One of the most fundamental problems in simultaneous localization and mapping (SLAM) is the ability to take into account data association (DA) uncertainties. In this paper, this problem is addressed by proposing a multi-hypotheses sampling distribution for particle filtering-based SLAM algorithms. By modeling the measurements and landmarks as random finite sets, an importance density approximation that incorporates DA uncertainties is derived. Then, a tractable Gaussian mixture model approximation of the multi-hypotheses importance density is proposed in which each mixture component represents a different DA. Finally, an iterative method for approximating the mixture components of the sampling distribution is utilized and a partitioned update strategy is developed. Using synthetic and experimental data, it is demonstrated that the proposed importance density improves the accuracy and robustness of landmark-based SLAM in cluttered scenarios over state-of-the-art methods. At the same time, the partitioned update strategy makes it possible to include multiple DA hypotheses in the importance density approximation, leading to a favorable linear complexity scaling, in terms of the number of landmarks in the field-of-view.

Received signal strength based device-free localization applications utilize a model that relates the measurements to position of the wireless sensors and person, and the underlying inverse problem is solved either using an imaging method or a nonlinear Bayesian filter. In this paper, it is shown that the Bayesian filters nearly reach the posterior Cramer-Rao bound and they are superior with respect to imaging approaches in terms of localization accuracy because the measurements are directly related to position of the person. However, Bayesian filters are known to suffer from divergence issues and in this paper, the problem is addressed by introducing a novel Bayesian filter. The developed filter augments the measurement model of a Bayesian filter with position estimates from an imaging approach. This bounds the filter's measurement residuals by the position errors of the imaging approach and as an outcome, the developed filter has robustness of an imaging method and tracking accuracy of a Bayesian filter. The filter is demonstrated to achieve a localization error of 0.11 m in a 75 m2open indoor deployment and an error of 0.29 m in a 82 m2apartment experiment, decreasing the localization error by 30-48 percent with respect to a state-of-the-art imaging method.

This paper is concerned with the estimation of unknown drift functions of stochastic differential equations (SDEs) from observations of their sample paths. We propose to formulate this as a non-parametric Gaussian process regression problem and use an Ito-Taylor expansion for approximating the SDE. To address the computational complexity problem of Gaussian process regression, we cast the model in an equivalent state-space representation, such that (non-linear) Kalman filters and smoothers can be used. The benefit of these methods is that computational complexity scales linearly with respect to the number of measurements and hence the method remains tractable also with large amounts of data. The overall complexity of the proposed method is O(N log N), where N is the number of measurements, due to the requirement of sorting the input data. We evaluate the performance of the proposed method using simulated data as well as with real-data applications to sunspot activity and electromyography.

In this letter, we consider Gaussian approximations of the optimal importance density in sequential importance sampling for nonlinear, non-Gaussian state-space models. The proposed method is based on generalized statistical linear regression and posterior linearization using conditional expectations. Simulation results show that the method outperforms the compared methods in terms of the effective sample size and provides a better local approximation of the optimal importance density.

Received signal strength based respiration rate monitoring is emerging as an alternative non-contact technology. These systems make use of the radio measurements of short-range commodity wireless devices, which vary due to the inhalation and exhalation motion of a person. The success of respiration rate estimation using such measurements depends on the signal-to-noise ratio, which alters with properties of the person and with the measurement system. To date, no model has been presented that allows evaluation of different deployments or system configurations for successful breathing rate estimation. In this paper, a received signal strength model for respiration rate monitoring is introduced. It is shown that measurements in linear and logarithmic scale have the same functional form, and the same estimation techniques can be used in both cases. The model is numerically and empirically evaluated, and its properties are discussed in depth. The most important model implications are validated under varying signal-to-noise ratio conditions using the performances of three estimators: batch frequency estimator, recursive Bayesian estimator, and model-based estimator. The results are in coherence with the findings, and they imply that different estimators are advantageous in different signal-to-noise ratio regimes.

Electrocardiography (ECG) using lightweight and inexpensive ambulatory ECG devices makes it possible to monitor patients during their daily activities and can give important insight in arrhythmias and other cardiac diseases. However, everyday activities cause several kinds of motion artifacts which deteriorate the ECG quality and thus complicate both automated and manual ECG analysis. In this paper, we discuss some of the challenges associated with long-term ambulatory ECG and propose a baseline wander compensation algorithm based on inertial measurement units (IMUs) attached to each ECG electrode. The IMUs are used for estimating the local electrode motion which in turn is used as the reference signal for baseline wander reduction. We evaluate the proposed algorithm on data gathered in clinical trials and show that the baseline wander is successfully removed, without compromising the ECG's morphology.

