This paper introduces a sensing management method for integrated sensing and communications (ISAC) in cell-free massive multiple-input multiple-output (MIMO) systems. Conventional communication systems employ channel estimation procedures that impose significant overhead during data transmission, consuming resources that could otherwise be utilized for data. To address this challenge, we propose a state-based approach that leverages sensing capabilities to track the user when there is no communication request. Upon receiving a communication request, predictive beamforming is employed based on the tracked user position, thereby reducing the need for channel estimation. Our framework incorporates an extended Kalman filter (EKF) based tracking algorithm with adaptive sensing management to perform sensing operations only when necessary to maintain high tracking accuracy. The simulation results demonstrate that our proposed sensing management approach provides uniform downlink communication rates that are higher than with existing methods by achieving overhead-free predictive beamforming.

Maintaining consistent uncertainty estimates in localization systems is crucial as the perceived uncertainty commonly affects high-level system components, such as control or decision processes. A method for constructing an observability-constrained magnetic field-aided inertial navigation system is proposed to address the issue of erroneous yaw observability, which leads to inconsistent estimates of yaw uncertainty. 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.

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.

This paper considers the problem of detecting and tracking objects in a sequence of images. The problem is formulated in a filtering framework, using the output of objectdetection algorithms as measurements. An extension to the filtering formulation is proposed that incorporates class information from the previous frame to robustify the classification. Further, the properties of the object-detection algorithm are exploited to quantify the uncertainty of the bounding box detection in each frame. The complete filtering method is evaluated on camera trap images of the four large Swedish carnivores, bear, lynx, wolf, and wolverine. The experiments show that the class tracking formulation leads to a more robust classification.

A new class of iterated linearization-based nonlinear filters, dubbed dynamically iterated filters, is presented. Contrary to regular iterated filters such as the iterated extended Kalman filter (IEKF), iterated unscented Kalman filter (IUKF) and iterated posterior linearization filter (IPLF), dynamically iterated filters also take nonlinearities in the transition model into account. The general filtering algorithm is shown to essentially be a (locally over one time step) iterated Rauch-Tung-Striebel smoother. Three distinct versions of the dynamically iterated filters are especially investigated: analogues to the IEKF, IUKF and IPLF. The developed algorithms are evaluated on 25 different noise configurations of a tracking problem with a nonlinear transition model and linear measurement model, a scenario where conventional iterated filters are not useful. Even in this “simple” scenario, the dynamically iterated filters are shown to have superior root mean-squared error performance as compared with their respective baselines, the EKF and UKF. Particularly, even though the EKF diverges in 22 out of 25 configurations, the dynamically iterated EKF remains stable in 20 out of 25 scenarios, only diverging under high noise.

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.

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 theqniterated extended Kalman filter (qn–iekf). Firstly, it is shown that theiukfand the iterated posterior linearization filter (iplf) can be viewed asqnalgorithms, by finding a Hessian correction in theqn–iekfsuch that theiplfiterate updates are identical to that of theqn–iekf. Secondly, it is shown that theiplf/iukfupdate can be rewritten such that it is approximately identical to theqn–iekf, albeit for an additional correction term. This enables a richer understanding of the properties of iterated filtering algorithms based on statistical linearization.

An optical flow inspired magnetic-field based odometry estimation process is presented. The estimation process is based upon taking "image" like measurements of the magnetic-field using a magnetometer array. From the measurements a model of the local field is learned. Using the learned model the pose change that gives the smallest prediction error of the measurement at the next time instant is calculated. Two models for describing the magnetic-field are presented, and the performance of the odometry estimation process when using the two models is evaluated. The evaluation shows that at a high signal-to-noise ratio the pose change can be estimated with an error of only a few percentage of the true pose change. Further, the evaluation shows that the uncertainty of the estimate can be consistently estimated. Thus, the proposed odometry estimation process can be used to reduce the navigation error growth rate of, for example, inertial navigation systems by providing reliable odometry information when passing by magnetized objects.

