Nonlinear Estimation With State-Dependent Gaussian Observation Noise

Spinello, Davide; Stilwell, Daniel J.

doi:10.1109/tac.2010.2042006

Cited by 60 publications

(34 citation statements)

References 38 publications

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“…Proof: First, it is easily shown from Theorem 1 that the zero-solution of the system (6) withw k = 0 is locally asymptotically stable in the mean square, and the ellipsoid Ω(P, ρ) is contained in the mean-square domain of attraction since the inequality (12) is implied by (17). It remains to show that, under zero-initial condition, the filtering errorz k satisfies the H ∞ performance con-…”

Section: Resultsmentioning

confidence: 99%

“…By using the well-known Schur Complement Lemma and noting the relation of ρπ = ε 2 2 , the condition (11) is also easily guaranteed by (20). We now consider the inequality (17). Set…”

Section: Resultsmentioning

confidence: 99%

“…A variety of performance requirements have been proposed in the literature for the filter design, such as the H ∞ specification, the minimum variance requirement, the distributed collaborative behavior and the so-called admissible variance constraint. For example, the extended Kalman filters have been designed in [11] for nonlinear deterministic systems and in [17] for nonlinear stochastic systems. The robust filtering problems have been extensively studied in [19,22] for systems with norm-bounded uncertainties and in [9,15] for uncertain systems with integral quadratic constraint.…”

Section: Introductionmentioning

confidence: 99%

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H∞ filtering with randomly occurring sensor saturations and missing measurements

2012

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In this paper, the H∞ filtering problem is investigated for a class of nonlinear systems with randomly occurring incomplete information. The considered incomplete information includes both the sensor saturations and the missing measurements. A new phenomenon of sensor saturation, namely, randomly occurring sensor saturation (ROSS), is put forward in order to better reflect the reality in a networked environment such as sensor networks. A novel sensor model is then established to account for both the ROSS and missing measurement in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. Based on this sensor model, a regional H∞ filter with a certain ellipsoid constraint is designed such that the filtering error dynamics is locally mean-square asymptotically stable and the H∞-norm requirement is satisfied. Note that the regional l2 gain filtering feature is specifically developed for the random saturation nonlinearity. The characterization of the desired filter gains is derived in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. Finally, a simulation example is employed to show the effectiveness of the filtering scheme proposed in this paper.

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Section: Resultsmentioning

confidence: 99%

“…By using the well-known Schur Complement Lemma and noting the relation of ρπ = ε 2 2 , the condition (11) is also easily guaranteed by (20). We now consider the inequality (17). Set…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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H∞ filtering with randomly occurring sensor saturations and missing measurements

2012

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“…With the derived Bayesian paradigm and under Gaussian distribution assumptions, a Maximum a Posteriori (MAP) cost function is established, which leads to the MAP estimates of the input and state. As the nonlinearity hinders analytical calculation of the estimates, a GaussNewton method will be used for approximate calculation [3], [17].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear simultaneous input and state estimation with application to flow field estimation

Fang

Callafon

2011

IEEE Conference on Decision and Control and European Control Conference

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This paper studies the problem of simultaneous input and state estimation for a nonlinear dynamical system. A Bayesian paradigm is proposed to provide statistical derivation of joint input and state estimators. Using the Bayesian paradigm, a Maximum a Posteriori (MAP) based estimation scheme is developed as a joint estimator. The scheme involves nonlinear MAP optimization, which is addressed by a classical Gauss-Newton method. The effectiveness of the proposed scheme is illustrated via a simulation based study on ocean flow field estimation using submersible drogues that can measure position and acceleration intermittently.

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“…However, in case of state dependence, there is an additional burden of estimating the measurement uncertainty after each state update. State dependent measurement uncertainties have been used in systems for satellite tracking [27] and robot navigation [28]. We use an approach similar to [27], [5] to formulate the expressions for the state dependent measurement uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Estimating SE(3) elements using a dual quaternion based linear Kalman filter

Srivatsan¹,

Rosen²,

Mohamed³

et al.

Robotics: Science and Systems XII

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Abstract-Many applications in robotics such as registration, object tracking, sensor calibration, etc. use Kalman filters to estimate a time invariant SE(3) element by locally linearizing a non-linear measurement model. Linearization-based filters tend to suffer from inaccurate estimates, and in some cases divergence, in the presence of large initialization errors. In this work, we use a dual quaternion to represent the SE(3) element and use multiple measurements simultaneously to rewrite the measurement model in a truly linear form with state dependent measurement noise. Use of the linear measurement model bypasses the need for any linearization in prescribing the Kalman filter, resulting in accurate estimates while being less sensitive to initial estimation error. To show the broad applicability of this approach, we derive linear measurement models for applications that use either position measurements or pose measurements. A procedure to estimate the state dependent measurement uncertainty is also discussed. The efficacy of the formulation is illustrated using simulations and hardware experiments for two applications in robotics: rigid registration and sensor calibration.

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Nonlinear Estimation With State-Dependent Gaussian Observation Noise

Cited by 60 publications

References 38 publications

H∞ filtering with randomly occurring sensor saturations and missing measurements

H∞ filtering with randomly occurring sensor saturations and missing measurements

Nonlinear simultaneous input and state estimation with application to flow field estimation

Estimating SE(3) elements using a dual quaternion based linear Kalman filter

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