Road roughness significantly affects vehicle vibrations and ride quality. We introduce a Kalman filter (KF)-based method for estimating road roughness in terms of the international roughness index (IRI) by fusing inertial and speed measurements, offering a cost-effective solution for pavement monitoring. The method involves system identification on a physical vehicle to estimate realistic model parameters, followed by KF-based reconstruction of the longitudinal road profile to compute IRI values. It explores IRI estimation using vertical and lateral vibrations, the latter more common in modern vehicles. Validation on 230 km of real-world data shows promising results, with IRI estimation errors ranging from 1% to 10% of the reference values. However, accuracy deteriorates significantly when using only lateral vibrations, highlighting their limitations. These findings demonstrate the potential of KF-based estimation for efficient road roughness monitoring.

Due to recent events that have demonstrated the vulnerabilities of global navigation satellite systems (GNSS) there has been an increased interest in alternative methods for localization. One traditional alternative method is terrain-aided navigation (TAN), where a platform localizes itself by measuring the terrain elevation and comparing it to a digital elevation map (DEM). While single-agent TAN has been extensively studied, multi-agent TAN remains less explored. This paper addresses the multi-agent TAN problem with a focus on its properties. We formulate a weighted least squares (WLS) estimator for computing a snapshot solution to the problem and formulate a CramérRao Lower Bound (CRLB) to evaluate it. Using the expressions for the estimator and the CRLB we are able to highlight some insightful properties of the problem. The findings are verified in a simulation study where we evaluate the performance with respect to the altitude sensor accuracy, the group formation accuracy, the number of agents and their formation. Notably, we observe that the solution is relatively insensitive to errors in agent position, suggesting that low-accuracy inertial navigation systems and distance sensors are sufficient for determining their positions. Increasing the number of agents beyond a few seems to have a large effect on both the efficiency and robustness of the estimator, which lessens as the number of agents increases. However, increasing the number of agents does not compensate for poor altitude sensor quality. Additionally, while spatial separation between agents is important for effective map utilization, further separation beyond a certain point does not enhance performance. These findings provide design guidelines for multi-agent TAN systems and identify areas for further research.

As human settlement expands into the natural habitats of wild animals, the conflicts between humans and wildlife increases. The human-elephant conflict causes a tremendous amount of damage, often to poor villages close to the savannah. In this paper, we continue our earlier reported research on a geophone network aimed for elephant localisation by focusing on the detection challenge. We have now collected larger sets of seismic data with footsteps from both elephants and other big animals including humans. To detect the footsteps, a method is developed that analyses features of the geophone signal, which are then compared to those of an elephant footstep. The method detects $54 \%$ of the footsteps and has a classification accuracy of $89 \%$. Subsequently, the detected elephant footstep is used to calculate the direction of arrival (DOA) angle using a delay-andsum beamformer. The direction to an elephant is estimated with good precision on distances ranging from 8 to 30 meters. This research, not only, showcases a practical solution for mitigating human-elephant conflicts, but also underscores the potential of seismic technology in wildlife management and conservation efforts.

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.

The Particle filter can in theory estimate the state of any nonlinear system, but in practice it suffers from an exponential complexity in terms of the number of particles as the dimension of the state increases. The marginalized particle filter can potentially reduce this problem by improving the estimates, particularly for lower number of particles. However, it turns out that for certain systems, it does not provide any improvement in the accuracy of the estimate. The core cause of degeneracy is linked to when the uncertainty of the linear state conditioned on the nonlinear state is 0. Conditions for determining when this occurs are presented and applied to common constant velocity, constant acceleration and constant jerk models with various sampling methods. Interestingly, some combinations are useful while others should be avoided. These findings are supported using simulated systems.

Network-centric multitarget tracking under communication constraints is considered, where dimension-reduced track estimates are exchanged. Previous work on target tracking in this subfield has focused on fusion aspects only and derived optimal ways of reducing dimensionality based on fusion performance. In this work we propose a novel problem formalization where estimates are reduced based on association performance. The problem is analyzed theoretically and problem properties are derived. The theoretical analysis leads to an optimization strategy that can be used to partly preserve association quality when reducing the dimensionality of communicated estimates. The applicability of the suggested optimization strategy is demonstrated numerically in a multitarget scenario.

Human-wildlife conflicts are a global problem which is central to the Global Goal 15 (life on land). One particular case is elephants, that can cause harm to both people, property and crops. An early warning system that can detect and warn people in time would allow effective mitigation measures. The proposed method is based on a small local network of geophones that sense the seismic waves of elephant footsteps. It is known that elephant footsteps induce low frequency ground waves that can be picked up by geophones in the ground. First, a method is described that detect the particular signature of such footsteps, and then the detections are used to estimate the direction of arrival (DOA). Finally, a Kalman filter is applied to the measurements in order to track the elephant. Field tests performed at a local zoo shows promising results with accurate DOA estimates at 15 meters distance and acceptable accuracy at 40 meters.

Conventional direction of arrival (DOA) estimators are based on array processing using either time differences or beam-forming. 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 Cramér-Rao lower bound computations. We demonstrate the performance using a circular array with eight microphones with promising results.

