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Tracking on the rotation group is a key component of many modern systems for estimation and tracking of the orientation of rigid bodies. To address this problem, here, we describe a Bayesian algorithm that relies on directional measurements, acquired, for example, by an inertial measurements unit (IMU), for tracking on the special orthogonal (rotation) group. Its novelty lies in the use of maximum entropy distributions on these groups as models for the priors, and justifiable relaxation algorithms that permit the recursive implementation of such a model to provide a filter. We provide the solutions in a recursive closed form. In the two-dimensional case, the parameters of the prior and posterior distributions can be computed exactly and the solution has low complexity. Adoption of this approach eliminates the problem of angle wrapping. In higher dimensions, the exact solution cannot be computed, and it is necessary to make appropriate relaxations, which is done here. We demonstrate in simulations that, in contrast with some other approaches, our algorithm produces very accurate and statistically meaningful outputs. Pseudocode, specific to the IMU measurements is also provided. [ABSTRACT FROM AUTHOR]

We consider optimal Bayesian detection of a slowly varying tone of unknown amplitude in situations characterized by very low signal-to-noise ratio (SNR) and a large number of measurements, as found in certain gravitational wave and passive sonar problems. We use a hidden Markov model (HMM) framework but, unlike typical HMM-based frequency line tracking methods, we develop a true track-before-detect algorithm, which does not threshold the blocked Fourier data and only considers frequency trails that have phase continuity across all HMM steps. We model the frequency and phase evolution as a phase-wrapped Ornstein–Uhlenbeck process. The resulting optimal detector is computationally efficient. The detectability improvement arising from phase continuity is characterized via comparative simulation for a mock, simplified gravitational wave search problem. [ABSTRACT FROM AUTHOR]

We describe three single-scan probabilistic data association (PDA) based algorithms for tracking manoeuvering targets in clutter. These algorithms are derived by integrating the interacting multiple model (IMM) estimation algorithm with the PDA approximation. Each IMM model a posteriori state estimate probability density function (pdf) is approximated by a single Gaussian pdf. Each algorithm recursively updates the probability of target existence, in the manner of integrated PDA (IPDA). The probability of target existence is a track quality measure, which can be used for false track discrimination. The first algorithm presented, IMM-IPDA, is a single target tracking algorithm. Two multitarget tracking algorithms are also presented. The IMM-JIPDA algorithm calculates a posteriori probabilities of all measurement to track allocations, in the manner of the joint IPDA (JIPDA). The number of measurement to track allocations grows exponentially with the number of shared measurements and the number of tracks which share the measurements. Therefore, IMM-JIPDA can only be used in situations with a small number of crossing targets and low clutter measurement density. The linear multitarget IMM-IPDA (IMM-LMIPDA) is also a multitarget tracking algorithm, which achieves the multitarget capabilities by integrating linear multitarget (LM) method with IMM-IPDA. When updating one track using the LM method, the other tracks modulate the clutter measurement density and are subsequently ignored. In this fashion, LM achieves multitarget capabilities using the number of operations which are linear in the number of measurements and the number of tracks, and can be used in complex scenarios, with dense clutter and a large number of targets. [ABSTRACT FROM AUTHOR]

Sonobuoy fields, consisting of a large network of emitter and receiver sonar sensors on buoys, are increasingly being used for detection and tracking of underwater targets in a defined maritime area. This study presents a Gaussian mixture version of a multitarget-multisensor (MS) Bayesian-type tracker developed specifically for multistatic sonobuoy fields. Its foundation is the optimal Bayesian MS filter for a single target in clutter. The multi target feature is incorporated using the linearmultitarget paradigm, which is a fast and accurate approximation assuming the density of underwater targets is low. Reliable track initiation and false track discrimination for low signal-to-noise ratio targets are achieved using the amplitude feature of reported detections. The developed tracker is capable of processing measurements with different modalities, depending on the transmitted signal waveform. It is integrated and tested within a realistic multistatic sonar emulator developed by DST Group. [ABSTRACT FROM AUTHOR]

Sonobuoy fields, consisting of many distributed emitter and receiver sonar sensors on buoys, are used to seek and track underwater targets in a defined search area. The authors seek a scheduling protocol, selecting both the emitter and its waveform in each time interval that optimises tracking performance. This study describes a stationary scheduling algorithm for sonobuoy fields called the continuous probability states algorithm. The algorithm replaces a full partially observed Markov decision process by a computationally feasible Markov decision process by focusing on probability of target detection. This approach is shown to result in high-quality tracks for multiple targets in a realistic simulation of a sonobuoy field. [ABSTRACT FROM AUTHOR]

Work of Pezeshki, Calderbank and others [1, 2] has shown that choice of transmission order of Golay complementary waveforms in radar pulse trains can significantly improve Doppler resilience in detecting nonzero Doppler targets. For multiple targets a Weighted average Doppler (WD) algorithm [3] based on our earlier work has been shown to provide improvements. In this paper, we demonstrate that the Weighted Sidelobe Minimization procedure, developed in our recent work that combines the outputs of WD and the existing Binominal Design algorithms for ordering transmitted complementary waveform sequences using a point-wise minimization process (PMP), is also effective for the elimination of false target returns arising from sea clutter. A detailed analysis based on a Swerling II target model in terms of target detection probability is presented to validate the use of PMP. Our validation is strengthened by numerical simulations for both fixed and randomized scenarios. [ABSTRACT FROM AUTHOR]

Golay complementary waveforms can, in theory, yield radar returns of high range resolution with essentially zero sidelobes. In practice, when deployed conventionally, while high signal-to-noise ratios can be achieved for static target detection, significant range sidelobes are generated by target returns of nonzero Doppler causing unreliable detection. We consider signal processing techniques using Golay complementary waveforms to improve radar detection performance in scenarios involving multiple nonzero Doppler targets. A signal processing procedure based on an existing, so called, Binomial Design algorithm that alters the transmission order of Golay complementary waveforms and weights the returns is proposed in an attempt to achieve an enhanced illumination performance. The procedure applies one of three proposed waveform transmission ordering algorithms, followed by a pointwise nonlinear processor combining the outputs of the Binomial Design algorithm and one of the ordering algorithms. The computational complexity of the Binomial Design algorithm and the three ordering algorithms are compared, and a statistical analysis of the performance of the pointwise nonlinear processing is given. Estimation of the areas in the Delay-Doppler map occupied by significant range sidelobes for given targets are also discussed. Numerical simulations for the comparison of the performances of the Binomial Design algorithm and the three ordering algorithms are presented for both fixed and randomized target locations. The simulation results demonstrate that the proposed signal processing procedure has a better detection performance in terms of lower sidelobes and higher Doppler resolution in the presence of multiple nonzero Doppler targets compared to existing methods. [ABSTRACT FROM AUTHOR]

We describe a method for processing radar signals, combining the outputs of two – a Weighted average Doppler algorithm and an existing Binominal Design algorithm via a point-wise minimum processor. The method renders a better performance in range sidelobe suppression for the detection of multiple moving targets using Golay complementary waveforms than the existing Binominal Design algorithm. The effectiveness of the method is justified by analyzing the corresponding ambiguity functions. We also show the performance of the new signal processing method by simulations under a realistic scenario. [ABSTRACT FROM AUTHOR]