Intelligent Interactive Displays in Vehicles with Intent Prediction: A Bayesian framework

2018 IEEE Western New York Image and Signal Processing Workshop (WNYISPW)

2018

In some problems there is information about the destination of a moving object. An example is an airliner flying from an origin to a destination. Such problems have three main components: an origin, a destination, and motion in between. To emphasize that the motion trajectories end up at the destination, we call them destination-directed trajectories. The Markov sequence is not flexible enough to model such trajectories. Given an initial density and an evolution law, the future of a Markov sequence is determined probabilistically. One class of conditionally Markov (CM) sequences, called the CM L sequence (including the Markov sequence as a special case), has the following main components: a joint endpoint density (i.e., an initial density and a final density conditioned on the initial) and a Markov-like evolution law. This paper proposes using the CM L sequence for modeling destination-directed trajectories. It is demonstrated how the CM L sequence enjoys several desirable properties for destination-directed trajectory modeling. Some simulations of trajectory modeling and prediction are presented for illustration.

“…, 100) and [x k+n|k ,ŷ k+n|k ] is its prediction using measurements up to time k = 9, and M = 1000 is the number of Monte Carlo runs. The ratio of 13, which is huge.…”

Section: Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Destination-Directed Trajectory Modeling and Prediction Using Conditionally Markov Sequences

2018 IEEE Western New York Image and Signal Processing Workshop (WNYISPW)

2018

“…[14] extended the results of [13] to the Gaussian case. The work of [15]- [16] for intent inference, e.g., in an intelligent interactive vehicle's display, can be interpreted in the reciprocal process setting. [17] studied the relationship between acausal systems and reciprocal processes.…”

Section: Introductionmentioning

confidence: 99%

Gaussian Conditionally Markov Sequences: Algebraically Equivalent Dynamic Models

IEEE Trans. Aerosp. Electron. Syst.

2020

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...

“…The Gaussian counterpart of the generalized reciprocal sequence defined in [10] was studied in [11]. [12]- [13] used bridging distributions for the purpose of intent inference, for example, in selecting an icon on an in-vehicle interactive display. A CM sequence was used in [14] for trajectory modeling with destination information.…”

Section: Introductionmentioning

confidence: 99%

Trajectory Modeling and Prediction with Waypoint Information Using a Conditionally Markov Sequence

2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

2018

Information about the waypoints of a moving object, e.g., an airliner in an air traffic control (ATC) problem, should be considered in trajectory modeling and prediction. Due to the ATC regulations, trajectory design criteria, and restricted motion capability of airliners there are long range dependencies in trajectories of airliners. Waypoint information can be used for modeling such dependencies in trajectories. This paper proposes a conditionally Markov (CM) sequence for modeling trajectories passing by waypoints. A dynamic model governing the proposed sequence is obtained. Filtering and trajectory prediction formulations are presented. The use of the proposed sequence for modeling trajectories with waypoints is justified.