We consider a decentralized sensor network of multiple nodes with limited communication capability where the cross-correlations between local estimates are unknown. To reduce the bandwidth the individual nodes determine which subset of local information is the most valuable from a global perspective. Three information selection methods (ISM) are derived. The proposed ISM require no other information than the communicated estimates. The simulation evaluation shows that by using the proposed ISM it is possible to determine which subset of local information is globally most valuable such that both reduced bandwidth and high performance are achieved.

Modern maritime navigation is heavily dependent on satellite systems. Availability of an accurate position is critical for safe operations, but satellite-based navigation systems are vulnerable to interference, jamming, and spoofing. In this work, we propose a method for maritime navigation independent of GNSS, able to provide absolute positioning of the vessel based on marine radar scans. A measurement model is presented where a Digital Elevation Model is used to predict the output of a marine radar, given a hypothetical position. The model, as used by an on-line particle filter, is used to track the movements of a ship from real recorded data. This demonstrates the feasibility of this method for robust positioning, without the need of external positioning signals, in a maritime environment. The tracking only uses sensors commonly available on maritime vessels, and demonstrates its application using freely available elevation data.

A wearable microphone array platform is used to localize stationary sound sources and amplify the sound in the desired directions using several beamforming methods. The platform is equipped with inertial sensors and a magnetometer allowing predictions of source locations during orientation changes and compensation for the displacement in the array configuration. The platform is modular, open and 3D printed to allow for easy reconfiguration of the array and for reuse in other applications, e.g., mobile robotics. The software components are based on open source. A new method for source localization and signal reconstruction using Taylor expansion of the signals is proposed. This and various standard and non-standard Direction of Arrival (DOA) methods are evaluated in simulation and experiments with the platform to track and reconstruct multiple and single sources. Results show that sound sources can be localized and tracked robustly and accurately while rotating the platform and that the proposed method outperforms standard methods at reconstructing the signals.

In this paper, recursive Bobrovsky-Zakai bounds for filtering, prediction and smoothing of nonlinear dynamic systems are presented. The similarities and differences to an existing Bobrovsky-Zakai bound in the literature for the filtering case are highlighted. The tightness of the derived bounds are illustrated on a simple example where a linear system with non-Gaussian measurement likelihood is considered. The proposed bounds are also compared with the performance of some well-known filters/predictors/smoothers and other Bayesian bounds.

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.

In this paper, marginal versions of the Bayesian Bhattacharyya lower bound (BBLB), which is a tighter alternative to the classical Bayesian Cramér- Rao bound, for discrete-time filtering are proposed. Expressions for the second and third-order marginal BBLBs are obtained and it is shown how these can be approximately calculated using particle filtering. A simulation example shows that the proposed bounds predict the achievable performance of the filtering algorithms better.

This paper deals with state inference and parameter identification in Jump Markov Non-Linear System. The state inference problem is solved efficiently using a recently proposed Rao-Blackwellized Particle Filter, where the discrete state is integrated out analytically. Within the RBPF framework, Recursive Maximum Likelihood parameter identification is performed using gradient ascent algorithms. The proposed learning method has the advantage over (online) Expectation Maximization methods, that it can be easily applied to cases where the probability density functions defining the Jump Markov Non-Linear System are not members of the exponential family. Two benchmark problems illustrate the parameter identification performance.

Acoustic frequency tracking of a harmonic signal with continuously varying frequency is considered. The Rao-Blackwellized point mass filter (RBPMF), previously proposed by the authors for mechanical vibration tracking, is applied to the problem. The RBPMF is compared with two periodogram-based methods, and the similarities and differences between them are explained. Both experimental and simulation results in a Doppler frequency tracking scenario are presented, and the results show that the RBPMF can have significantly less estimation error than the competing methods.

One-dimensional Bayesian filtering and smoothing problems can be solved numerically using a number of algorithms, even in nonlinear and non-Gaussian cases. In this educational paper we advocate for the benefits of visualizing the obtained posterior densities as complement to, e.g., estimation error analysis. In addition to a review of Bayesian filtering and smoothing and the respective point mass and particle solutions, we devise a novel algorithm for filtering when the likelihood cannot be evaluated. Several instructive examples are discussed and easily adjustable matlab code is provided as complement to this paper.

In this paper, an indoor vehicle multi-level positioning algorithm is proposed that makes use of an indoor map, as well as dead-reckoning sensor information that is available in every car. A particle filter framework is used for online optimal Bayesian vehicle positioning with indoor-outdoor transitions. The method is validated experimentally in two indoor multi-level car parks. The achieved results indicate that accurate indoor positioning is possible already today without relying on expensive technology such as e.g. laser scanners or additional hardware.

Classification of motion mode (walking, running, standing still) and device mode (hand-held, in pocket, in backpack) is an enabler in personal navigation systems for the purpose of saving energy and design parameter settings and also for its own sake. Our main contribution is to publish one of the most extensive datasets for this problem, including inertial data from eight users, each one performing three pre-defined trajectories carrying four smartphones and seventeen inertial measurement units on the body. All kind of metadata is available such as the ground truth of all modes and position. A second contribution is the first study on a joint classifier of motion and device mode, respectively, where preliminary but promising results are presented.