An inference method for Gaussian process augmented state-space models are presented. This class of grey-box models enables domain knowledge to be incorporated in the inference process to guarantee a minimum of performance, still they are flexible enough to permit learning of partially unknown model dynamics and inputs. To facilitate online (recursive) inference of the model a sparse approximation of the Gaussian process based upon inducing points is presented. To illustrate the application of the model and the inference method, an example where it is used to track the position and learn the behavior of a set of cars passing through an intersection, is presented. Compared to the case when only the state-space model is used, the use of the augmented state-space model gives both a reduced estimation error and bias.

Smartphone-based driver monitoring is quickly gaining ground as a feasible alternative to competing in-vehicle and aftermarket solutions. Currently the main challenges for data analysts studying smartphone-based driving data stem from the mobility of the smartphone. In this paper, we use kernel-based k-means clustering to infer the placement of smartphones within vehicles. The trip segments are mapped into fifteen different placement clusters. As a part of the presented framework, we discuss practical considerations concerning e.g., trip segmentation, cluster initialization, and parameter selection. The proposed method is evaluated on more than 10 000 kilometers of driving data collected from approximately 200 drivers. To validate the interpretation of the clusters, we compare the data associated with different clusters and relate the results to real-world knowledge of driving behavior. The clusters associated with the label “Held by hand” are shown to display high gyroscope variances, low maximum speeds, low correlations between the measurements from smartphone-embedded and vehicle-fixed accelerometers, and short segment durations.

A model-based method to perform odometry using an array of magnetometers that sense variations in a local magnetic field is presented. The method requires no prior knowledge of the magnetic field, nor does it compile any map of it. Assuming that the local variations in the magnetic field can be described by a curl and divergence free polynomial model, a maximum likelihood estimator is derived. To gain insight into the array design criteria and the achievable estimation performance, the identifiability conditions of the estimation problem are analyzed and the Cramér-Rao bound for the one-dimensional case is derived. The analysis shows that with a second-order model it is sufficient to have six magnetometer triads in a plane to obtain local identifiability. Further, the Cramér-Rao bound shows that the estimation error is inversely proportional to the ratio between the rate of change of the magnetic field and the noise variance, as well as the length scale of the array. The performance of the proposed estimator is evaluated using real-world data. The results show that, when there are sufficient variations in the magnetic field, the estimation error is of the order of a few percent of the displacement. The method also outperforms current state-of-the-art method for magnetic odometry.

The expectation-maximization algorithm is a commonly employed tool for system identification. However, for a large set of state-space models, the maximization step cannot be solved analytically. In these situations, a natural remedy is to make use of the expectation-maximization gradient algorithm, i.e., to replace the maximization step by a single iteration of Newton's method. We propose alternative expectation-maximization algorithms that replace the maximization step with a single iteration of some other well-known optimization method. These algorithms parallel the expectation-maximization gradient algorithm while relaxing the assumption of a concave objective function. The benefit of the proposed expectation-maximization algorithms is demonstrated with examples based on standard observation models in tracking and localization.

By arranging a large number of inertial sensors in an array and fusing their measurements, it is possible to create inertial sensor assemblies with a high performance-to-price ratio. Recently, a maximum likelihood estimator for fusing inertial array measurements collected at a given sampling instance was developed. In this paper, the maximum likelihood estimator is extended by introducing a motion model and deriving a maximum a posteriori estimator that jointly estimates the array dynamics at multiple sampling instances. Simulation examples are used to demonstrate that the proposed sensor fusion method have the potential to yield significant improvements in estimation accuracy. Further, by including the motion model, we resolve the sign ambiguity of gyro-free implementations, and thereby open up for implementations based on accelerometer-only arrays.

This paper describes an Arduino Due based platform for digital signal processing (DSP) education. The platform consists of an in-house developed shield for robust interfacing with analog audio signals and user inputs, and an off-the-shelf Arduino Due that executes the students' DSP code. This combination enables direct use of the Arduino integrated development environment (IDE), with its low barrier to entry for students, its low maintenance need and cross platform interoperability, and its large user base. Relevant hardware and software features of the platform are discussed throughout, as are design choices made in relation to learning objectives, and the planned use of the platform in our own DSP course.

