In this paper, we present a novel algorithm for quantifying uncertainty and information gained within 3D Gaussian Splatting (3D-GS) through P-Optimality. While 3D-GS has proven to be a useful world model with high-quality rasterizations, it does not natively quantify uncertainty or information, posing a challenge for real-world applications such as 3D-GS SLAM. We propose to quantify information gain in 3D-GS by reformulating the problem through the lens of optimal experimental design, which is a classical solution widely used in literature. By restructuring information quantification of 3D-GS through optimal experimental design, we arrive at multiple solutions, of which T-Optimality and D-Optimality perform the best quantitatively and qualitatively as measured on two popular datasets. Additionally, we propose a block diagonal covariance approximation which provides a measure of correlation at the expense of a greater computation cost.

In this paper, we present a novel algorithm for probabilistically updating and rasterizing semantic maps within 3D Gaussian Splatting (3D-GS). Although previous methods have introduced algorithms which learn to rasterize features in 3D-GS for enhanced scene understanding, 3D-GS can fail without warning which presents a challenge for safety-critical robotic applications. To address this gap, we propose a method which advances the literature of continuous semantic mapping from voxels to ellipsoids, combining the precise structure of 3D-GS with the ability to quantify uncertainty of probabilistic robotic maps. Given a set of images, our algorithm performs a probabilistic semantic update directly on the 3D ellipsoids to obtain an expectation and variance through the use of conjugate priors. We also propose a probabilistic rasterization which returns per-pixel segmentation predictions with quantifiable uncertainty. We compare our method with similar probabilistic voxel-based methods to verify our extension to 3D ellipsoids, and perform ablation studies on uncertainty quantification and temporal smoothing.

In this article, we develop a modular neural network for real-time (>10 Hz) semantic mapping in uncertain environments, which explicitly updates per-voxel probabilistic distributions within a neural network layer. Our approach combines the reliability of classical probabilistic algorithms with the performance and efficiency of modern neural networks. Although robotic perception is often divided between modern differentiable methods and classical explicit methods, a union of both is necessary for real-time and trustworthy performance. We introduce a novel convolutional Bayesian kernel inference (ConvBKI) layer which incorporates semantic segmentation predictions online into a 3-D map through a depthwise convolution layer by leveraging conjugate priors. We compare ConvBKI against state-of-the-art deep learning approaches and probabilistic algorithms for mapping to evaluate reliability and performance. We also create a robot operating system package of ConvBKI and test it on real-world perceptually challenging off-road driving data.

Robotic perception is currently at a cross-roads between modern methods, which operate in an efficient latent space, and classical methods, which are mathematically founded and provide interpretable, trustworthy results. In this paper, we introduce a Convolutional Bayesian Kernel Inference (Con-vBKI) layer which learns to perform explicit Bayesian inference within a depthwise separable convolution layer to maximize efficency while maintaining reliability simultaneously. We apply our layer to the task of real-time 3D semantic mapping, where we learn semantic-geometric probability distributions for LiDAR sensor information and incorporate semantic predictions into a global map. We evaluate our network against state-of-the-art semantic mapping algorithms on the KITTI data set, demonstrating improved latency with comparable semantic label inference results.

This paper shows experimentally that standard wireless networks which measure received signal strength (RSS) can be used to reliably detect human breathing and estimate the breathing rate, an application we call “BreathTaking”. We present analysis showing that, as a first order approximation, breathing induces sinusoidal variation in the measured RSS on a link, with amplitude a function of the relative amplitude and phase of the breathing-affected multipath. We show that although an individual link may not reliably detect breathing, the collective spectral content of a network of devices reliably indicates the presence and rate of breathing. We present a maximum likelihood estimator (MLE) of breathing rate, amplitude, and phase, which uses the RSS data from many links simultaneously. We show experimental results which demonstrate that reliable detection and frequency estimation is possible with 30 seconds of data, within 0.07 to 0.42 breaths per minute (bpm) RMS error in several experiments. The experiments also indicate that the use of directional antennas may improve the systems robustness to external motion.

Device-free localization (DFL) is the estimation of the position of a person or object that does not carry any electronic device or tag. Existing model-based methods for DFL from RSS measurements are unable to locate stationary people in heavily obstructed environments. This paper introduces measurement-based statistical models that can be used to estimate the locations of both moving and stationary people using received signal strength (RSS) measurements in wireless networks. A key observation is that the statistics of RSS during human motion are strongly dependent on the RSS "fade level” during no motion. We define fade level and demonstrate, using extensive experimental data, that changes in signal strength measurements due to human motion can be modeled by the skew-Laplace distribution, with parameters dependent on the position of person and the fade level. Using the fade-level skew-Laplace model, we apply a particle filter to experimentally estimate the location of moving and stationary people in very different environments without changing the model parameters. We also show the ability to track more than one person with the model.

A wireless network can use the variance of measured received signal strength (RSS) on the links in a network to infer the locations of people or objects moving in the network deployment area. This paper provides a statistical model for the RSS variance as a function of a person's position with respect to the transmitter (TX) and receiver (RX) locations. We show that the ensemble mean of the RSS variance has an approximately linear relationship with the expected value of total affected power (ETAP), for a range of ETAP. We derive approximate expressions for the ETAP as a function of the person's position, for scattering and reflection, which are tested via simulation. Counterintuitively, we show that reflection, not scattering, causes the RSS variance contours to be shaped similar to Cassini ovals. Results reported in past literature and from a new experiment reported in this paper are shown to be as predicted by the analysis.

This paper presents a new method for imaging, localizing, and tracking motion behind walls in real time. The method takes advantage of the motion-induced variance of received signal strength measurements made in a wireless peer-to-peer network. Using a multipath channel model, we show that the signal strength on a wireless link is largely dependent on the power contained in multipath components that travel through space containing moving objects. A statistical model relating variance to spatial locations of movement is presented and used as a framework for the estimation of a motion image. From the motion image, the Kalman filter is applied to recursively track the coordinates of a moving target. Experimental results for a 34-node through-wall imaging and tracking system over a 780 square foot area are presented.

In this paper, we discuss the emerging application of device-free localization (DFL) using wireless sensor networks, which find people and objects in the environment in which the network is deployed, even in buildings and through walls. These networks are termed “RF sensor networks” because the wireless network itself is the sensor, using radio-frequency (RF) signals to probe the deployment area. DFL in cluttered multipath environments has been shown to be feasible, and in fact benefits from rich multipath channels. We describe modalities of measurements made by RF sensors, the statistical models which relate a person's position to channel measurements, and describe research progress in this area.

Radio Tomographic Imaging (RTI) is an emerging technology for imaging the attenuation caused by physical objects in wireless networks. This paper presents a linear model for using received signal strength (RSS) measurements to obtain images of moving objects. Noise models are investigated based on real measurements of a deployed RTI system. Mean-squared error (MSE) bounds on image accuracy are derived, which are used to calculate the accuracy of an RTI system for a given node geometry. The ill-posedness of RTI is discussed, and Tikhonov regularization is used to derive an image estimator. Experimental results of an RTI experiment with 28 nodes deployed around a 441 square foot area are presented.