Metric magnitude of a point cloud is a measure of its ``size." It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization algorithms. But its usability is limited due to the computational cost when the dataset is large or when the computation must be carried out repeatedly (e.g. in model training). In this paper, we study the magnitude computation problem, and show efficient ways of approximating it. We show that it can be cast as a convex optimization problem, but not as a submodular optimization. The paper describes two new algorithms -- an iterative approximation algorithm that converges fast and is accurate in practice, and a subset selection method that makes the computation even faster. It has previously been proposed that the magnitude of model sequences generated during stochastic gradient descent is correlated to the generalization gap. Extension of this result using our more scalable algorithms shows that longer sequences bear higher correlations. We also describe new applications of magnitude in machine learning -- as an effective regularizer for neural network training, and as a novel clustering criterion.

Autonomous systems are highly vulnerable to a variety of adversarial attacks on Deep Neural Networks (DNNs). Training-free model-agnostic defenses have recently gained popularity due to their speed, ease of deployment, and ability to work across many DNNs. To this end, a new technique has emerged for mitigating attacks on image classification DNNs, namely, preprocessing adversarial images using super resolution - upscaling low-quality inputs into high-resolution images. This defense requires running both image classifiers and super resolution models on constrained autonomous systems. However, super resolution incurs a heavy computational cost. Therefore, in this paper, we investigate the following question: Does the robustness of image classifiers suffer if we use tiny super resolution models? To answer this, we first review a recent work called Super-Efficient Super Resolution (SESR) [1] that achieves similar or better image quality than prior art while requiring 2 × to 330 × fewer Multiply-Accumulate (MAC) operations. We demonstrate that despite being orders of magnitude smaller than existing models, SESR achieves the same level of robustness as significantly larger networks. Finally, we estimate end-to-end performance of super resolution-based defenses on a commercial Arm Ethos-U55 micro-NPU. Our findings show that SESR achieves nearly 3 × higher FPS than a baseline while achieving similar robustness.

We present new array beampattern synthesis approaches via semidefinite relaxation (SDR) for arbitrary array. Compared to the conventional approaches of using weight vectors at the array output for array pattern synthesis, which we refer to as the vector weighting approaches (VWA), weight matrices are used at the array output by MWA for much improved flexibility for optimal array pattern synthesis, and globally optimal solutions can be determined efficiently due to convex optimization formulations. Numerical examples are presented to show the excellent performance of MWA.

A new method for calculating the collision free areas of a manipulator's configuration space (C-space) is demonstrated in this paper. Rather than mapping a point obstacle to an n-dimensional surface in the C-space, the dual problem is considered. That is, regions of the C-space that are guaranteed to be collision free are determined. Whilst some configurations that are collision free are not captured by this method, its speed and low memory usage make it ideal for motion planning in the C-space. It is especially useful for mobile manipulators such as wall climbing robots, where the surrounding terrain changes with each step the robot takes. Being able to compute the mapping of Cartesian to C-space representations of objects in real time is essential, as the workspace for these robots is not static and therefore cannot be precalculated. Once the free areas of C-space have been determined, more conventional path planning techniques which have been developed for point robots moving around forbidden areas can be used for the generation of a motion plan. This means that motion planning can be guaranteed to have an exhaustive search through all possible paths and return the lowest cost path - something that has previously been difficult to achieve with other manipulator motion planning techniques. The technique is demonstrated for a 2-degree of freedom planar manipulator, and will be extended in the future to apply to higher dimensional C-spaces. Further developments are suggested for further optimisation of the technique, most notably the idea of partitioning the C-space.

This paper presents the estimation of the position of the ground plane for navigation of on-road or off-road vehicles, in particular for obstacle detection using stereo vision. Ground plane estimation plays an important role in stereo vision based obstacle detection tasks. V-disparity image is widely used for ground plane estimation. However, it heavily relies on distinct road features which may not exist. In here, we introduce a global correlation method to extract the position of the ground plane in V-disparity image even without distinct road features.

A number of methods have been developed for finding collision free paths for a manipulator moving from one configuration to another. In each of these cases the desired goal configuration must be chosen beforehand. However, in most applications there may be more than one configuration that satisfies the desired position and orientation requirements of the end effector. One of these configurations must be chosen for the path planner; generally we want to select the configuration that results in the lowest cost movement from the manipulator's current position. Until the motion plan is calculated, we cannot know which goal configuration to choose. This paper demonstrates a method for selecting the lowest cost path without needing to calculate a motion plan from the start position to all of the possible goal configurations. Generating motion plans is computationally expensive and it is desirable to limit these computations where ever possible. This is especially true in the case of mobile manipulators where the surrounding terrain for the motion planning calculation changes at each step, meaning that computational savings of reusing calculations from previous runs cannot be realised. The method demonstrated in this paper is shown to be much more suited to these types of applications than more traditional motion planning methods

Maximum likelihood (ML) parameter estimation for multi-dimensional adaptive problems is addressed. Multiple adaptive outputs are ordinarily combined by utilizing the full dimension data. However, many adaptive problems utilize subspace processing for each adaptive beam which can increase the difficulty of many super-resolution techniques. This paper shows that the steering vector structure can be utilized to allow ML techniques for a fixed grid of hypothesis vectors to be computationally feasible for many scenarios.

Advanced airborne radar systems are required to detect targets in the presence of both clutter and jamming. Ground clutter is extended in both angle and range, and is spread in Doppler frequency because of the platform motion. Space-time adaptive processing (STAP) refers to the simultaneous processing of the signals from an array antenna during a multiple pulse coherent waveform. STAP can provide improved detection of targets obscured by mainlobe clutter, defection of targets obscured by sidelobe clutter, and detection in combined clutter and jamming environments. Fully adaptive STAP is impractical for reasons of computational complexity and estimation with limited data, so partially adaptive approaches are required. The paper presents a taxonomy of partially adaptive STAP approaches that are classified according to the type of preprocessor, or equivalently, by the domain in which adaptive weighting occurs. Analysis of the rank of the clutter covariance matrix in each domain provides insight and conditions for preprocessor design.

The authors consider the use of a multiple-beam adaptive array (MBAA) in a packet radio system. In an MBAA, a given set of antenna elements is used to form several antenna patterns simultaneously. When it is used in a packet radio system, an MBAA can successfully receive two or more overlapping packets at the same time. Each beam captures a different packet by automatically pointing its pattern toward one packet while nulling other, contending packets. It is shown how an MBAA can be integrated into a single-hop slotted ALOHA packet radio system, and the resulting throughput is analyzed for both finite- and infinite-user populations.>

The use of an adaptive antenna array as a means of improving the performance of a slotted ALOHA packet radio network is presented. An adaptive array creates a strong capture effect at a packet radio terminal by automatically steering the receiver antenna pattern toward one packet and nulling other contending packets in a slot. A special code preamble and randomized arrival times within each slot allow the adaptive array to lock onto one packet in each slot. The throughput and delay performance of a network with an adaptive array are computed by applying the standard Markov chain analysis of slotted ALOHA. It is shown that throughput levels comparable to carrier sense multiple access (CSMA) are attainable with an adaptive array without the need for stations to be able to hear each other. The performance depends primarily on the number of adaptive array nulls, the array resolution, and the length of the randomization interval within each slot.>