We present a maximum likelihood estimator for estimating the positions of accelerometers in an inertial sensor array. This method simultaneously estimates the positions of the accelerometers and the motion dynamics of the inertial sensor array and, therefore, does not require a predefined motion sequence nor any external equipment. Using an iterative block coordinate descent optimization strategy, the calibration problem can be solved with a complexity that is linear in the number of time samples. The proposed method is evaluated by Monte-Carlo simulations of an inertial sensor array built out of 32 inertial measurement units. The simulation results show that, if the array experiences sufficient dynamics, the position error is inversely proportional to the number of time samples used in the calibration sequence. Further, results show that for the considered array geometry and motion dynamics in the order of 2000° /s and 2000° /s2, the positions of the accelerometers can be estimated with an accuracy in the order of 10-6m using only 1000 time samples. This enables fast on-the-fly calibration of the geometric errors in an inertial sensor array by simply twisting it by hand for a few seconds.

Just as it has irrevocably reshaped social life, the fast growth of smartphone ownership is now beginning to revolutionize the driving experience and change how we think about automotive insurance, vehicle safety systems, and traffic research. This paper summarizes the first ten years of research in smartphone-based vehicle telematics, with a focus on user-friendly implementations and the challenges that arise due to the mobility of the smartphone. Notable academic and industrial projects are reviewed, and system aspects related to sensors, energy consumption, and human-machine interfaces are examined. Moreover, we highlight the differences between traditional and smartphone-based automotive navigation, and survey the state of the art in smartphone-based transportation mode classification, vehicular ad hoc networks, cloud computing, driver classification, and road condition monitoring. Future advances are expected to be driven by improvements in sensor technology, evidence of the societal benefits of current implementations, and the establishment of industry standards for sensor fusion and driver assessment.

We propose a framework for the detection of dangerous vehicle cornering events, based on statistics related to the no-sliding and no-rollover conditions. The input variables are estimated using an unscented Kalman filter applied to global navigation satellite system (GNSS) measurements of position, speed, and bearing. The resulting test statistic is evaluated in a field study where three smartphones are used as measurement probes. A general framework for performance evaluation and estimator calibration is presented as depending on a generic loss function. Furthermore, we introduce loss functions designed for applications aiming to either minimize the number of missed detections and false alarms, or to estimate the risk level in each cornering event. Finally, the performance characteristics of the estimator are presented as depending on the detection threshold, as well as on design parameters describing the driving behavior. Since the estimation only uses GNSS measurements, the framework is particularly well suited for smartphone-based insurance telematics applications, aiming to avoid the logistic and monetary costs associated with, e.g., on-board-diagnostics or black-box dependent solutions. The design of the estimation algorithm allows for instant feedback to be given to the driver and, hence, supports the inclusion of real-time value-added services in usage-based insurance programs.

A method is proposed to fuse the information from two navigation systems whose relative position is unknown, but where there exists an upper limit on how far apart the two systems can be. The proposed information fusion method is applied to a scenario in which a pedestrian is equipped with two foot-mounted zero-velocity-aided inertial navigation systems; one system on each foot. The performance of the method is studied using experimental data. The results show that the method has the capability to significantly improve the navigation performance when compared to using two uncoupled foot-mounted systems.

Pedestrian Dead-Reckoning (PDR) and Radio Frequency (RF) ranging/positioning are complementary techniques for position estimation but they usually locate different points in the body (RF in the head/hand and PDR in the foot). We propose to fuse the information from both navigation points using a constraint filter with an upper bound in the distance between the estimated positions of both sensors.

We consider the problem of estimating a random state vector when there is information about the maximum distances between its subvectors. The estimation problem is posed in a Bayesian framework in which the minimum mean square error (MMSE) estimate of the state is given by the conditional mean. Since finding the conditional mean requires multidimensional integration, an approximate MMSE estimator is proposed. The performance of the proposed estimator is evaluated in a positioning problem. Finally, the application of the estimator in inequality constrained recursive filtering is illustrated by applying the estimator to a dead-reckoning problem. The MSE of the estimator is compared with two related posterior Cramér-Rao bounds.