Many positioning systems rely on accurate time of arrival measurements. In this paper, we address not only the accuracy but also the relevance of Time of Arrival (TOA) measurement error modeling. We discuss how better knowledge of these errors can improve relative distance estimation, and compare the impact of differently detailed measurement error information. These models are compared in simulations based on models derived from an Ultra Wideband (UWB) measurement campaign. The conclusion is that significant improvements can be made without providing detailed received signal information but with a generic and relevant measurement error model.

Narrowband Internet of Things (NB-IoT) is an emerging cellular technology designed to target low-cost devices, high coverage, long device battery life (more than ten years), and massive capacity. We investigate opportunities for device tracking in NB-IoT systems using Observed Time Difference of Arrival (OTDOA) measurements. Reference Signal Time Difference (RSTD) reports are simulated to be sent to the mobile location center periodically or on an on-demand basis. We investigate the possibility of optimizing the number of reports per minute budget on horizontal positioning accuracy using an on-demand reporting method based on the Signal to Noise Ratio (SNR) of the measured cells received by the User Equipment (UE). Wireless channels are modeled considering multipath fading propagation conditions. Extended Pedestrian A (EPA) and Extended Typical Urban (ETU) delay profiles corresponding to low and high delay spread environments, respectively, are simulated for this purpose. To increase the robustness of the filtering method, measurement noise outliers are detected using confidence bounds estimated from filter innovations.

We propose a filter for piecewise affine state-space models. In each filtering recursion, the true filtering posterior distribution is a mixture of truncated normal distributions. The proposed filter approximates the mixture with a single normal distribution via moment matching. The proposed algorithm is compared with the extended Kalman filter (EKF) in a numerical simulation, where the proposed method obtains, on average, better root mean square error than the EKF.

Parametric Cramér-Rao lower bounds (CRLBs) are given for discrete-time systems with non-zero process noise. Recursive expressions for the conditional bias and mean-square-error (MSE) (given a specific state sequence) are obtained for Kalman filter estimating the states of a linear Gaussian system. It is discussed that Kalman filter is conditionally biased with a non-zero process noise realization in the given state sequence. Recursive parametric CRLBs are obtained for biased estimators for linear state estimators of linear Gaussian systems. Simulation studies are conducted where it is shown that Kalman filter is not an efficient estimator in a conditional sense.

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.

The speed of a wheeled vehicle is usually estimated using wheel speed sensors (WSS) or GPS. If these signals are unavailable, other methods must be used. We propose a novel approach exploiting the fact that vibrations from rotating axles, with fundamental frequency proportional to vehicle speed, are transmitted via the vehicle chassis. Using an accelerometer, these vibrations can be tracked to estimate vehicle speed while other sources of vibrations act as disturbances. A state-space model for the dynamics of the harmonics is presented and formulated such that there is a conditional linear-Gaussian substructure, enabling efficient Rao-Blackwellized methods. A variant of the Rao-Blackwellized point-mass filter is derived, significantly reducing computational complexity, and reducing the memory requirements from quadratic to linear in the number of grid points. It is applied to experimental data from the sensor cluster of a car and validated using the rotational frequency from WSS data. The proposed method shows improved performance and robustness in comparison to a Rao-Blackwellized particle filter implementation and a frequency spectrum maximization method.

In this letter, numerical algorithms for computing the marginal version of the Bayesian Cramér-Rao bound (M-BCRB) for jump Markov nonlinear systems and jump Markov linear Gaussian systems are proposed. Benchmark examples for both systems illustrate that the M-BCRB is tighter than three other recently proposed BCRBs.

A marginal version of the Weiss-Weinstein bound (WWB) is proposed for discrete-time nonlinear filtering. The proposed bound is calculated analytically for linear Gaussian systems and approximately for nonlinear systems using a particle filtering scheme. Via simulation studies, it is shown that the marginal bounds are tighter than their joint counterparts.

Cramér-Rao lower bounds (CRLBs) are proposed for deterministic parameter estimation under model mismatch conditions where the assumed data model used in the design of the estimators differs from the true data model. The proposed CRLBs are defined for the family of estimators that may have a specified bias (gradient) with respect to the assumed model. The resulting CRLBs are calculated for a linear Gaussian measurement model and compared to the performance of the maximum likelihood estimator for the corresponding estimation problem.

A skew-t variational Bayes filter (STVBF) is applied to indoor positioning with time-of-arrival (TOA) based distance measurements and pedestrian dead reckoning (PDR). The proposed filter accommodates large positive outliers caused by occasional non-line-of-sight (NLOS) conditions by using a skew-t model of measurement errors. Real-data tests using the fusion of inertial sensors based PDR and ultra-wideband based TOA ranging show that the STVBF clearly outperforms the extended Kalman filter (EKF) in positioning accuracy with the computational complexity about three times that of the EKF.

