The Conditionally Minimax Nonlinear Filtering Method and Modern Approaches to State Estimation in Nonlinear Stochastic Systems

Борисов, А. A.; Bosov, A. V.; Кибзун, А. И.; Miller, Gregory; Semenikhin, K. V.

doi:10.1134/s0005117918010010

Cited by 6 publications

(5 citation statements)

References 23 publications

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“…A detailed description of the CMNF approach to estimating the state of nonlinear stochastic systems, including a thorough justification of the fact that ( 13) is the solution to the problem ( 14) and the existence of solution conditions (14), can be found in [67]. The following papers are devoted to the further application of the concept along with a comparative numerical study [68][69][70]. Full detailed research is given in [65].…”

Section: Conditionally Minimax Nonlinear Filter (Cmnf)mentioning

confidence: 99%

Navigation of Underwater Drones and Integration of Acoustic Sensing with Onboard Inertial Navigation System

Miller

2021

Drones

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The navigation of autonomous underwater vehicles is a major scientific and technological challenge. The principal difficulty is the opacity of the water media for usual types of radiation except for the acoustic waves. Thus, an acoustic transducer (array) composed of an acoustic sonar is the only tool for external measurements of the AUV attitude and position. Another difficulty is the inconstancy of the speed of propagation of acoustic waves, which depends on the temperature, salinity, and pressure. For this reason, only the data fusion of the acoustic measurements with data from other onboard inertial navigation system sensors can provide the necessary estimation quality and robustness. This review presents common approaches to underwater navigation and also one novel method of velocity measurement. The latter is an analog of the well-known Optical Flow method but based on a sequence of sonar array measurements.

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Section: Conditionally Minimax Nonlinear Filter (Cmnf)mentioning

confidence: 99%

Navigation of Underwater Drones and Integration of Acoustic Sensing with Onboard Inertial Navigation System

Miller

2021

Drones

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“…The details on the CMNF approach to the nonlinear stochastic systems state estimation, including the thorough justification of Equation (22) being the solution to Equation (23) and the conditions of the solution in Equation (23) existence, could be found in [22]. Further application of the concept along with the comparative numerical study is the matter of the works [23,24].…”

Section: Conditionnaly Minimax Nonlinear Filtermentioning

confidence: 99%

“…The fact that the CMNF estimate, Equation (22), is the solution to the minimax problem, Equation (23), means that at each time instant t k it delivers the minimum for the worst case (with respect to the a priori uncertainty in the distributions P k and P k ) of the mean-square error of the predictionX k and correctionX k . It should be noted that bothX k andX k are unbiased estimates of X k and the quality of these estimates is a priori known:…”

Section: Conditionnaly Minimax Nonlinear Filtermentioning

confidence: 99%

“…An alternative to traditional Kalman filtering is the conditionally optimal nonlinear filter proposed by V. S. Pugachev and developed by his successors into the conditionally minimax nonlinear filter (CMNF) [22]. This theory permits to develop the estimation procedure with given properties, for example, either with minimum dispersion or without bias, which is extremely important, for example, in target tracking based on bearing-only observations [23,24].In acoustic position estimation and target tracking, the bearing-only observation plays the principal role. As it was observed many years ago, the bearing angles may be transformed into linear observation, but with bias [25].…”

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confidence: 99%

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On AUV Control with the Aid of Position Estimation Algorithms Based on Acoustic Seabed Sensing and DOA Measurements

Miller

2019

Sensors

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This article discusses various approaches to the control of autonomous underwater vehicles (AUVs) with the aid of different velocity-position estimation algorithms. Traditionally this field is considered as the area of the extended Kalman filter (EKF) application: It became a universal tool for nonlinear observation models and its use is ubiquitous. Meanwhile, the specific characteristics of underwater navigation, such as an incomplete sets of measurements, constraints on the range metering or even impossibility of range measurements, observations provided by rather specific acoustic beacons, sonar observations, and other features seriously narrow the applicability of common instruments due to a high level of uncertainty and nonlinearity. The AUV navigation system, not being able to rely on a single source of position estimation, has to take into account all available information. This leads to the necessity of various complex estimation and data fusion algorithms, which are the matter of the present article. Here we discuss some approaches to the AUV position estimation such as conditionally minimax nonlinear filtering (CMNF) and unbiased pseudo-measurement filters (UPMFs) in conjunction with velocity estimation based on the seabed profile acoustic sensing. The presented estimation algorithms serve as a basis for a locally optimal AUV motion control algorithm, which is also presented. environment, all electromagnetic (and therefore video tools) have a very restricted range of operation, and only acoustic waves permit sensing and communication for rather long distances. The problem is that acoustic measurements are notably barren in comparison with the electromagnetic ones: They do not have such features as color or contrast and just measure the direction of arrival (DOA) and/or the distance from the vehicle to the reflecting surface, such as obstacle, seabed, or ship. Therefore, even using multiple irradiating sensors like acoustic sonars, one can only obtain an image of distances to the seabed relief. An introduction of acoustical beacons with known positions can help to determine the own AUV position by using an angular observation filter, and this is the area of the (short and/or long) baseline methods application [2]. These methods are especially effective in the limited area of operation; moreover, they may be used in the case of a moving baseline established on a ship [3] and even in docking maneuvering [4]. Acoustic methods used in active mode give access to the distance measurements, which make the position estimation problem much easier, though in some areas of application such measurements are not acceptable or must be restricted due to the energetic or masking constraints [5].The possibility of the sonar employment in AUV navigation has already been mentioned by some authors either in application to the situation, when an accurate seabed map is available, or in the case of presence of significant seabed features [6]. Moreover, the active pinging can be used to determine one's speed over the seabed by ...

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“…An alternative to suboptimal filters is the conditionally minimax nonlinear filtering (CMNF) [38]. Initially and in development [39], this method focused on applications in aircraft tracking tasks, which remain relevant for modern tasks [40]. However, the same approach has shown effectiveness in specific tasks for AUVs.…”

Section: Introductionmentioning

confidence: 99%

Tracking a Maneuvering Object by Indirect Observations with Random Delays

Bosov

2023

Drones

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A mathematical model for the target tracking problem is proposed. The model makes it possible to describe conditions when the time for an observer to receive the results of indirect observations of a moving object depends not only on the state of the observation environment but also on the state of the object itself. The source of such a model is the observation process, by stationary means, of an autonomous underwater vehicle, in which the time for obtaining up-to-date data depends on the unknown distance between the object and the observer. As part of the study of the problem, the equations of the optimal Bayesian filter are obtained. But this filter is not possible to implement. For practical purposes, it is proposed to use the conditionally minimax nonlinear filter, which has shown promising results in other complex tracking models. The conditions for the filter’s evaluation and its accuracy characteristics are given. A large-scale numerical experiment illustrating the filter’s operation and the observation system’s features with random delays are described.

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The Conditionally Minimax Nonlinear Filtering Method and Modern Approaches to State Estimation in Nonlinear Stochastic Systems

Cited by 6 publications

References 23 publications

Navigation of Underwater Drones and Integration of Acoustic Sensing with Onboard Inertial Navigation System

Navigation of Underwater Drones and Integration of Acoustic Sensing with Onboard Inertial Navigation System

On AUV Control with the Aid of Position Estimation Algorithms Based on Acoustic Seabed Sensing and DOA Measurements

Tracking a Maneuvering Object by Indirect Observations with Random Delays

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