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In stochastic estimation problems, we aim to estimate an unknown state of interest given a set of measurements received from noisy sensory devices, such as radar, light detection and ranging, etc. A common model of the measurements’ random error is white Gaussian noise. This noise model is usually used to derive an estimator of the unknown state; accordingly, the state is described as a random variable with a Gaussian density. In some applications, the unknown state is known to take only positive values, e.g., estimating size or dimension. In such a case, the classical approaches based on Gaussian densities might fail, i.e., produce a negative value. In this article, a recursive Bayesian filter is proposed based on modeling the unknown state as Wishart distributed random matrix. This model ensures that the probability densities of the random variables are restricted to positive real values, even though the measurement’s noise is still modeled as white Gaussian noise. The feasibility of the proposed Bayesian–Wishart filter is demonstrated within the framework of extended target tracking. A target contour measurement model of a symmetric star-convex shape is presented and integrated in the proposed filter to track the target’s extent. [ABSTRACT FROM AUTHOR]

In the research literature there are numerous publications on Track-to-Track fusion (T2TF) and Track-to-Track association (T2TA). These algorithms assume that the problem of target existence is solved on a per sensor basis. More sophisticated detection methods incorporate the full knowledge of a distributed system by making this decision on a global level. Statistical models that reflect false decisions of individual sensors based on their local data can yield optimal results under linear Gaussian conditions. In particular it has been shown that the Distributed Kalman Filter (DKF) is able to reconstruct the global Sequential Likelihood Ratio Test (SLRT). This, however, is hindered by nonlinear models in many applications. In this paper, this approach is applied to the Federated Kalman filter and to the general setting for T2TA/T2TF such that it can also be applied in non-linear scenarios. [ABSTRACT FROM AUTHOR]

The state estimation plays an important role in analyzing many real world systems. Such systems can be classified into being linear or non-linear and depending on the statistical properties of the inherent uncertainties as being Gaussian or non-Gaussian. Unlike linear Gaussian systems, a close form estimator does not exist for non-linear/non-Gaussian systems. Typical solutions like EKF/UKF can fail, whileMonte Carlo methods even though more accurate, are computationally expensive. Recently proposed log homotopy based particle flow filters, also known as Daum-Huang filters (DHF) provide an alternative way for non-linear, non-Gaussian state estimation. There have been a number of DHF derived, based on solutions of the homotopy flow equation. The performance of these new filters depends strongly on the implementation methodology. In this paper, we study a non-linear system, perturbed by Gaussian and non-Gaussian noises. We highlight the key factors affecting the DHF performance and investigate them individually in detail. We then make recommendations based on our results. It is shown that a properly designed DHF can outperform a basic particle filter, with less execution time. [ABSTRACT FROM AUTHOR]

One of the main challenges in the domain of ground target tracking based on measurements from airborne ground moving target indication (GMTI) radar is the masking of targets due to the Doppler blind zone of the sensor. This blind zone arises from the clutter cancellation by space-time adaptive processing (STAP) to separate moving target returns from the general clutter background. Low-Doppler targets can easily be masked by such a blind zone, leading to sequences of missed detections that strongly deteriorate the performance of a standard tracking filter. This work investigates the Doppler blind zone in the case of bistatic transmitter and receiver configurations and its impact on the tracking of ground targets. The knowledge on the Doppler blind zone is incorporated into a Bayesian unscented Kalman filter multiple hypothesis tracker (UKF-MHT) tracking filter that is also capable of using road-map information. Based on different simulation scenarios, it is demonstrated that in contrast to a monostatic configuration with sideways-looking radar, the blind zone width determined by the minimum detectable velocity is not constant in general. The obtained track results reveal the benefit of exploiting this additional knowledge, especially in combination complementary with road-map information if available. [ABSTRACT FROM PUBLISHER]

This paper considers recursive tracking of one mobile emitter using a sequence of time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurement pairs obtained by one pair of sensors. We consider only a single emitter without data association issues (no missed detections or false measurements). Each TDOA measurement defines a region of possible emitter locations around a unique hyperbola. This likelihood function is approximated by a Gaussian mixture, which leads to a dynamic bank of Kalman filters tracking algorithm. The FDOA measurements update relative probabilities and estimates of individual Kalman filters. This approach results in a better track state probability density function approximation by a Gaussian mixture, and tracking results near the Cramér-Rao lower bound. Proposed algorithm is also applicable in other cases of nonlinear information fusion. The performance of proposed Gaussian mixture approach is evaluated using a simulation study, and compared with a bank of EKF filters and the Cramér-Rao lower bound. [ABSTRACT FROM AUTHOR]

In target tracking applications, the full information on the kinematic target states accumulated over a certain time window up to the present time is contained in the joint probability density function of these state vectors, given the time series of all sensor data. This joint density may also be called an accumulated state density (ASD) and provides a unified treatment of filtering and retrodiction insofar as by marginalizing the ASD, the standard filtering and retrodiction densities are obtained. In addition, ASDs fully describe the posterior correlations between the states at different instants of time. The notion of ASDs and closed formulae for calculating them are discussed. The practical usefulness of considering ASDs is illustrated by applications, where out-of-sequence (OoS) measurements are to be processed within the framework of a centralized measurement fusion architecture, i.e., when the sensor data do not arrive in the temporal order, in which they were produced. The approach can be applied to Kalman, multiple hypothesis tracking (MHT), and interacting multiple model (IMM) filtering. [ABSTRACT FROM AUTHOR]