This paper presents a method for global pose estimation using inertial sensors, monocular vision, and ultra wide band (UWB) sensors. It is demonstrated that the complementary characteristics of these sensors can be exploited to provide improved global pose estimates, without requiring the introduction of any visible infrastructure, such as fiducial markers. Instead, natural landmarks are jointly estimated with the pose of the platform using a simultaneous localization and mapping framework, supported by a small number of easy-to-hide UWB beacons with known positions. The method is evaluated with data from a controlled indoor experiment with high precision ground truth. The results show the benefit of the suggested sensor combination and suggest directions for further work.

In this paper an extension to the sampling based motion planning framework CL-RRT is presented. The framework uses a system model and a stabilizing controller to sample the perceived environment and build a tree of possible trajectories that are evaluated for execution. Complex system models and constraints are easily handled by a forward simulation making the framework widely applicable. To increase operational safety we propose a sampling recovery scheme that performs a deterministic brake profile regeneration using collision information from the forward simulation. This greatly increases the number of safe trajectories and also reduces the number of samples that produce infeasible results. We apply the framework to a Scania G480 mining truck and evaluate the algorithm in a simple yet challenging obstacle course and show that our approach greatly increases the number of feasible paths available for execution.

Micro-Doppler radar signatures have great potential for classifying pedestrians and animals, as well as their motion pattern, in a variety of surveillance applications. Due to the many degrees of freedom involved, real data need to be complemented with accurate simulated radar data to be able to successfully design and test radar signal processing algorithms. In many cases, the ability to collect real data is limited by monetary and practical considerations, whereas in a simulated environment, any desired scenario may be generated. Motion capture (MOCAP) has been used in several works to simulate the human micro-Doppler signature measured by radar; however, validation of the approach has only been done based on visual comparisons of micro-Doppler signatures. This work validates and, more importantly, extends the exploitation of MOCAP data not just to simulate micro-Doppler signatures but also to use the simulated signatures as a source ofa prioriknowledge to improve the classification performance of real radar data, particularly in the case when the total amount of data is small.

We present an adaptive smoother for linear state-space models with unknown process and measurement noise covariances. The proposed method utilizes the variational Bayes technique to perform approximate inference. The resulting smoother is computationally efficient, easy to implement, and can be applied to high dimensional linear systems. The performance of the algorithm is illustrated on a target tracking example.

Filtering and smoothing algorithms for linear discrete- time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that have normal prior and skew-$t$-distributed measurement noise. The proposed filter and smoother are compared with conventional low- complexity alternatives in a simulated pseudorange positioning scenario. In the simulations the proposed methods achieve better accuracy than the alternative methods, the computational complexity of the filter being roughly 5 to 10 times that of the Kalman filter.

A marginal version of the enumeration Bayesian Cramér-Rao Bound (EBCRB) for jump Markov systems is proposed. It is shown that the proposed bound is at least as tight as EBCRB and the improvement stems from better handling of the nonlinearities. The new bound is illustrated to yield tighter results than BCRB and EBCRB on a benchmark example.

In this paper, the measurements of individual wheel speeds and the absolute position from a global positioning system are used for high-precision estimation of vehicle tire radii. The radii deviation from its nominal value is modeled as a Gaussian random variable and included as noise components in a simple vehicle motion model. The novelty lies in a Bayesian approach to estimate online both the state vector and the parameters representing the process noise statistics using a marginalized particle filter (MPF). Field tests show that the absolute radius can be estimated with submillimeter accuracy. The approach is tested in accordance with regulation 64 of the United Nations Economic Commission for Europe on a large data set (22 tests, using two vehicles and 12 different tire sets), where tire deflations are successfully detected, with high robustness, i.e., no false alarms. The proposed MPF approach outperforms common Kalman-filter-based methods used for joint state and parameter estimation when compared with respect to accuracy and robustness.

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.

This paper presents an approach for 6D pose estimation where MEMS inertial measurements are complemented with magnetometer measurements assuming that a model (map) of the magnetic field is known. The resulting estimation problem is solved using a Rao-Blackwellized particle filter. In our experimental study the magnetic field is generated by a magnetic coil giving rise to a magnetic field that we can model using analytical expressions. The experimental results show that accurate position estimates can be obtained in the vicinity of the coil, where the magnetic field is strong.

We consider the filtering problem in linear state space models with heavy tailed process and measurement noise. Our work is based on Student's t distribution, for which we give a number of useful results. The derived filtering algorithm is a generalization of the ubiquitous Kalman filter, and reduces to it as special case. Both Kalman filter and the new algorithm are compared on a challenging tracking example where a maneuvering target is observed in clutter.

Calibration of ground sensor networks is a complex task in practice. To tackle the problem, we propose an approach based on simultaneous tracking of targets of opportunity and sparse estimation of the bias parameters. The evidence approximation method is used to get a sparse estimate of the bias parameters, and the method is here extended with a novel marginalization step where a state smoother is invoked. A simulation study shows that the non-zero bias parameters are detected and well estimated using only one target of opportunity passing by the network.

Starting from the electromagnetic theory, we derive a Bayesian non-parametric model allowing for joint estimation of the magnetic field and the magnetic sources in complex environments. The model is a Gaussian process which exploits the divergence- and curl-free properties of the magnetic field by combining well-known model components in a novel manner. The model is estimated using magnetometer measurements and spatial information implicitly provided by the sensor. The model and the associated estimator are validated on both simulated and real world experimental data producing Bayesian nonparametric maps of magnetized objects.

