocks. This high level of stability enables systems based on these clocks to operate independently of external sources.

In recent decades, atomic clocks have developed from being solely research instruments to indispensable and infrastructure-critical devices. Atomic clocks are now widely used in Global Navigation Satellite Systems (GNSS), data centres, power and mobile networks, financial markets for transaction time stamping, and research and development. Presently, many applications requiring high-precision timing rely on GNSS signals. However, this makes crucial infrastructure vulnerable to GNSS tampering and failure, with significant socio-economic consequences. Therefore, local high-performance atomic clocks are needed to safeguard against this. Other applications need to function in a GNSS-denied environment such as the navigation of submarines or electronic warfare and other security situations. Clock performance beyond GNSS capability is also required for state-of-the-art scientific research and advanced timekeeping. Current portable clocks currently have limited stability and accuracy or are too large and sensitive for applications on mobile platforms. While there has been immense progress in the miniaturisation of the laser systems and spectroscopy units for high-precision optical atomic clocks there are still two main challenges to overcome: The reference laser that requires a high-finesse optical cavity and the optical-frequency comb (OFC) that is required to convert the optical reference signal to a usable electronic signal. Here we propose to employ Raman transitions to create a highly stable and accurate atomic clock. In contrast to optical atomic clocks, the atomic reference stability is not transferred to the frequency of a single laser but is encoded in the frequency difference between two Raman lasers. This significantly relaxes requirements on the OFC and the optical cavity for the clock lasers. For the realisation of a THz-clock, we propose using calcium ions trapped in an RF ion trap and the Raman transition between the D3/2-level and the D5/2-level. The frequency splitting between these two states is 1.819 THz and the expected fractional frequency accuracy of the clock is better than 10-14 (systematic accuracy better than 1e-15) with a 20-litre form factor, significantly smaller than current optical clock systems. Due to its high accuracy in conjunction with small SWAP as well as robustness, this novel clock is exceptionally fit for applications on mobile platforms and in locations with low environmental control. Such portability, makes it particularly well suited for applications in the defence and security sector and as GNNS holdover clocks for telecom and utility networks as well as data centres and financial markets with holdover times of several months. Additionally, it enables novel schemes for frequency dissemination and synchronisation across large-scale telecom networks. Within this project, we will set up the THz-clock with equipment provided by CPI, characterise its performance and test the system in some application-relevant scenarios. CPI will perform environmental testing in their test facility, Leonardo will test the clock's performance on a mobile platform, and BT will investigate next-generation schemes for frequency dissemination and synchronisation across large optical fibre networks.