In a motorized vehicle a number of easily measurable signals with frequency components related to the rotational speed of the engine can be found, e.g., vibrations, electrical system voltage level, and ambient sound. These signals could potentially be used to estimate the speed and related states of the vehicle. Unfortunately, such estimates would typically require the relations (scale factors) between the frequency components and the speed for different gears to be known. Consequently, in this article we look at the problem of estimating these gear scale factors from training data consisting only of speed measurements and measurements of the signal in question. The estimation problem is formulated as a maximum likelihood estimation problem and heuristics is used to find initial values for a numerical evaluation of the estimator. Finally, a measurement campaign is conducted and the functionality of the estimation method is verified on real data.

The effects of data time synchronization errors in a loosely coupled Global-Positioning-System (GPS)-aided inertial navigation system (INS) are studied and quantified in terms of the increased mean square error (MSE) of the navigation solution. An expression for evaluating the MSE of the navigation solution, given the vehicle trajectory and the model of the INS error dynamics, is derived. Thereafter, a software-based time synchronization method, where the time synchronization error is included as a state to be estimated by the data integration filter, is proposed. A practical approach to the implementation of the proposed time synchronization method is also briefly described. Moreover, an expression for the MSE of the navigation solution in the system that employs the proposed synchronization method is derived. Finally, through simulations and tests with real-world data, the correctness of the derived MSE expressions is validated, and the application of the proposed synchronization method is shown. The test results show that, with the proposed synchronization approach, a data time synchronization, which is accurate to the order of a few milliseconds, can be achieved.

Foot-mounted zero-velocity-update (ZUPT) aided inertial navigation system (INS) is a conceptually well known with publications in the area typically focusing on improved methods for filtering and addition of sensors and heuristics. Despite this, the performance characteristics, which would ultimately justify and give guidelines for such system modifications of ZUPT-aided INSs and other related systems, are in some aspects poorly documented. Unfortunately, the systems are non-linear, meaning that the performance is dependent on the system set-up, parameter setting, and the true trajectory. This complicates the process of evaluating performance and partially explains the few publications with detailed performance characterisation results. Therefore in this article we suggest and motivate methodologies for evaluating performance of ZUPT-aided INS and other related systems, we apply them to a suggested baseline set-up of the system, and study some aspects of the performance characteristics.

In this paper, a simple method to calibrate the accelerometer cluster of an inertial measurement unit (IMU) is proposed. The method does not rely on using a mechanical calibration platform that rotates the IMU into different precisely controlled orientations. Although the IMU is rotated into different orientations, these orientations do not need to be known. Assuming that the IMU is stationary at each orientation, the norm of the input is considered equal to the gravity acceleration. As the orientations of the IMU are unknown, the calibration of the accelerometer cluster is stated as a blind system identification problem where only the norm of the input to the system is known. Under the assumption that the sensor noises have a white Gaussian distribution the system identification problem is solved using the maximum likelihood estimation method. The accuracy of the proposed calibration method is compared with the Cramér-Rao bound for the considered calibration problem.

A study of the performance of four zero-velocity detectors for a foot-mounted inertial sensor based pedestrian navigation system is presented. The four detectors are the acceleration moving variance detector, the acceleration magnitude detector, the angular rate energy detector, and a novel generalized likelihood ratio test detector, refereed to as the SHOE. The performance of each detector is assessed by the accuracy of the position solution provided by the navigation system employing the detector to perform zero-velocity updates. The results show that for leveled ground forward gait at a speed of 5 km/h, the angular rate energy detector and the SHOE give the highest performance, with a position accuracy of 0.14% of the travelled distance. The results also indicate that during leveled ground forward gait, the gyroscope signals hold the most reliable information for zero-velocity detection.

In-car positioning and navigation has been a killer application for Global Positioning System (GPS) receivers, and a variety of electronics for consumers and professionals have been launched on a large scale. Positioning technologies based on stand-alone GPS receivers are vulnerable and, thus, have to be supported by additional information sources to obtain the desired accuracy, integrity, availability, and continuity of service. A survey of the information sources and information fusion technologies used in current in-car navigation systems is presented. The pros and cons of the four commonly used information sources, namely, 1) receivers for radio-based positioning using satellites, 2) vehicle motion sensors, 3) vehicle models, and 4) digital map information, are described. Common filters to combine the information from the various sources are discussed. The expansion of the number of satellites and the number of satellite systems, with their usage of available radio spectrum, is an enabler for further development, in combination with the rapid development of microelectromechanical inertial sensors and refined digital maps.