We consider received-signal-strength-based robust geolocation in mixed line-of-sight/non-line-of-sight propagation environments. Herein, we assume a mode-dependent propagation model with unknown parameters. We propose to jointly estimate the geographical coordinates and propagation model parameters. In order to approximate the maximum-likelihood estimator (MLE), we develop an iterative algorithm based on the well-known expectation and maximization criterion. As compared to the standard ML implementation, the proposed algorithm is simpler to implement and capable of reproducing the MLE. Simulation results show that the proposed algorithm attains the best geolocation accuracy as the number of measurements increases.

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.

Monitoring and tracking human activities around restricted areas is an important issue in security and surveillance applications. The movement of different parts of the human body generates unique micro-Doppler features which can be extracted effectively using joint time-frequency analysis. In this paper, we describe the simultaneous tracking of both location and micro-Doppler features of a human using particle filters (PF). The results obtained using the data from a 77 GHz radar prove the successful usage of particle filters in tracking micro-Doppler features of the human gait.

In this study, we investigate online Bayesian estimation of the measurement noise density of a given state space model using particle filters and Dirichlet process mixtures. Dirichlet processes are widely used in statistics for nonparametric density estimation. In the proposed method, the unknown noise is modeled as a Gaussian mixture with unknown number of components. The joint estimation of the state and the noise density is done via particle filters. Furthermore, the number of components and the noise statistics are allowed to vary in time. An extension of the method for the estimation of time varying noise characteristics is also introduced.

With the electromagnetic theory as basis, we present a sensor model for three-axis magnetometers suitable for localization and tracking applications. The model depends on a physical magnetic dipole model of the target and its relative position to the sensor. Furthermore, the dependency between the magnetic dipole and the target orientation has been modeled enabling tracking of a maneuvering target. Due to multi-modality, a bank of Extended Kalman Filters is proposed for tracking road vehicles. Results from field test data indicate excellent tracking of target position.

A UAV navigation system relying on GPS is vulnerable to signal failure, making a drift free backup system necessary. We introduce a vision based geo-referencing system that uses pre-existing maps to reduce the long term drift. The system classifies an image according to its environmental content and thereafter matches it to an environmentally classified map over the operational area. This map matching provides a measurement of the absolute location of the UAV, that can easily be incorporated into a sensor fusion framework. Experiments show that the geo-referencing system reduces the long term drift in UAV navigation, enhancing the ability of the UAV to navigate accurately over large areas without the use of GPS.

This paper is concerned with the problem of estimating the relative translation and orientation between an inertial measurement unit and a camera which are rigidly connected. The key is to realise that this problem is in fact an instance of a standard problem within the area of system identification, referred to as a gray-box problem. We propose a new algorithm for estimating the relative translation and orientation, which does not require any additional hardware, except a piece of paper with a checkerboard pattern on it. Furthermore, covariance expressions are provided for all involved estimates. The experimental results shows that the method works well in practice.

Detection of spurious features is instrumental in many computer vision applications. The standard approach is feature based, where extracted features are matched between the image frames. This approach requires only vision, but is computer intensive and not yet suitable for real-time applications. We propose an alternative based on algorithms from the statistical fault detection literature. It is based on image data and an inertial measurement unit (IMU). The principle of analytical redundancy is applied to batches of measurements from a sliding time window. The resulting algorithm is fast and scalable, and requires only feature positions as inputs from the computer vision system. It is also pointed out that the algorithm can be extended to also detect non-stationary features (moving targets for instance). The algorithm is applied to real data from an unmanned aerial vehicle in a navigation application.

A class of nonlinear transformation-based filters (NLTF) for state estimation is proposed. The nonlinear transformations that can be used include first (TT1) and second (TT2) order Taylor expansions, the unscented transformation (UT), and the Monte Carlo transformation (MCT) approximation. The unscented Kalman filter (UKF) is by construction a special case, but also nonstandard implementations of the Kalman filter (KF) and the extended Kalman filter (EKF) are included, where there are no explicit Riccati equations. The theoretical properties of these mappings are important for the performance of the NLTF. TT2 does by definition take care of the bias and covariance of the second order term that is neglected in the TT1 based EKF. The UT computes this bias term accurately, but the covariance is correct only for scalar state vectors. This result is demonstrated with a simple example and a general theorem, which explicitly shows the difference between TT1, TT2, UT, and MCT.

We consider probabilistic methods to compute the near midair collision risk using state estimate and covariance from a target tracking filter based on angle-only sensors such as digital video cameras. Existing work is only concerned with risk estimation at a certain time instant, while the focus here is to compute the integrated risk over the critical time horizon. This novel formulation leads to evaluating the probability for level-crossing. The analytic expression for this involves a multi-dimensional integral which is hardly tractable in practice. Further, a huge number of Monte Carlo simulations would be needed to get sufficient reliability for the small risks that the applications require. Instead, we propose a sound numerical approximation that leads to a one-dimensional integral which is suitable for real-time implementations.

