Performance Analysis of Bearings-only Tracking Problems for Maneuvering Target and Heterogeneous Sensor Applications

State estimation, i.e. determining the trajectory, of a maneuvering target from noisy measurements collected by a single or multiple passive sensors (e.g. passive sonar and radar) has wide civil and military applications, for example underwater surveillance, air defence, wireless communications, and self-protection of military vehicles. These passive sensors are listening to target emitted signals without emitting signals themselves which give them concealing properties. Tactical scenarios exists where the own position shall not be revealed, e.g. for tracking submarines with passive sonar or tracking an aerial target by means of electro-optic image sensors like infrared sensors. This estimation process is widely known as bearings-only tracking. On the one hand, a challenge is the high degree of nonlinearity in the estimation process caused by the nonlinear relation of angular measurements to the Cartesian state. On the other hand, passive sensors cannot provide direct target location measurements, so bearings-only tracking suffers from poor target trajectory estimation accuracy due to marginal observability from sensor measurements. In order to achieve observability, that means to be able to estimate the complete target state, multiple passive sensor measurements must be fused. The measurements can be recorded spatially distributed by multiple dislocated sensor platforms or temporally distributed by a single, moving sensor platform. Furthermore, an extended case of bearings-only tracking is given if heterogeneous measurements from targets emitting different types of signals, are involved. With this, observability can also be achieved on a single, not necessarily moving platform. In this work, a performance bound for complex motion models, i.e. piecewisely maneuvering targets with unknown maneuver change times, by means of bearings-only measurements from a single, moving sensor platform is derived and an efficient estimator is implemented and analyzed. Furthermore, an observability analysis is carried out for targets emitting acoustic and electromagnetic signals. Here, the different signal propagation velocities can be exploited to ensure observability on a single, not necessarily moving platform. Based on the theoretical performance and observability analyses a distributed fusion system has been realized by means of heterogeneous sensors, which shall detect an event and localize a threat. This is performed by a microphone array to detect sound waves emitted by the threat as well as a radar detector that detects electromagnetic emissions from the threat. Since multiple platforms are involved to provide increased observability and also redundancy against possible breakdowns, a WiFi mobile ad hoc network is used for communications. In order to keep up the network in a breakdown OLSR (optimized link state routing) routing approach is employed

Estimation from quantized Gaussian measurements: when and how to use dither

Subtractive dither is a powerful method for removing the signal dependence of quantization noise for coarsely quantized signals. However, estimation from dithered measurements often naively applies the sample mean or midrange, even when the total noise is not well described with a Gaussian or uniform distribution. We show that the generalized Gaussian distribution approximately describes subtractively dithered, quantized samples of a Gaussian signal. Furthermore, a generalized Gaussian fit leads to simple estimators based on order statistics that match the performance of more complicated maximum likelihood estimators requiring iterative solvers. The order statistics-based estimators outperform both the sample mean and midrange for nontrivial sums of Gaussian and uniform noise. Additional analysis of the generalized Gaussian approximation yields rules of thumb for determining when and how to apply dither to quantized measurements. Specifically, we find subtractive dither to be beneficial when the ratio between the Gaussian standard deviation and quantization interval length is roughly less than one-third. When that ratio is also greater than 0.822/K^0.930 for the number of measurements K > 20, estimators we present are more efficient than the midrange.https://arxiv.org/abs/1811.06856Accepted manuscrip

On particle filters in radar target tracking

The dissertation focused on the research, implementation, and evaluation of particle filters for radar target track filtering of a maneuvering target, through quantitative simulations and analysis thereof. Target track filtering, also called target track smoothing, aims to minimize the error between a radar target's predicted and actual position. From the literature it had been suggested that particle filters were more suitable for filtering in non-linear/non-Gaussian systems. Furthermore, it had been determined that particle filters were a relatively newer field of research relating to radar target track filtering for non-linear, non-Gaussian maneuvering target tracking problems, compared to the more traditional and widely known and implemented approaches and techniques. The objectives of the research project had been achieved through the development of a software radar target tracking filter simulator, which implemented a sequential importance re-sampling particle filter algorithm and suitable target and noise models. This particular particle filter had been identified from a review of the theory of particle filters. The theory of the more conventional tracking filters used in radar applications had also been reviewed and discussed. The performance of the sequential importance re-sampling particle filter for radar target track filtering had been evaluated through quantitative simulations and analysis thereof, using predefined metrics identified from the literature. These metrics had been the root mean squared error metric for accuracy, and the normalized processing time metric for computational complexity. It had been shown that the sequential importance re-sampling particle filter achieved improved accuracy performance in the track filtering of a maneuvering radar target in a non-Gaussian (Laplacian) noise environment, compared to a Gaussian noise environment. It had also been shown that the accuracy performance of the sequential importance re-sampling particle filter is a function of the number of particles used in the sequential importance re-sampling particle filter algorithm. The sequential importance re-sampling particle filter had also been compared to two conventional tracking filters, namely the alpha-beta filter and the Singer-Kalman filter, and had better accuracy performance in both cases. The normalized processing time of the sequential importance re-sampling particle filter had been shown to be a function of the number of particles used in the sequential importance re-sampling particle filter algorithm. The normalized processing time of the sequential importance re-sampling particle filter had been shown to be higher than that of both the alpha-beta filter and the Singer-Kalman filter. Analysis of the posterior Cramér-Rao lower bound of the sequential importance re-sampling particle filter had also been conducted and presented in the dissertation

