Frequently, we use the Moore-Penrose pseudoinverse (MPP) even in cases when we do not require all of its defining properties. But if the running time and the storage size are critical, we can do better. By discarding some constraints needed for the MPP, we gain freedom to optimize other aspects of the new pseudoinverse. A sparser pseudoinverse reduces the amount of computation and storage. We propose a method to compute a sparse pseudoinverse and show that it offers sizable improvements in speed and storage, with a small loss in the least-squares performance. Differently from previous approaches, we do not attempt to approximate the MPP, but rather to produce an exact but sparse pseudoinverse. In the underdetermined (compressed sensing) scenario we prove that the rescaled sparse pseudoinverse yields an unbiased estimate of the unknown vector, and we demonstrate its potential in iterative sparse recovery algorithms, pointing out directions for future research.
The satellite-based Global Positioning System (GPS) provides robust localization on smartphones outdoors. In indoor environments, however, no system is close to achieving a similar level of ubiquity, with existing solutions offering different trade-offs in terms of accuracy, robustness and cost. In this paper, we develop a multi-modal positioning system, targeted at smartphones, which aims to get the best out of each of its constituent modalities. More precisely, we combine Bluetooth low energy (BLE) beacons, round-trip-time (RTT) enabled WiFi access points and the smartphone's inertial measurement unit (IMU) to provide a cheap robust localization system that, unlike fingerprinting methods, requires no pre-training. To do this, we use a probabilistic algorithm based on a conditional random field (CRF). We show how to incorporate sparse visual information to improve the accuracy of our system, using pose estimation from pre-scanned visual landmarks, to calibrate the system online. Our method achieves an accuracy of around 2 meters on two realistic datasets, outperforming other distance-based localization approaches. We also compare our approach with an ultra-wideband (UWB) system. While we do not match the performance of UWB, our system is cheap, smartphone compatible and provides satisfactory performance for many applications.
Super-directional loudspeaker arrays can be used to achieve high directivity in a limited low-frequency range. As opposed to microphone arrays, the distance between the loudspeakers has to be relatively large, resulting in aliasing starting at relatively low frequencies. On the other hand, mounting a loudspeaker on a rigid baffle (e.g., a rigid cylinder or sphere) increases its directivity with frequency. Using super-directional array techniques at low frequencies and leveraging loudspeakers' increased directivity at high frequencies enables achieving high directivity both at low and high frequencies. The design of baffled circular loudspeaker arrays and an improved beamforming procedure for achieving high directivity in a broad frequency range is described.
We consider the problem of multiple-loudspeaker low-frequency room equalization for a wide listening area, where the equalized loudspeaker is helped using the remaining ones. Using a spatial discretization of the listening area, we formulate the problem as a multipoint error minimization between desired and synthesized magnitude frequency responses. The desired response and cost function are formulated with a goal of capturing the room's spectral power profile, and penalizing strong resonances. Considering physical and psychoacoustical observations, we argue for the use of gain-limited, short, and well-localized equalization filters, with an additional delay for loudspeakers that help the equalized one. We propose a convex optimization framework for computing room equalization filters, where the mentioned filter requirements are incorporated as convex constraints. We verify the effectiveness of our equalization approach through simulations.
For safe and efficient operation, mobile robots need to perceive their environment, and in particular, perform tasks such as obstacle detection, localization, and mapping. Although robots are often equipped with microphones and speakers, the audio modality is rarely used for these tasks. Compared to the localization of sound sources, for which many practical solutions exist, algorithms for active echolocation are less developed and often rely on hardware requirements that are out of reach for small robots.We propose an end-to-end pipeline for sound-based localization and mapping that is targeted at, but not limited to, robots equipped with only simple buzzers and low-end microphones. The method is model-based, runs in real time, and requires no prior calibration or training. We successfully test the algorithm on the e-puck robot with its integrated audio hardware, and on the Crazyflie drone, for which we design a reproducible audio extension deck. We achieve centimeter-level wall localization on both platforms when the robots are static during the measurement process. Even in the more challenging setting of a flying drone, we can successfully localize walls, which we demonstrate in a proof-of-concept multi-wall localization and mapping demo.
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