This paper is concerned with the problem of estimating the relative translation and orientation of an inertial measurement unit and a spherical camera, which are rigidly connected. The key is to realize that this problem is in fact an instance of a standard problem within the area of system identification, referred to as a gray-box problem. We propose a new algorithm for estimating the relative translation and orientation, which does not require any additional hardware, except a piece of paper with a checkerboard pattern on it. The experimental results show that the method works well in practice.

This paper presents a method for identifying dynamic models of Autonomous Underwater Vehicles (AUV) from logged data and a physically motivated model structure. Such models are instrumental for model-based control system design, but also for integrated navigation systems. We motive our work from the perspective of developing second generation integrated navigation systems, which use a sensor fusion approach to merge external information with a dynamic model for purposes of redundancy, integrity, and for fault detection and isolation.

This contribution presents a unified framework for localization and tracking in sensor networks based on fusing a variety of signal energy measurements as provided by for instance acoustic, seismic, magnetic, radio, microwave and infrared sensors. The received energy from such sensors generally decays exponentially, and a log range model is introduced for the sensor observations in logarithmic scale, which is linear in transmitted power and the path loss exponent. Field trial sensor data confirms the validity of the log range model. The novelty in this contribution lies in a systematic least squares approach to eliminate these nuisance parameters and also the sensor noise variances. Details on how to solve the resulting low-dimensional non-linear least squares criterion are given, and how to extend the algorithms to target tracking. Explicit formulas for the Cramer-Rao lower bound are given for both localization and tracking.

This contribution aims at unifying two trends in applied particle filtering (PF). The first trend is the major impact in simultaneous localization and mapping (slam) applications, utilizing the FastSLAM algorithm. The second one is the implications of the marginalized particle filter (MPF) or the Rao-Blackwellized particle filter (RBPF) in positioning and tracking applications. An algorithm is introduced, which merges FastSLAM and MPF, and the result is an MPF algorithm for slam applications, where state vectors of higher dimensions can be used. Results using experimental data from a 3D slam development environment, fusing measurements from inertial sensors (accelerometer and gyro) and vision are presented.

This paper presents a new automotive safety function called Emergency Lane Assist (ELA). ELA combines conventional lane guidance systems with a threat assessment module that tries to activate the lane guidance interventions according to the actual risk level of lane departure. The goal is to only prevent dangerous lane departure maneuvers. The ELA safety function is based on a statistical method that evaluates a list of safety concepts and tries to maximize the impact on accident statistics while minimizing development and hardware component costs. ELA runs in a demonstrator and successfully intervenes during lane changes that are likely to result in a collision and is also able to take control of the vehicle and return it to a safe position in the original lane. It has also been tested on 2000 km of roads in traffic without giving any false interventions

In augmented reality (AR), the position and orientation of the camera have to be estimated with high accuracy and low latency. This nonlinear estimation problem is studied in the present paper. The proposed solution makes use of measurements from inertial sensors and computer vision. These measurements are fused using a Kalman filtering framework, incorporating a rather detailed model for the dynamics of the camera. Experiments show that the resulting filter provides good estimates of the camera motion, even during fast movements

We propose a ground target recognition method based on 3-D laser radar data. The method handles general 3-D scattered data. It is based on the fact that man-made objects of complex shape can be decomposed to a set of rectangles. The ground target recognition method consists of four steps; 3-D size and orientation estimation, target segmentation into parts of approximately rectangular shape, identification of segments that represent the target's functional/main parts, and target matching with CAD models. The core in this approach is rectangle estimation. The performance of the rectangle estimation method is evaluated statistically using Monte Carlo simulations. A case study on tank recognition is shown, where 3-D data from four fundamentally different types of laser radar systems are used. Although the approach is tested on rather few examples, we believe that the approach is promising.

A frequency-domain approach to continuous-time autoregressive (AR) signal modeling is proposed. The algorithm allows for data pre-filtering as opposed to conventional AR modelling in the time domain. We illustrate the method by extracting resonance frequencies from data from a real-life application.

In many real-time applications, sample values and time stamps are delivered in pairs, where sampling times are non-uniform. Frequency analysis using non-uniform data occurs in various real life problems and embedded systems, such as vibrational analysis in cars and control of packet network queue lengths. Our contribution is first to overview different ways to approximate the Fourier transform, and secondly to give analytical expressions for how non-uniform sampling affects these approximations. The results are expressed in terms of frequency windows describing how a single frequency in the continuous time signal is smeared out in the frequency domain, or, more precisely, in the expected value of the Fourier transform approximation.

Time interleaved A/D converters (ADC) can be used to increase the sample rate of an ADC system. However, a problem with time interleaved ADC is that distortion is introduced in the output signal due to various mismatch errors between the ADC. One way to decrease the impact of the mismatch errors is to introduce additional ADC in the interleaved structure and randomly select an ADC at each sample instance. The periodicity of the errors is then removed and the spurious distortion is changed to a more noiselike distortion, spread over the whole spectrum. In this paper, a probabilistic model of the randomly interleaved ADC system is presented. The noise spectrum caused by gain errors is also analyzed.

