Gaussian filtering and smoothing for continuous-discrete dynamic systems

Särkkä, Simo; Sarmavuori, Juha

doi:10.1016/j.sigpro.2012.09.002

Cited by 114 publications

(103 citation statements)

References 39 publications

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“…Approaches to implement this was not covered in [8] and in [12] a Taylor expansion was used. However, by plugging in a Gaussian approximation to f X(t)|Y (t) (x(t)), the Type I smoother of [11] is derived. The Type II and III smoothers are also discussed by [11], which originate from the smoother formulation developed in [10].…”

Section: The Non-linear Smoothing Theory Approachmentioning

confidence: 99%

See 1 more Smart Citation

Iterative statistical linear regression for Gaussian smoothing in continuous-time non-linear stochastic dynamic systems

Tronarp

Särkkä

2019

Signal Processing

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This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary Gaussian process. Two methods are developed based on 1) taking the limit of statistical linear regression of the discretised process and 2) minimising an upper bound to a cost functional. Their difference is manifested in the diffusion of the approximate processes. This in turn gives novel derivations of preexisting Gaussian smoothers when Method 1 is used and a new class of Gaussian smoothers when Method 2 is used. Furthermore, based on the aforementioned development the iterative Gaussian smoothers in discrete-time are generalised to the continuous-time setting by iteratively re-linearising the stochastic differential equation with respect to the current Gaussian process approximation to the smoothed process. The method is verified in two challenging tracking problems, a reentry problem and a radar tracked coordinated turn model with state dependent diffusion. The results show that the method has competitive estimation accuracy with state-of-the-art smoothers.

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Section: The Non-linear Smoothing Theory Approachmentioning

confidence: 99%

“…The development in Section 3 is subsequently combined with a linear smoothing theory to arrive at novel derivations of the smoothers presented in [10,11]. The main result is presented in Section 5 where the discrete time iterative Gaussian smoothers [20,21,22] are generalised to continuous-time models.…”

Section: Introductionmentioning

confidence: 99%

Iterative statistical linear regression for Gaussian smoothing in continuous-time non-linear stochastic dynamic systems

Tronarp

Särkkä

2019

Signal Processing

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“…In this section, we describe an EKF and an extended Kalman smoother [25] we used with the models presented in Section IV and V. We consider a resetting hybrid system [20] that has continuous state variables governed by differential equations and resetting laws that reset state variables at discrete time instances. Future work includes nonlinear filtering using a linear matrix inequality state-dependent algebraic Riccati equation (LMI-SDARE) filter [26].…”

Section: Nonlinear Estimationmentioning

confidence: 99%

Omnidirectional-vision-based estimation for containment detection of a robotic mower

Yang

Chung

Hutchinson

et al. 2015

2015 IEEE International Conference on Robotics and Automation (ICRA)

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In this paper, we present an omnidirectionalvision-based localization and mapping system which can detect whether a robotic mower is contained in a permitted area. We exploit a robot-centric mapping framework that exploits a differential equation of motion of the landmarks, which are referenced with respect to the robot body frame. The estimator in our system generates a 3D point-based map with landmarks. Concurrently, the estimator defines a boundary of the mowing area with the estimated trajectory of the mower. The estimated boundary and the landmark map are provided for the estimation of the mowing location and for the containment detection. We validate the effectiveness of our system through numerical simulations and present the results of the outdoor experiment that we conducted with our robotic mower.

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“…The latter approach is compatible with the classical framework of continuous-discrete Gaussian filtering [Maybeck, 1982] as well as with the classical continuousdiscrete extended Kalman filter (CD-EKF) [Jazwinski, 1970] and recently proposed continuous-discrete unscented Kalman filter (CD-UKF) [Särkkä, 2007]. Cubature integration based filters and smoothers using the latter approach was also recently proposed in [Särkkä and Sarmavuori, 2012].…”

Section: Introductionmentioning

confidence: 96%