In this paper, the derivation of the Bayesian Bhattacharyya bound for discrete-time filtering as proposed ina paper by Reece and Nicholson is revisited. It turns out that the results presented in the aforementioned contribution are incorrect, as some expectations appearing in the information matrix recursions are missing. This paper gives a generalized derivation of the N-th order Bayesian Bhattacharyya bound and presents corrected expressions for the case N = 2. A nonlinear toy example is used to illustrate the results

The general Simultaneous Localisation and Mapping (SLAM) problem aims at estimating the state of a moving platform simultaneously with building a map of the local environment. There are essentially three classes of algorithms. EKF- SLAM and FastSLAM solve the problem on-line, while Nonlinear Least Squares (NLS) is a batch method. All of them scales badly with either the state dimension, the map dimension or the batch length. We investigate the EM algorithm for solving a generalized version of the NLS problem. This EM-SLAM algorithm solves two simpler problems iteratively, hence it scales much better with dimensions. The iterations switch between state estimation, where we propose an Extended Rauch-Tung-Striebel smoother, and map estimation, where a quasi-Newton method is suggested. The proposed method is evaluated in real experiments and also in simulations on a platform with a monocular camera attached to an inertial measurement unit. It is demonstrated to produce lower RMSE than with a standard Levenberg-Marquardt solver of NLS problem, at a computational cost that increases considerably slower. 

This work evaluates a previously introduced algorithm called Particle-Based Rapid Incremental Smoother within the framework of state inference and parameter identification in Jump Markov Non-Linear System. It is applied to the recursive form of two well-known Maximum Likelihood based algorithms who face the common challenge of online computation of smoothed additive functionals in order to accomplish the task of model parameter estimation. This work extends our previous contributions on identification of Markovian switching systems with the goal to reduce the computational complexity. A benchmark problem is used to illustrate the results.

Most navigation systems today rely on global navigation satellite systems (gnss), including in cars. With support from odometry and inertial sensors, this is a sufficiently accurate and robust solution, but there are future demands. Autonomous cars require higher accuracy and integrity. Using the car as a sensor probe for road conditions in cloud-based services also sets other kind of requirements. The concept of the Internet of Things requires stand-alone solutions without access to vehicle data. Our vision is a future with both invehicle localization algorithms and after-market products, where the position is computed with high accuracy in gnss-denied environments. We present a localization approach based on a prior that vehicles spend the most time on the road, with the odometer as the primary input. When wheel speeds are not available, we present an approach solely based on inertial sensors, which also can be used as a speedometer. The map information is included in a Bayesian setting using the particle filter (PF) rather than standard map matching. In extensive experiments, the performance without gnss is shown to have basically the same quality as utilizing a gnss sensor. Several topics are treated: virtual measurements, dead reckoning, inertial sensor information, indoor positioning, off-road driving, and multilevel positioning.

GPS is widely used for localization and tracking, however traditional GPS receivers consume too much energy for many applications. This paper implements and evaluates the performance of a low-energy GPS prototype. The main difference is that a traditional GPS needs to sample signals transmitted by satellites for 30 seconds to estimate its position. Our prototype reduces this time by three orders of magnitude and it can compute positions from only 2 milliseconds of data. We present a new algorithm that increases robustness by filtering on estimated residuals instead of using an altitude database. In addition, we show that our new algorithm works with both fixed and moving targets. The solution consists of (1) a portable device that samples the GPS signal and (2) a server that utilizes Doppler navigation and Coarse Time Navigation to estimate positions. We performed tests in a wide variety of environments and situations. These tests show that our prototype provides a median positioning error of roughly 40 meters even when the GPS receiver is moving at 80 kilometres per hour.

We still have very little knowledge about how ourbrains decouple different sound sources, which is known assolving the cocktail party problem. Several approaches; includingERP, time-frequency analysis and, more recently, regression andstimulus reconstruction approaches; have been suggested forsolving this problem. In this work, we study the problem ofcorrelating of EEG signals to different sets of sound sources withthe goal of identifying the single source to which the listener isattending. Here, we propose a method for finding the number ofparameters needed in a regression model to avoid overlearning,which is necessary for determining the attended sound sourcewith high confidence in order to solve the cocktail party problem.

This paper proposes a diagonal covariance matrix approximation for Wide-Sense Stationary (WSS) signals with correlated Gaussian noise. Existing signal models that incorporate correlations often require regularization of the covariance matrix, so that the covariance matrix can be inverted. The disadvantage of this approach is that matrix inversion is computational intensive and regularization decreases precision. We use Bienayme's theorem to approximate the covariance matrix by a diagonal one, so that matrix inversion becomes trivial, even with nonuniform rather than only uniform sampling that was considered in earlier work. This approximation reduces the computational complexity of the estimator and estimation bound significantly. We numerically validate this approximation and compare our approach with the Maximum Likelihood Estimator (MLE) and Cramer-Rao Lower Bound (CRLB) for multivariate Gaussian distributions. Simulations show that our approach differs less than 0.1% from this MLE and CRLB when the observation time is large compared to the correlation time. Additionally, simulations show that in case of non-uniform sampling, we increase the performance in comparison to earlier work by an order of magnitude. We limit this study to correlated signals in the time domain, but the results are also applicable in the space domain.

We study severely quantized received signal strength (RSS)-based cooperative localization in wireless sensor networks. We adopt the well-known sum-product algorithm over a wireless network (SPAWN) framework in our study. To address the challenge brought by severely quantized measurements, we adopt the principle of importance sampling and design appropriate proposal distributions. Moreover, we propose a parametric SPAWN in order to reduce both the communication overhead and the computational complexity. Experiments with real data corroborate that the proposed algorithms can achieve satisfactory localization accuracy for severely quantized RSS measurements. In particular, the proposed parametric SPAWN outperforms its competitors by far in terms of communication cost. We further demonstrate that knowledge about non-connected sensors can further improve the localization accuracy of the proposed algorithms.

This paper is concerned with cooperative Terrain Aided Navigation of a network of aircraft using fusion of Radar Altimeter and inter-node range measurements. State inference is performed using a Rao-Blackwellized Particle Filter with online measurement noise statistics estimation. For terrain coverage measurement noise parameter identification, an online Expectation Maximization algorithm is proposed, where local sufficient statistics at each node are calculated in the E-step, which are then distributed to neighboring nodes using a random gossip algorithm to perform the M-step at each node. Simulation results show that improvement on positioning and calibration performance can be achieved compared to a non-cooperative approach.

Positioning in cellular networks is often based on mobile-assisted measurements of serving and neighboring base stations. Traditionally, positioning is considered to be enabled when the mobile provides measurements of three different base stations. In this paper, we additionally investigate positioning based on time series of Time Of Flight (TOF) and Time Difference of Arrival (TDOA) measurements gathered from two base stations with known positions, where the specific base stations involved depend on the trajectory of the mobile station.. The set of two base stations is different along the trajectory. Each report contains TOF for the serving base station, and one TDOA measurement for the most favorable neighboring base station relative the serving base station. We derive explicit analytical solution related to the intersection of the absolute distance circle (from TOF) and relative distance hyperbola (from TDOA). We consider both geometric noise-free problem and the more realistic problem with additive noise as delivered in the 3rd Generation Partnership Project (3GPP) Long-Term Evolution (LTE). Positioning performance is evaluated using the Cramer-Rao lower bound.