In this paper a tool for synthetic generation of scanning laser radar data is described and its performance is evaluated. By analyzing data from the system, we recognize objects on the ground. In the measurement system it is possible to add several design parameters, which make it possible to test an estimation scheme under different types of system design. The measurement system model includes laser characteristics, object geometry, reflection, speckles, atmospheric attenuation, turbulence and a direct detection receiver. A parametric method that estimates an object's size and orientation is described. There are measurement errors present and thus, the parameter estimation is based on a measurement error model. The parameter estimation accuracy is limited by the Cramer-Rao lower bound. Validations of both the measurement error model and the measurement system are shown. Data from both models generate parameter estimates that are close to the Cramer-Rao lower bound.

The problem of position estimation from time difference of arrival (TDOA) measurements occurs in a range of applications from wireless communication networks to electronic warfare positioning. Correlation analysis of the transmitted signal to two receivers gives rise to one hyperbolic function. With more than two receivers, we can compute more hyperbolic functions, which ideally intersect in one unique point. With TDOA measurement uncertainty, we face a non-linear estimation problem. We suggest and compare a Monte Carlo based method for positioning and a gradient search algorithm using a nonlinear least squares framework. The former has the feature of being easily extended to a dynamic framework where a motion model of the transmitter is included. A small simulation study is presented.

We have studied a sea navigation method relying on a digital underwater terrain map and sonar measurements. The method is applicable for both ships and underwater vessels. We have used experimental data to build an underwater map and to investigate the estimation performance. Since the problem is non-linear, due to the measurement relation, we apply a sequential Monte Carlo method, or particle filter, for the state estimation. The fundamental limitations in navigation uncertainty can be described in terms of the Cramer-Rao lower bound, which is interpreted in terms of the inertial navigation system (INS) error, the sensor accuracy and the terrain map excitation. Hence, the Cramer-Rao lower bound can be interpreted and used in the design for INS systems, sensor performance or, if these are given, how much terrain or depth excitation that is needed for use in positioning and navigation.

The Kalman filter computes the maximum a posteriori (MAP) estimate of the states for linear state space models with Gaussian noise. We interpret the Kalman filter as the solution to a convex optimization problem, and show that we can generalize the MAP state estimator to any noise with a log-concave density function and any combination of linear equality and convex inequality constraints on the states. We illustrate the principle on a hidden Markov model, where the state vector contains probabilities that are positive and sum to one.

All cellular radio systems have radio resource management algorithms which rely on some sort of resource quantity. In the uplink of a WCDMA system, a natural choice of such a quantity is the uplink noise rise, i.e., total received power over noise power. Unfortunately this quantity is hard to measure. In this paper, we propose and evaluate four different noise rise estimates. The best performing estimate provides an average error of less than 1 dB for practical load levels. Due to low standard deviation of single estimates it is possible to apply a simple error correction algorithm.

A method for blind estimation of static time errors in time interleaved A/D converters is investigated. The method assumes that amplitude and gain errors are removed before the time error estimation. Even if the amplitude and gain errors are estimated and removed, there will be small errors left. In this paper, we investigate how the amplitude and gain errors influence the time error estimation performance.

As a part of aircraft navigation, three-dimensional position must be computed continuously. For accuracy and reliability reasons, several sensors are integrated together, and here we are dealing with dead-reckoning integrated with terrain-aided positioning. Terrain-aided positioning suffers from severe nonlinear structure, meaning that we have to solve a nonlinear recursive Bayesian estimation problem. This is not possible to do exactly, but recursive Monte Carlo methods, also known as particle filters, provide a promising approximate solution. To reduce the computational load of the normally rather computer intensive particle filter we present an algorithm which takes advantage of linear structure. The algorithm is based on a Rao-Blackwellisation technique, meaning that we marginalise the full conditional posterior density with respect to the linear part. The linear part of the state vector is estimated using multiple Kalman filters, and the particle filter is then used for the remaining part. Simulations show that the computational load is reduced significantly.

We derive a Kalman filter based on data from a sliding window. This is used for a new approach to fault detection and diagnosis, where the state estimate from past data is compared to the state estimate of some of the future data. We suggest a method to judge the quality of diagnosis in a simple way. For fault estimation in the diagnosis, the general concept of stochastic observability in linear systems is introduced. Its role in the design step is illustrated on a problem of estimating the true velocity of a car.

Event-based sampling occurs when the time instants are measured everytime the amplitude passes certain pre-defined levels. This is in contrast with classical signal processing where the amplitude is measured at regular time intervals. The signal processing problem is to separate the signal component from noise in both amplitude and time domains. Event-based sampling occurs in a variety of applications. The purpose here is to explain the new types of signal processing problems that occur, and identify the need for processing in both the time and event domains. We focus on rotating axles, where amplitude disturbances are caused by vibrations and time disturbances from measurement equipment. As one application, we examine tire pressure monitoring in cars where suppression of time disturbance is of utmost importance.