Practical Accuracy Limits of Radiation-Aware Magneto-Inductive 3D Localization

The key motivation for the low-frequency magnetic localization approach is that magnetic near-fields are well predictable by a free-space model, which should enable accurate localization. Yet, limited accuracy has been reported for practical systems and it is unclear whether the inaccuracies are caused by field distortion due to nearby conductors, unconsidered radiative propagation, or measurement noise. Hence, we investigate the practical performance limits by means of a calibrated magnetoinductive system which localizes an active single-coil agent with arbitrary orientation, using 4 mW transmit power at 500 kHz. The system uses eight single-coil anchors around a 3m x 3m area in an office room. We base the location estimation on a complex baseband model which comprises both reactive and radiative propagation. The link coefficients, which serve as input data for location estimation, are measured with a multiport network analyzer while the agent is moved with a positioner device. This establishes a reliable ground truth for calibration and evaluation. The system achieves a median position error of 3.2 cm and a 90th percentile of 8.3 cm. After investigating the model error we conjecture that field distortion due to conducting building structures is the main cause of the performance bottleneck. The results are complemented with predictions on the achievable accuracy in more suitable circumstances using the Cram\'er-Rao lower bound.Comment: To appear at the IEEE ICC 2019 Workshops. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based Localization

In this paper, we show how to analyze the achievable position accuracy of magnetic localization based on Bayesian Cramér-Rao lower bounds and how to account for deterministic inputs in the bound. The derivation of the bound requires an analytical model, e.g., a map or database, that links the position that is to be estimated to the corresponding magnetic field value. Unfortunately, finding an analytical model from the laws of physics is not feasible due to the complexity of the involved differential equations and the required knowledge about the environment. In this paper, we therefore use a Gaussian process (GP) that approximates the true analytical model based on training data. The GP ensures a smooth, differentiable likelihood and allows a strict Bayesian treatment of the estimation problem. Based on a novel set of measurements recorded in an indoor environment, the bound is evaluated for different sensor heights and is compared to the mean squared error of a particle filter. Furthermore, the bound is calculated for the case when only the magnetic magnitude is used for positioning and the case when the whole vector field is considered. For both cases, the resulting position bound is below 10cm indicating an high potential accuracy of magnetic localization

Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications

Inferring information from a set of acquired data is the main objective of any signal processing (SP) method. In particular, the common problem of estimating the value of a vector of parameters from a set of noisy measurements is at the core of a plethora of scientific and technological advances in the last decades; for example, wireless communications, radar and sonar, biomedicine, image processing, and seismology, just to name a few. Developing an estimation algorithm often begins by assuming a statistical model for the measured data, i.e. a probability density function (pdf) which if correct, fully characterizes the behaviour of the collected data/measurements. Experience with real data, however, often exposes the limitations of any assumed data model since modelling errors at some level are always present. Consequently, the true data model and the model assumed to derive the estimation algorithm could differ. When this happens, the model is said to be mismatched or misspecified. Therefore, understanding the possible performance loss or regret that an estimation algorithm could experience under model misspecification is of crucial importance for any SP practitioner. Further, understanding the limits on the performance of any estimator subject to model misspecification is of practical interest. Motivated by the widespread and practical need to assess the performance of a mismatched estimator, the goal of this paper is to help to bring attention to the main theoretical findings on estimation theory, and in particular on lower bounds under model misspecification, that have been published in the statistical and econometrical literature in the last fifty years. Secondly, some applications are discussed to illustrate the broad range of areas and problems to which this framework extends, and consequently the numerous opportunities available for SP researchers.Comment: To appear in the IEEE Signal Processing Magazin