Track Extraction With Hidden Reciprocal Chains

Stamatescu, George; White, L.B.; Bruce-Doust, Riley

doi:10.1109/tac.2017.2741919

Cited by 21 publications

(27 citation statements)

References 26 publications

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“…As stated in the introduction, after quantizing the state space, [9]- [12] used finite state reciprocal sequences for trajectory modeling with destination information. However, such quantization is not always feasible-it can be computationally prohibitive.…”

Section: Illustrative Examplesmentioning

confidence: 99%

Gaussian Conditionally Markov Sequences: Algebraically Equivalent Dynamic Models

Rezaie

2020

IEEE Trans. Aerosp. Electron. Syst.

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The conditionally Markov (CM) sequence contains different classes, including Markov, reciprocal, and so-called CML and CMF (two CM classes defined in our previous work). Markov sequences are special reciprocal sequences, and reciprocal sequences are special CML and CMF sequences. Each class has its own forward and backward dynamic models. The evolution of a CM sequence can be described by different models. For a given problem, a model in a specific form is desired or needed, or one model can be easier to apply and better than another. Therefore, it is important to study the relationship between different models and to obtain one model from another. This paper studies this topic for models of nonsingular Gaussian (NG) CML, CMF , reciprocal, and Markov sequences. Two models are probabilistically equivalent (PE) if their stochastic sequences have the same distribution, and are algebraically equivalent (AE) if their stochastic sequences are path-wise identical. A unified approach is presented to obtain an AE forward/backward CML/CMF /reciprocal/Markov model from another such model. As a special case, a backward Markov model AE to a forward Markov model is obtained. While existing results are restricted to models with nonsingular state transition matrices, our approach is not. In addition, a simple approach is presented for studying and determining Markov models whose sequences share the same reciprocal/CML model.In theory, Gaussian CM processes were introduced in [22] based on mean and covariance functions.[23] extended the definition of Gaussian CM processes (presented in [22]) to the general (Gaussian/non-Gaussian) case. In [1], we defined other (Gaussian/non-Gaussian) CM processes, studied (stationary/non-stationary) NG CM sequences, obtained dynamic models and characterizations of CM L and CM F sequences, and discussed their applications. Reciprocal processes were introduced in [24].[25]-[27] studied reciprocal processes in a general setting. Based on a valuable observation, [23] commented on the relationship between Gaussian CM and Gaussian reciprocal processes.[28] elaborated on the comment of [23] and presented a relationship between the CM process and the reciprocal process for the general (Gaussian/non-Gaussian) case.[29]- [30] presented and studied a dynamic model of NG reciprocal sequences.[28] and [31]-[32] studied reciprocal sequences from the CM viewpoint and developed dynamic models, called reciprocal CM L and reciprocal CM F models, with white dynamic noise for the NG reciprocal sequence. A characterization of the NG Markov sequence was presented in [33].[34] considered modeling and estimation of finite-state reciprocal sequences.The evolution of a Markov sequence can be modeled by a Markov, reciprocal, or CM L model 2 . Similarly, a reciprocal sequence can have a model in the form of the one in [29] or in the form of a CM L (CM F ) model of [28]. Therefore, a CM sequence can have more than one model. One model can be easier to apply than another for an application. For example, the reciprocal CM L mo...

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Section: Illustrative Examplesmentioning

confidence: 99%

Gaussian Conditionally Markov Sequences: Algebraically Equivalent Dynamic Models

Rezaie

2020

IEEE Trans. Aerosp. Electron. Syst.

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“…The problem of finding the most likely path for the evolution of a distribution is related to a discrete Schrödinger bridge problem [26]. Schrödinger's thought experiment [29] has indirectly given rise to the concept of reciprocal processes [4], [20], [23], which connects this work to tracking of moving objects using reciprocal processes [16], [30], [32]. However, as mentioned before, we consider estimating the flow of an ensemble rather than single target tracking.…”

Section: Introductionmentioning

confidence: 99%

Estimating ensemble flows on a hidden Markov chain

Haasler

Ringh

Chen

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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We propose a new framework to estimate the evolution of an ensemble of indistinguishable agents on a hidden Markov chain using only aggregate output data. This work can be viewed as an extension of the recent developments in optimal mass transport and Schrödinger bridges to the hidden Markov chain setting. The flow of the ensemble is estimated by solving a maximum likelihood problem, which has a nice convex formulation, and we develop a fast numerical algorithm for it. We illustrate in two numerical examples how this framework can be used to track the flow of identical and indistinguishable dynamical systems.

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“…In [5] the behavior of acausal systems was described using reciprocal processes. Based on quantized state space, [6]- [9] used finite-state reciprocal sequences for detection of anomalous trajectory pattern, intent inference, and tracking. [10] used the idea of reciprocal processes for intent inference in intelligent interactive displays of vehicles.…”

Section: Introductionmentioning

confidence: 99%

“…e0 and eN in(9) are not necessarily the same as e0 and eN in(10). Just for simplicity we use the same notation.…”

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confidence: 99%

Models and Representations of Gaussian Reciprocal and Conditionally Markov Sequences

Rezaie

2018

Proceedings of the 2nd International Conference on Vision, Image and Signal Processing

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Conditionally Markov (CM) sequences are powerful mathematical tools for modeling random phenomena. There are several classes of CM sequences one of which is the reciprocal sequence. Reciprocal sequences have been widely used in many areas including image processing, intelligent systems, and acausal systems. To use them in application, we need not only their applicable dynamic models, but also some general approaches to designing parameters of dynamic models. Dynamic models governing two important classes of nonsingular Gaussian (NG) CM sequences (called CM L and CM F models), and a dynamic model governing the NG reciprocal sequence (called reciprocal CM L model) were presented in our previous work. In this paper, these models are studied in more detail and general approaches are presented for their parameter design. It is shown that every reciprocal CM L model can be induced by a Markov model and parameters of the reciprocal CM L model can be obtained from those of the Markov model. Also, it is shown how NG CM sequences can be represented in terms of a NG Markov sequence and an independent NG vector. This representation provides a general approach for parameter design of CM L and CM F models. In addition, it leads to a better understanding of CM sequences, including the reciprocal sequence.

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Track Extraction With Hidden Reciprocal Chains

Cited by 21 publications

References 26 publications

Gaussian Conditionally Markov Sequences: Algebraically Equivalent Dynamic Models

Gaussian Conditionally Markov Sequences: Algebraically Equivalent Dynamic Models

Estimating ensemble flows on a hidden Markov chain

Models and Representations of Gaussian Reciprocal and Conditionally Markov Sequences

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