Transmission power control is essential in systems of the third-generation (3G) in order to optimize the bandwidth utilization, which is critical when variable data rates are used. One remaining problem is oscillations in the output powers, due to round-trip delays in the power control loops together with the power up-down command device. The oscillations are naturally quantified using discrete time-describing functions, which are introduced and applied. More importantly, time delay compensation (TDC) is proposed to mitigate the oscillations. When employing TDC, the power control algorithm exhibits greater stability, which is important from a network perspective. Simulations illustrate the oscillations and the benefits of TDC. Moreover, the fading tracking capability is improved, and thus, less fading margin is needed. The results apply not only to wideband code division multiple access (WCDMA), but to other direct-sequence (DS) CDMA systems power controlled in a similar manner as well.

Transmission power control is essential in CDMA systems in order to reduce the near-far effect and to optimize the bandwidth utilization, which is critical when variable data rates are used. One remaining problem is oscillations in the output powers due to round-trip delays in the power control loops together with the power up-down command device. The oscillations are naturally quantified using discrete-time describing functions, which are introduced and applied. More importantly, time delay compensation (TDC) is proposed to mitigate the oscillations. It is also formally proven that TDC result in a stable overall system, with power control errors that converges to a defined bounded region. These bounds are tighter, compared to when not employing TDC. Simulations illustrate the oscillations and the significant performance gains using TDC.

An ADC using several parallel cells suffers from offset differences between the cells, which causes non-harmonic distortion. A method for removing the offset in the digital domain is proposed. The method is based on a PRBS-controlled chopper at the ADC input, which transforms any input signal to noise. The randomization controls the batch size required for removing the offset by a mean value calculation. The measured results are SFDR=72 dB and SNDR=59.0 dB at 22 MS/s, an improvement of 19 dB and 10 dB respectively.

The problem to track time-varying parameters in cellular radio systems is studied, and the focus is on estimation based only on the signals that are readily available. Previous work have demonstrated very good performance, but were relying on analog measurement that are not available. Most of the information is lost due to quantization and sampling at a rate that might be as low as 2 Hz (GSM case). For that matter a maximum likelihood estimator have been designed and exemplified in the case of GSM. Simulations indicate good performance both when most parameters are varying slowly, and when subject to fast variations as in realistic cases. Since most computations take place in the base stations, the estimator is ready for implementation in a second generation wireless system. No update of the software in the mobile stations is needed.

The problem of input identifiability in blind deconvolution is considered where the input belongs to a known discrete alphabet. Input identifiability is an algorithm independent property, which does not necessarily imply channel identifiability. Sufficient conditions for input identifiability are derived in terms of algebraic relations on the observed output. It is shown how these new results relate to and unify other known sufficient conditions.

The problem of detection and discrimination of double talk and change in the echo path in a telephone channel is considered. The phenomenon echo path change requires fast adaptation of the channel model to be able to equalize the echo dynamics. On the other hand, the adaption rate should be reduced when double talk occurs. Thus, it is critical to quickly detect a change in the echo path while not confusing it with double talk, which gives a similar effect. The proposed likelihood based approach compares a global channel model with a local one over a sliding window, both estimated with the recursive least squares algorithm.

This paper presents a novel approach to blind equalization (deconvolution), which is based on direct examination of possible input sequences. In contrast to many other approaches, it does not rely on a model of the approximative inverse of the channel dynamics. To start with, the blind equalization identifiability problem for a noise-free finite impulse response channel model is investigated. A necessary condition for the input, which is algorithm independent, for blind deconvolution is derived. This condition is expressed in an information measure of the input sequence. A sufficient condition for identifiability is also inferred, which imposes a constraint on the true channel dynamics. The analysis motivates a recursive algorithm where all permissible input sequences are examined. The exact solution is guaranteed to be found as soon as it is possible. An upper bound on the computational complexity of the algorithm is given. This algorithm is then generalized to cope with time-varying infinite impulse response channel models with additive noise. The estimated sequence is an arbitrary good approximation of the maximum a posteriori estimate. The proposed method is evaluated on a Rayleigh fading communication channel. The simulation results indicate fast convergence properties and good tracking abilities.>

The authors' approach to blind equalization examines the possible input sequences directly by using a bank of filters and, in contrast to common approaches, does not try to find an approximative inverse of the channel dynamics. The identifiability question of a noise-free finite impulse response (FIR) model is investigated. A sufficient condition for the input sequence (persistently exciting of a certain order) is given which guarantees that both the channel model and the input sequence can be determined exactly in finite time. A recursive algorithm is given for a time-varying infinite impulse response (IIR) channel model with additive noise, which does not require a training sequence. The estimated sequence is an arbitrarily good approximation of the maximum a posteriori estimate. The proposed method is evaluated on a Rayleigh fading communication channel. It shows fast convergence properties and good tracking ability.>

The problem of estimating the time instants when the dynamical properties of a signal make abrupt changes is studied. This segmentation problem is usually considered as exponential in time. The author presents a specific but natural signal mode-called a changing regression model-and points out a method to compute an optimal estimate of the segmentation problem linearly in time. The linear constant is always less than one and decreases to zero as the measurement noise decreases to zero. The method is thus asymptotically efficient in the measurement noise.>