Square root simplex sampling cubature Kalman filtering method

A Kalman filtering and square root technology, applied in the field of nonlinear filtering, can solve problems such as inability to ensure numerical stability, rounding errors, etc.

Inactive Publication Date: 2015-04-08
NORTHWESTERN POLYTECHNICAL UNIV
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Problems solved by technology

However, there are various rounding errors in numerical calculations during the filtering recursion process, which cannot ensure numerical stability.

Method used

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  • Square root simplex sampling cubature Kalman filtering method
  • Square root simplex sampling cubature Kalman filtering method
  • Square root simplex sampling cubature Kalman filtering method

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Embodiment Construction

[0030] The present invention will be further described below in conjunction with the accompanying drawings and embodiments, and the present invention includes but not limited to the following embodiments.

[0031] A square-root simplex volumetric Kalman filter method mainly includes computing the predicted state of the system and its covariance matrix P k|k-1 ; Compute the predicted measure and its covariance matrix P zz ; Calculate filter gain G k ;Update to get the system status and its covariance matrix P k|k and so on.

[0032] refer to figure 1 , setting the state-space model of the nonlinear system:

[0033] x k =f(x k-1 )+w k-1 (1)

[0034] z k =h(x k )+v k (2)

[0035] where x k is the n-dimensional system state vector at time k, f and h are known nonlinear functions, z k is the system measurement vector, w k-1 and v k is zero mean, covariance is Q k-1 and R k Gaussian white noise.

[0036] Next, based on the above nonlinear system model...

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Abstract

The invention provides a square root simplex sampling cubature Kalman filtering method. The method comprises calculating a system prediction state and a covariance matrix successively; calculating prediction measuration and a covariance matrix; calculating filtering gains; performing updating to obtain the system state and the covariance matrix. By the aid of the method, the problem that covariance matrixes are not positive definite caused by round-off errors of computers is solved by introducing the square root filtering technology, the filtering method robustness is improved, and the calculation amount can be greatly reduced by the simplex sampling method, and the filtering accuracy is improved compared with traditional filtering methods.

Description

technical field [0001] The invention belongs to the field of nonlinear filtering, and in particular relates to a square root monomorphic volume Kalman filtering method. Background technique [0002] Nonlinear filtering is one of the research hotspots in modern control, and it is widely used in engineering applications such as target tracking, satellite orbit / attitude estimation, and detector navigation and control. Bayesian filtering is a method that can be solved recursively through appropriate assumptions and approximations. It is the mainstream idea to solve nonlinear filtering problems. It has also been widely studied and applied, and a series of results have been achieved. [0003] Among them, the Extended Kalman Filter (EKF) algorithm is a traditional algorithm of the Bayesian filtering method. It performs a first-order linearization approximation to the nonlinear function through the Taylor expansion, ignoring the nonlinear characteristics of the system. When the init...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F19/00
Inventor 周德云王先明周颖纪敏郑宜航
Owner NORTHWESTERN POLYTECHNICAL UNIV
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