Adaptive Basis Function Selection for Computationally Efficient Predictions

Basis Function (BF) expansions are a cornerstone of any engineer's toolbox for computational function approximation which shares connections with both neural networks and Gaussian processes. Even though BF expansions are an intuitive and straightforward model to use, they suffer from quadratic computational complexity in the number of BFs if the predictive variance is to be computed. We develop a method to automatically select the most important BFs for prediction in a sub-domain of the model domain. This significantly reduces the computational complexity of computing predictions while maintaining predictive accuracy. The proposed method is demonstrated using two numerical examples, where reductions up to 50-75% are possible without significantly reducing the predictive accuracy.

Joint State and Parameter Estimation Using the Partial Errors-in-Variables Principle

This letter proposes a new method for joint state and parameter estimation in uncertain dynamical systems. We exploit the partial errors-in-variables (PEIV) principle and formulate a regression problem in the sense of weighted total least squares, where the uncertainty in the parameter prior is explicitly considered. Based thereon, the PEIV regression can be solved iteratively through the Kalman smoothing and the regularized least squares for estimating the state and the parameter, respectively. The simulations demonstrate improved accuracy of the proposed method compared to existing approaches, including the joint maximum a posterior-maximum likelihood, the expectation maximisation, and the augmented state extended Kalman smoother.

An Observability-Constrained Magnetic-Field-Aided Inertial Navigation System

A method to construct an observability-constrained magnetic-field-aided inertial navigation system is proposed. The proposed method builds upon the previously proposed observability-constrained extended Kalman filter and extends it to work with a magnetic-field-based odometry-aided inertial navigation system. The proposed method is evaluated using simulation and real-world data, showing that (i) the system observability properties are preserved, (ii) the estimation accuracy increases, and (iii) the perceived uncertainty calculated by the EKF is more consistent with the true uncertainty of the filter estimates.

Matrix-Valued Measures and Wishart Statistics for Target Tracking Applications

Ensuring sufficiently accurate models is crucial in target tracking systems. If the assumed models deviate too much from the truth, the tracking performance might be severely degraded. While the models are in general defined using multivariate conditions, the measures used to validate them are most often scalar-valued. In this paper, we propose matrix-valued measures for both offline and online assessment of target tracking systems. Recent results from Wishart statistics, and approximations thereof, are adapted and it is shown how these can be incorporated to infer statistical properties for the eigenvalues of the proposed measures. In addition, we relate these results to the statistics of the baseline measures. Finally, the applicability of the proposed measures are demonstrated using two important problems in target tracking: (i) distributed track fusion design; and (ii) filter model mismatch detection.

Bayesian Simultaneous Localization and Multi-Lane Tracking Using Onboard Sensors and a SD Map

High-definition map with accurate lane-level information is crucial for autonomous driving, but the creation of these maps is a resource-intensive process. To this end, we present a cost-effective solution to create lane-level roadmaps using only the global navigation satellite system (GNSS) and a camera on customer vehicles. Our proposed solution utilizes a prior standard-definition (SD) map, GNSS measurements, visual odometry, and lane marking edge detection points, to simultaneously estimate the vehicle's 6D pose, its position within a SD map, and also the 3D geometry of traffic lines. This is achieved using a Bayesian simultaneous localization and multi-object tracking filter, where the estimation of traffic lines is formulated as a multiple extended object tracking problem, solved using a trajectory Poisson multi-Bernoulli mixture (TPMBM) filter. In TPMBM filtering, traffic lines are modeled using B-spline trajectories, and each trajectory is parameterized by a sequence of control points. The proposed solution has been evaluated using experimental data collected by a test vehicle driving on highway. Preliminary results show that the traffic line estimates, overlaid on the satellite image, generally align with the lane markings up to some lateral offsets.

