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We propose a Bayesian framework for the received-signal-strength-based cooperative localization problem with unknown path loss exponent. Our purpose is to infer the marginal posterior of each unknown parameter: the position or the path loss exponent. This probabilistic inference problem is solved using message passing algorithms that update messages and beliefs iteratively. For numerical tractability, we combine the variable discretization and Monte-Carlo-based numerical approximation schemes. To further improve computational efficiency, we develop an auxiliary importance sampler that updates the beliefs with the help of an auxiliary variable. An important ingredient of the proposed auxiliary importance sampler is the ability to sample from a normalized likelihood function. To this end, we develop a stochastic sampling strategy that mathematically interprets and corrects an existing heuristic strategy. The proposed message passing algorithms are analyzed systematically in terms of computational complexity, demonstrating the computational efficiency of the proposed auxiliary importance sampler. Various simulations are conducted to validate the overall good performance of the proposed algorithms., Funding Agencies|National Natural Science Foundation of ChinaNational Natural Science Foundation of China [61701426]; Guangdong Province [2017ZT07X152]; Shenzhen Fundamental Research Fund [ZDSYS201707251409055]

We study the fundamental problem of fusing one round trip time (RTT) observation associated with a serving base station with one time-difference of arrival (TDOA) observation associated to the serving base station and a neighbor base station to localize a 2-D mobile station (MS). This situation can arise in 3GPP Long Term Evolution (LTE) when the number of reported cells of the mobile station is reduced to a minimum in order to minimize the signaling costs and to support a large number of devices. The studied problem corresponds geometrically to computing the intersection of a circle with a hyperbola, both with measurement uncertainty, which generally has two equally likely solutions. We derive an analytical representation of these two solutions that fits a filter bank framework that can keep track of different hypothesis until potential ambiguities have been resolved. Further, a performance bound for the filter bank is derived. The proposed filter bank is first evaluated in a simulated scenario, where the set of serving and neighbor base stations is changing in a challenging way. The filter bank is then evaluated on real data from a field test, where the result shows a precision better than 40 m 95% of the time.

Posterior Cramér-Rao bounds (CRBs) are derived for the estimation performance of three Gaussian process-based state-space models. The parametric CRB is derived for the case with a parametric state transition and a Gaussian process-based measurement model. We illustrate the theory with a target tracking example and derive both parametric and posterior filtering CRBs for this specific application. Finally, the theory is illustrated with a positioning problem, with experimental data from an office environment where the obtained estimation performance is compared to the derived CRBs., Funding agencies: ELLIT - Swedish Government; European Union FP7 Marie Curie training program on Tracking in Complex Sensor Systems (TRAX) [607400]; Senion; Shenzhen Science and Technology Innovation Council [JCYJ20170307155957688, JCYJ20170411102101881]; National Natural

In this paper, tightness relations (or inequalities) between Bayesian lower bounds (BLBs) on the mean-squared-error are derived which result from the marginalization of a joint probability density function (pdf) depending on both parameters of interest and extraneous or nuisance parameters. In particular,it is shown that for a large class of BLBs, the BLB derived from the marginal pdf is at least as tight as the corresponding BLB derived from the joint pdf. A Bayesian linear regression example is used to illustrate the tightness relations, Funding agencies: DGA/AID [2018.60.0072.00.470.75.01]; Excellence Center at Linkoping and Lund in Information Technology (ELLIIT)

It has been shown lately that any "standard" Bayesian lower bound (BLB) on the mean squared error (MSE) of the Weiss-Weinstein family (WWF) admits a "tighter" form which upper bounds the "standard" form. Applied to the Bayesian Cramer-Rao bound (BCRB), this result suggests to redefine the concept of efficient estimator relatively to the tighter form of the BCRB, an update supported by a noteworthy example. This paper lays the foundation to revisit some Bayesian estimation problems where the BCRB is not tight in the asymptotic region., Funding Agencies|DGA/MRIS [2018.60.0072.00.470.75.01]; Excellence Center at Linkoping and Lund in Information Technology (ELLIIT)

In this paper, marginal versions of the Bayesian Bhattacharyya lower bound (BBLB), which is a tighter alternative to the classical Bayesian Cramer-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., Funding agencies: ELLIIT

