Conditionally minimax algorithm for nonlinear system state estimation

Pankov, A. R.; Bosov, A. V.

doi:10.1109/9.310035

Cited by 15 publications

(13 citation statements)

References 9 publications

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“…where P k ∈ P (E Z k , cov(Z k , Z k ))-the set of all possible distributions of the compound vector Z k = (X k , α k (X k−1 , u k−1 )) T and P k ∈ P (E Z k , cov(Z k , Z k ))-the set of all possible distributions of the compound vector Z k = (X k −X k , β k (X k , Y k )) T . 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 only question left is the covariance matrices, which are necessary for the calculation of the linear estimator coefficients in Equation (22). The general CMNF approach implies that instead of the real covariances one uses their estimates, obtained by means of the Monte-Carlo sampling.…”

Section: Conditionnaly Minimax Nonlinear Filtermentioning

confidence: 99%

“…• CMNF: Conditionally minimax nonlinear Filter (22) with basic structure Functions (24) and covariances calculated by the Monte-Carlo sampling on a separate test set of 10 5 AUV paths; • UPMF: Unbiased pseudo-measurements Filter (21); • EKF: Extended Kalman filter, which provides a common approach to deal with the non-linearity in the system dynamics or observations [18].…”

Section: Auv Control Simulationmentioning

confidence: 99%

“…The first row corresponds to the position prediction by virtue of System (18) and the second row shows the results with prediction obtained by velocity estimation via seabed sensing, Equation (15). The columns correspond to the filtering algorithms applied: The conditionally minimax nonlinear Filter (22) with basic structure Functions (24), the unbiased pseudo-measurements filter, Equation (21), and the extended Kalman filter. Note that for the seabed sensing prediction only the CMNF filter allowed to acheive a reasonable estimate/control performance.…”

Section: Auv Control Simulationmentioning

confidence: 99%

“…However, careful analysis shows that all these filters, even if different from the viewpoint of complexity, give almost the same level of the AUV position estimation accuracy, especially in the case of bearing-only observations [21]. 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.…”

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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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Section: Conditionnaly Minimax Nonlinear Filtermentioning

confidence: 99%

Section: Conditionnaly Minimax Nonlinear Filtermentioning

confidence: 99%