MAINS: A Magnetic Field Aided Inertial Navigation System for Indoor Positioning

A Magnetic field Aided Inertial Navigation System (MAINS) for indoor navigation is proposed in this paper. MAINS leverages an array of magnetometers to measure spatial variations in the magnetic field, which are then used to estimate the displacement and orientation changes of the system, thereby aiding the inertial navigation system (INS). Experiments show that MAINS significantly outperforms the stand-alone INS, demonstrating a remarkable two orders of magnitude reduction in position error. Furthermore, when compared to the state-of-the-art magnetic-field-aided navigation approach, the proposed method exhibits slightly improved horizontal position accuracy. On the other hand, it has noticeably larger vertical error on datasets with large magnetic field variations. However, one of the main advantages of MAINS compared to the state-of-the-art is that it enables flexible sensor configurations. The experimental results show that the position error after 2 minutes of navigation in most cases is less than 3 meters when using an array of 30 magnetometers. Thus, the proposed navigation solution has the potential to solve one of the key challenges faced with current magnetic-field simultaneous localization and mapping (SLAM) solutions: the very limited allowable length of the exploration phase during which unvisited areas are mapped.

On the Relationship Between Iterated Statistical Linearization and Quasi-Newton Methods

This letter investigates relationships between iterated filtering algorithms based on statistical linearization, such as the iterated unscented Kalman filter (IUKF), and filtering algorithms based on quasi-Newton (QN) methods, such as the QN iterated extended Kalman filter (QN-IEKF). Firstly, it is shown that the IUKF and the iterated posterior linearization filter (IPLF) can be viewed as QN algorithms, by finding a Hessian correction in the QN-IEKF such that the IPLF iterate updates are identical to that of the QN-IEKF. Secondly, it is shown that the IPLF/IUKF update can be rewritten such that it is approximately identical to the QN-IEKF, albeit for an additional correction term. This enables a richer understanding of the properties of iterated filtering algorithms based on statistical linearization.

Unified Linearization-based Nonlinear Filtering

This letter shows that the following three classes of recursive state estimation filters: standard filters, such as the extended Kalman filter; iterated filters, such as the iterated unscented Kalman filter; and dynamically iterated filters, such as the dynamically iterated posterior linearization filters; can be unified in terms of a general algorithm. The general algorithm highlights the strong similarities between specific filtering algorithms in the three filter classes and facilitates an in-depth understanding of the pros and cons of the different filter classes and algorithms. We end with a numerical example showing the estimation accuracy differences between the three classes of filters when applied to a nonlinear localization problem.

Tightly Integrated Motion Classification and State Estimation in Foot-Mounted Navigation Systems

A framework for tightly integrated motion mode classification and state estimation in motion-constrained inertial navigation systems is presented. The framework uses a jump Markov model to describe the navigation system's motion mode and navigation state dynamics with a single model. A bank of Kalman filters is then used for joint inference of the navigation state and the motion mode. A method for learning unknown parameters in the jump Markov model, such as the motion mode transition probabilities, is also presented. The application of the proposed framework is illustrated via two examples. The first example is a foot-mounted navigation system that adapts its behavior to different gait speeds. The second example is a foot-mounted navigation system that detects when the user walks on flat ground and locks the vertical position estimate accordingly. Both examples show that the proposed framework provides significantly better position accuracy than a standard zero-velocity aided inertial navigation system. More importantly, the examples show that the proposed framework provides a theoretically well-grounded approach for developing new motion-constrained inertial navigation systems that can learn different motion patterns.

Using Received Power in Microphone Arrays to Estimate Direction of Arrival

Conventional direction of arrival (DOA) estimators are based on array processing using either time differences or beamforming. The proposed approach is based on the received power at each microphone, which enables simple hardware, low sampling frequency and small arrays. The problem is recast into a linear regression framework where the least squares method applies, and the main drawback is that different sound sources are not readily separable. Our proposed approach is based on a training phase where the directional sensitivity of each microphone element is estimated. This model is then used as a fingerprint of the observed power vector in a real-time estimator. The learned power vector is here modeled by a Fourier series expansion, which enables Cram\'er-Rao lower bound computations. We demonstrate the performance using a circular array with eight microphones with promising results.