Ellipsoidal set based tracking with nonlinear measurements

This article handles tracking multiple targets using bearing-only measurements in underwater noisy environments. For tracking multiple targets in underwater noisy environments, the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter provides good performance with its low computational load. Bearing-only measurements are passive and do not provide position information of a target. Note that the nonlinearity of the bearing-only measurements can be handled by Extended Kalman Filters (EKF) when applying the GM-PHD filter. However, range uncertainty of the target is large for bearing-only measurements. Thus, a single EKF leads to poor performance when it is applied in the GM-PHD. In this article, every bearing measurement gives birth to multiple target samples, which are distributed considering the feasible range of the passive sensor. Thereafter, every target sample is updated utilizing the measurement update step of the EKF. In this way, we run multiple EKFs associated to multiple target samples, instead of running a single EKF. To the best of our knowledge, our article is novel in tracking multiple targets in noisy environments, using the observer with bearing-only measurements. The effectiveness of the proposed GM-PHD is verified utilizing MATLAB simulations.

Passive target tracking deals with nonlinear filtering in which dynamics of the system are considered to be linear, while the target state is built on nonlinear measurements. In this paper, a comparative study is conducted for accurate state estimation of an underwater far-field moving target by exploiting the strength of well known nonlinear variant of Bayesian filter, i.e., extended Kalman filter (EKF) with discrete-time Kalman smoother, called Rauch–Tung–Striebel (RTS) smoother. Analysis is performed with two key parameters in target tracking by mean of variation in the number of sensors and different standard deviations of measured noise in the context of underwater bearings-only tracking technology. Exhaustive experiments are performed for finding the least root-mean square error between true and estimated position of target movement in the trajectory at every time instant. Relatively accurate estimation of the target state is observed from noisy measurements of sensors in case of RTS smoother than that of EKF for each scenario.

Neurovascular coupling (NVC) describes the effective matching of cerebral blood flow (CBF) to regions of neuro‐metabolic demand. There is increasing interest to assess human NVC for both basic research and its potential role in vascular‐cognitive impairment. The clinical utility of NVC relies on a standardized protocol for which the driving metabolic demands are highly‐selective. Various research groups deploy divergent strategies to elicit visual NVC responses, including inactive processes (visual grating), passive visual tracking (target with predictable motion) and active visual tracking (target with unpredictable motion). These strategies differ in degree of cognitive and metabolic demand and may elicit different NVC responses, thus precluding study comparison.The present NVC assessment evaluated temporal and regional responsiveness of blood flow (transcranial Doppler) to the visual cortex [via the posterior cerebral artery (PCA)] and blood pressure (Finapres NOVA) during visual stimulation in 19 healthy subjects while also measuring middle cerebral artery (MCA) blood flow. Visual stimulation included 10 cycles of 30‐seconds with eyes‐closed, followed by 30‐seconds with eyes‐open tracking a moving computerized target. Each subject completed three trials of passive tracking and three trials of active tracking (114 NVC protocols, 1140 individual hyperemias). A custom eye‐scanning apparatus followed eye motion to quantify visual target‐tracking vigilance. Additional custom software was used to quantify NVC.The data demonstrated that active tracking elicited greater NVC responses compared to passive tracking. Specifically, there was 26% greater change in the mean elevation of PCA blood velocity (p=<0.000) and 13% greater peak NVC response (p<0.01). The MCA response was also greater during active tracking (mean response 111% greater, peak response 41% greater; both p<0.001). Visual target‐tracking vigilance was linearly correlated to the degree of hyperemia in the MCA and PCA, as well blood pressure during NVC.It was observed that active and passive visual tracking elicit different NVC responses and cannot be reliably compared. That PCA and MCA responses were greater with active tracking suggests an elevated global CBF (i.e. not selective to regions perfused by the PCA) that may result from recruitment of brain centres responsible for sustained attention and executive function. In other words, active tracking leads to non‐selective elevations in global CBF and greater target‐tracking vigilance impacts the NVC response. These findings are a critical step to better understand and standardize the evaluation of NVC in humans and for potential clinical deployment of NVC assessments.Support or Funding InformationNatural Sciences and Engineering Research Council; Alberta Innovates Research Studentship; NSERC; CIHR; Libin Cardiovascular Institute; Hotchkiss Brain Institute; Compute CanadaThis abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Fields of distributed passive and multistatic active sonar sensors provide surveillance capabilities against quiet submarine threats in Anti-Submarine Warfare (ASW) scenarios. The joint cooperative use of passive and active sonar offers synergistic and complimentary acoustic performance as well as operational advantages. However, a significant challenge of heterogeneous, multi-sensor systems is the successful fusion of information from the various sensors to enable robust target detection, classification, localization, and tracking. This paper describes the formation of a passive acoustic track that may be used to cue an active multistatic acoustic tracking system. A cue from a passive acoustic track reduces the false track rate in the active tracker by focusing the search area and selectively initiating active tracks. The passive track is assumed to originate from a fixed passive acoustic horizontal line array (HLA) which is unable to determine target range or resolve the familiar left-right ambiguity. However, passive systems can predict Closest-Point-of-Approach (CPA) events. For each CPA event, a cue can be forwarded to the active system for multistatic active track initiation. This paper presents a minimal parametric representation for a passive acoustic track. It also describes an algorithm for obtaining initial estimates of parameters that can be used to initiate the passive track more effectively. A performance evaluation is given. This paper also describes the conversion of the passive track to pseudo-coordinates that are convenient for use with a multistatic tracking system. Lastly, a method for measuring passive track quality is described which determines if track quality is sufficient to justify cueing the active multistatic system.