In this paper, we propose an auxiliary-particle-filter-based two-filter smoother for Wiener state-space models. The proposed smoother exploits the model structure in order to obtain an analytical solution for the backward dynamics, which is introduced artificially in other two-filter smoothers. Furthermore, Gaussian approximations to the optimal proposal density and the adjustment multipliers are derived for both the forward and backward filters. The proposed algorithm is evaluated and compared to existing smoothing algorithms in a numerical example where it is shown that it performs similarly to the state of the art in terms of the root mean squared error at lower computational cost for large numbers of particles.

This paper is concerned with tracking of reference vectors in the continuous-discrete-time setting. For this end, an Itô stochastic differential equation, using the gyroscope as input, is formulated that explicitly accounts for the geometry of the problem. The filtering problem is solved by restricting the prediction and filtering distributions to the von Mises-Fisher class, resulting in ordinary differential equations for the parameters. A strategy for approximating Bayesian updates and marginal likelihoods is developed for the class of conditionally spherical measurement distributions' which is realistic for sensors such as accelerometers and magnetometers, and includes robust likelihoods. Furthermore, computationally efficient and numerically robust implementations are presented. The method is compared to other state-of-the-art filters in simulation experiments involving tracking of the local gravity vector. Additionally, the methodology is demonstrated in the calibration of a smartphone's accelerometer and magnetometer. Lastly, the method is compared to state-of-the-art in gravity vector tracking for smartphones in two use cases, where it is shown to be more robust to unmodeled accelerations.

Received signal strength (RSS)-based device-free localization applications utilize the communication between wireless devices for locating people within the monitored area. The technology is based on the fact that humans cause changes in properties of the wireless channel which is observed in the RSS, enabling localization of people without requiring them to carry any sensor, tag or device. Typically this inverse problem is solved using an empirical model that relates the RSS to location of the sensors and person, and utilizing either an imaging method or a particle filter (PF) for positioning. In this paper, we present an extended Kalman filtering (EKF) solution that incorporates some of the beneficial properties of the PF but has a lower computational overhead. In order to make the EKF work, we also need to reconsider how the measurements are sampled and processed, and a new processing scheme is proposed. The developments are validated using simulations and experimental data, and the results imply: i) the non-linear filters outperform a popular imaging method; ii) the robustness of the EKF and PF is improved using the proposed processing scheme; and iii) the EKF achieves similar performance as the PF as long as the new processing scheme is used.

In this paper, IMU and magnetometer models that enable pedestrian dead-reckoning without step detection or zero velocity updates on hand-held devices such as smartphones are proposed. The models are suitable for usage with any standard Bayesian filtering or smoothing technique and thus, do not require customized estimators. The method is evaluated in a real scenario using a dataset of approximately three minutes with a trajectory length of 302m. It is found that the overall shape of the estimated trajectory matches well with the GPS reference trajectory with an estimated trajectory length of 293m. Some problems in the heading estimation are observed.

Accurate and robust mobile robot localization is very important in many robot applications. Monte Carlo localization (MCL) is one of the robust probabilistic solutions to robot localization problems. The sensor model used in MCL directly influence the accuracy and robustness of the pose estimation process. The classical beam models assumes independent noise in each individual measurement beam at the same scan. In practice, the noise in adjacent beams maybe largely correlated. This will result in peaks in the likelihood measurement function. These peaks leads to incorrect particles distribution in the MCL. In this research, an adaptive sub-sampling of the measurements is proposed to reduce the peaks in the likelihood function. The sampling is based on the complete scan analysis. The specified measurement is accepted or not based on the relative distance to other points in the 2D point cloud. The proposed technique has been implemented in ROS and stage simulator. The result shows that selecting suitable value of distance between accepted scans can improve the localization error and reduce the required computations effectively.

Traffic monitoring using low-cost two-axis magnetometers is considered. Although detection of metallic vehicles is rather easy, detecting the driving direction is more challenging. We propose a simple algorithm based on a nonlinear transformation of the measurements, which is simple to implement in embedded hardware. A theoretical justification is provided, and the statistical properties of the test statistic are presented in closed form. The method is compared with the standard likelihood ratio test on both simulated data and real data from field tests, where very high detection rates are reported, despite the presence of sensor saturation, measurement noise, and near-field effects of the magnetic field.

We present an approach for computing the heading direction of a vehicle by processing measurements from a 2-axis magnetometer rapidly. The proposed method relies on a non-linear transformation of the measurement data comprising only two inner products. Deterministic analysis of the signal model shows how the heading direction is contained in the signal and the proposed estimator is analyzed in terms of its statistical properties. Experimental verification indicates that good performance is achieved under the presence of saturation, measurement noise, and near field effects.