The commercial interest in proximity services is increasing. Application examples include location-based information and advertisements, logistics, social networking, file sharing, etc. In this paper, we consider positioning of devices based on a time series of proximity reports from a mobile device to a network node. This corresponds to nonlinear measurements with respect to the device position in relation to the network nodes. Motion model will be needed together with the measurements to determine the position of the device. Therefore, sequential Monte Carlo methods, namely particle filtering and smoothing, are applicable for positioning. Positioning performance is evaluated in a typical office area with Bluetooth-low-energy beacons deployed for proximity detection and report, and is further compared to parametric Cramér-Rao lower bounds. Finally, the position accuracy is also evaluated with real experimental data., Funding agencies: European Union FP7 Marie Curie Training Programme on Tracking in Complex Sensor Systems (TRAX) [607400]; NSFC [61701426]; Shenzhen Science and Technology Innovation Council [JCYJ20170307155957688, JCYJ20170411102101881]

In this paper, Bayesian lower bounds (BLBs) are obtained via a general form of the Pythagorean theorem where the inner product derives from the joint or the a-posteriori probability density function (pdf). When joint pdf is considered, the BLBs obtained encompass the Weiss-Weinstein family (WWF). When a-posteriori pdf is considered, by resorting to an embedding between two ad hoc subspaces, it is shown that any ”standard” BLBs of the WWF admits a ”tighter” form which upper bounds the ”standard” form. Interestingly enough, this latter result may explain why the ”standard” BLBs of the WWF are not always as tight as expected, as exemplified in the case of the Bayesian Cram´er-Rao Bound. As a consequence an updated definition of efficiency is proposed, as well as the introduction of an updated class of efficient estimators., Funding agencies: DGA/MRIS [2015.60.0090.00.470.75.01]

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., Funding agencies: Linkoping-Lund Initiative on IT and Mobile Communications (ELLIT)

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 ondemand 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., Tracking in complex sensor systems, TRAX

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., Funding Agencies|CNPq - Conselho Nacional de Desenvolvimento Cientifico e Tecnologico; CISB - Centro de Pesquisa e Inovacao Sueco-Brasileiro and Saab AB; Vinnova Industry Excellence Center ELLIIT at Linkoping University

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

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

Assessing the fundamental performance limitationsin Bayesian filtering can be carried out using the parametricCram´er-Rao bound (CRB). The parametric CRB puts a lowerbound on mean square error (MSE) matrix conditioned on aspecific state trajectory realization. In this work, we derive theparametric CRB for state-space models, where the measurementequation is modeled by a Gaussian process regression.These models appear, for instance in proximity report-basedpositioning, where proximity reports are obtained by hardthresholding of received signal strength (RSS) measurements, thatare modeled through Gaussian process regression. The proposedparametric CRB is evaluated on selected state trajectories andfurther compared with the positioning performance obtained bythe particle filter. The results corroborate that the positioningaccuracy achieved in this framework is close to the parametricCRB., Funding Agencies|European Union Marie Curie training programme on Tracking in Complex Sensor Systems (TRAX) [607400]

Classification of motion mode (walking, running, standing still) and device mode (hand-held, in pocket, in back-pack) 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., Funding Agencies|European Union FP7 Marie Curie training program on Tracking in Complex Sensor Systems (TRAX) [607400]

Advances in sensor systems have resulted in the availability of high resolution sensors, capable of generating massive amounts of data. For complex systems to run online, the primary focus is on computationally efficient filters for the estimation of latent states related to the data. In this paper a novel method for efficient state estimation with the unscented Kalman Filter is proposed. The focus is on applications consisting of a massive amount of data. From a modelling perspective, this amounts to a measurement vector with dimensionality significantly greater than the dimensionality of the state vector. The efficiency of the filter is derived from a parallel filter structure which is enabled by the expectation propagation algorithm. A novel parallel measurement processing expectation propagation unscented Kalman filter is developed. The primary advantage of the novel algorithm is in the ability to achieve computational improvements with negligible loses in filter accuracy. An example of robot localization with a high resolution laser rangefinder sensor is presented. A 47.53% decrease in computational time was exhibited for a scenario with a processing platform consisting of 4 processors, with a negligible loss in accuracy., Funding Agencies|EC Seventh Framework Programme TRAcking in compleX sensor systems (TRAX) [607400]; UK Royal Society fund [E150823]

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., Funding Agencies|Wallenberg Autonomous System Program (WASP); Swedish Research Council; Excellence Center at Linkoping and Lund in Information Technology (ELLIIT)

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

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, Funding agencies: project Scalable Kalman Filters - Swedish Research Council (VR); Excellence Center ELLIIT