Extended target tracking (ETT) based on random matrices typically assumes that the measurement model is linear. However, nonlinear measurements (such as range and azimuth) depending on locations of a series of unknown scattering centers always exist in many practical tracking applications. To address this issue, this paper proposes an iteratively extended target tracking based on random matrices by using decorrelated unbiased conversion of nonlinear measurements (ETT-IDUCM). First, we utilize a decorrelated unbiased converted measurement (DUCM) method to convert nonlinear measurements depending on unknown scatters of target extent in polar coordinates into the ones in Cartesian coordinates with equivalent measurement noise covariances. Subsequently, a novel method, combining iteratively extended Kalman filter (IEKF) updates with variational Bayesian (VB) cycles is developed for precise estimation of the target's kinematic state and extension. This method leverages the synergy between external IEKF iterations, which use the estimated state as a new prediction and input for DUCM, and internal VB iterations, which realize a closed-form approximation of the joint posterior probability. This approach progressively enhances estimation accuracy. Simulation results demonstrate the ETT-IDUCM algorithm's superior precision in estimating the target's kinematic state and extension compared to existing methods.

A new filtering method is proposed to accurately estimate target state via decreasing the nonlinearity between radar polar measurements (or spherical measurements in three-dimensional (3D) radar) and target position in Cartesian coordinate. The degree of linearity is quantified here by utilizing correlation coefficient and Taylor series expansion. With the proposed method, the original measurements are converted from polar or spherical coordinate to a carefully chosen Cartesian coordinate system that is obtained by coordinate rotation transformation to maximize the linearity degree of the conversion function from polar/spherical to Cartesian coordinate. Then the target state is filtered along each axis of the chosen Cartesian coordinate. This method is compared with extended Kalman filter (EKF), Converted Measurement Kalman filter (CMKF), unscented Kalman filter (UKF) as well as Decoupled Converted Measurement Kalman filter (DECMKF). This new method provides highly accurate position and velocity with consistent estimation.

Observability analysis of two closed-loop guidance systems with bearings-only measurements

This study handles tracking multiple objects under bearings-only measurements of multiple heterogeneous sonar sensors in cluttered underwater environments. In order to track multiple objects in clutter environments, we apply Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter. In the GM-PHD filter, the Extended Kalman Filter (EKF) is applied, since the EKF can cope with non-linearity of bearings-only measurements. However, range uncertainty of the object is large for bearings-only measurements, which can generate poor performance in the GM-PHD. The bearing measurements of any two passive sonar sensors can intersect at one point, and the point provides the viable location of an object. Hence, if an intersection point of two bearing sensors satisfies the maximum sensing range constraint, then the point can generate an object sample in our GM-PHD Kalman filter. In addition, every object sample is updated under the measurement update step of the EKF. To the best of our knowledge, this paper is novel in tracking multiple objects in clutter, under bearings-only measurements of multiple heterogeneous sonar sensors. The efficacy of the proposed GM-PHD Kalman filter is demonstrated under MATLAB simulations.

Observability-based local path planning and obstacle avoidance using bearing-only measurements

We have developed a passive sonar tracking algorithm that makes use of variations in the amplitude of the signal received from a source in motion. Originally the likelihood function (probability density function (pdf) of received signal amplitude for a given source location) was calculated by Monte Carlo sampling of the environmental variables and running the acoustic propagation model to predict transmission loss (TL). For each possible source location, the pdf of TL was constructed. To calculate the posterior pdf using received signal amplitude data, Bayes' rule was used sequentially such that for each possible source location, the likelihood function evaluated at the value of the new received amplitude was multiplied by the prior probability associated with that source location. This approach depends fundamentally on how the environment is sampled and on the acoustic propagation model. More recently, the likelihood function has been expanded into the joint pdf of sequences of received signal amplitudes...

The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The claimed advantages with UKF are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model. We point out several less known links between EKF and UKF in terms of two conceptually different implementations of the Kalman filter: the standard one based on the discrete Riccati equation, and one based on a formula on conditional expectations that does not involve an explicit Riccati equation. First, it is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model. Second, a less cited version of the EKF based on a second-order Taylor expansion is shown to be quite closely related to UKF. The different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications.

This paper seeks to address whether active or passive tracking is preferable in terms of centroid-track error. Active tracking has the advantage of allowing for SWaP-limited source control to scale SNR. With coherent illumination, however, speckle noise gives rise to a fundamental limit in tracking precision. On the other hand, passive tracking relies on incoherent illumination with speckle-free return. The drawback in this case is that SNR itself is inherently limited, thus limiting precision with respect to tracking measurements. In our analysis, we first present the theory that drives limiting factors of both active and passive tracking schemes. From these limitations we then estimate Strehl ratio at various SNRs for direct comparison of active and passive performance. We consider objects of various shapes and sizes, study both well-resolved and unresolved objects, and anchor our findings to first-order simulation results that demonstrate significance in the design of tracking systems.

A major advantage of the use of passive sonar in the tracking multiple underwater targets is that they can be kept covert, which reduces the risk of being attacked. However, the nonlinearity of the passive Doppler and bearing measurements, the range unobservability problem, and the complexity of data association between measurements and targets make the problem of underwater passive multiple target tracking challenging. To deal with these problems, the cardinalized probability hypothesis density (CPHD) recursion, which is based on Bayesian information theory, is developed to handle the data association uncertainty, and to acquire existing targets’ numbers and states (e.g., position and velocity). The key idea of the CPHD recursion is to simultaneously estimate the targets’ intensity and the probability distribution of the number of targets. The CPHD recursion is the first moment approximation of the Bayesian multiple targets filter, which avoids the data association procedure between the targets and measurements including clutter. The Bayesian-filter-based extended Kalman filter (EKF) is applied to deal with the nonlinear bearing and Doppler measurements. The experimental results show that the EKF-based CPHD recursion works well in the underwater passive multiple target tracking system in cluttered and noisy environments.

The Kalman filter has earned its fame through its elegance, its compatibility with digital simulation, and its reasonable performance even when the somewhat restrictive assumptions on which it is based are not all met. Extensions of the Kalman filter are varied, and not all estimators dubbed Extended Kalman Filter (EKF) are equivalent. This chapter develops some filter extensions appropriate to target tracking, classification, and command architectures. These include estimation of essentially nonlinear and non-Gaussian motion models for targets, nonlinear conversion of range-bearing measurements into position measurements, and lack of true independence between target state and observation system errors. In target tracking, using models of target motion and a stream of measurements or observations, the Kalman filter provides the conditional distribution of the location of a target following an unpredictable path. From distribution we can not only accurately estimate the location of the target, but we can also place a capture region about the estimate that will contain the target with any pre-specified probability. The Kalman algorithm is based upon a linear-Gauss–Markov (LGM) model of the engagement. Even when there are nonlinearities in the engagement model, an expanded version of the Kalman filter (the EKF) generates plausible position estimates and capture regions. We will contrast realized performance with that predicted by the EKF. The shortcomings of the Kalman filter when used in command architectures are important, but in many cases they can be mitigated. In others alternative approaches like the GWE, explored in later chapters, are much more effective.

In long-range radar tracking problems with precise range measurements, the Extended Kalman Filter (EKF) tracking algorithm commonly used with non-linear radar measurements fails to achieve good performance. This is due to the fact that this algorithm approximates the measurement error distribution in Cartesian space using a Gaussian distribution when the true distribution is highly non-Gaussian, a situation which is referred to as the contact-lens problem in the literature. A recently developed technique uses Maximum Likelihood (ML) to fit Gaussian Mixture (GM) parameters to the non-Gaussian Cartesian measurement distribution in 2D. This approach was applied in a new GM Kalman filter which provides excellent range estimation performance at a fraction of the cost of a particle filter. This paper extends the ML modeling approach to three dimensional radar measurements. This presents a greater difficulty because the ML GM fits to a 3D radar measurement in Cartesian space have widely varying geometries compared to ML fits to a 2D measurement.