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首页> 外文期刊>Signal processing >Square-root accurate continuous-discrete extended-unscented Kalman filtering methods with embedded orthogonal and J-orthogonal QR decompositions for estimation of nonlinear continuous-time stochastic models in radar tracking
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Square-root accurate continuous-discrete extended-unscented Kalman filtering methods with embedded orthogonal and J-orthogonal QR decompositions for estimation of nonlinear continuous-time stochastic models in radar tracking

机译：具有嵌入式正交和J正交QR分解的平方根精确连续离散扩展无香卡尔曼滤波方法，用于估计雷达跟踪中的非线性连续时间随机模型

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摘要

This paper presents a number of new state estimation algorithms, which unify the best features of the accurate continuous-discrete extended and unscented Kalman filters in treating nonlinear continuous-time stochastic systems with discrete measurements. In particular, our mixed-type algorithms succeed in estimating continuous-discrete stochastic systems with nonlinear and/or nondifferentiable measurements. The main weakness of these methods is the need for the Cholesky decomposition of predicted covariance matrices. Such a factorization is highly sensitive to numerical integration and round-off errors committed, which may result in losing the covariance's positivity and, hence, failing the Cholesky decomposition. The latter problem is usually solved in the form of square-root filtering implementations, which propagate not the covariance matrix but its square root (Cholesky factor), only. Unfortunately, negative weights arising in applications of our mixed-type methods to high-dimensional stochastic systems preclude from designing conventional square-root filters. We address the mentioned issue with one-rank Cholesky factor updates or with hyperbolic QR transforms used for yielding J-orthogonal square-root filters. These novel algorithms are justified theoretically and examined and compared numerically to the non-squareroot one in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn, in the presence of Gaussian or glint noise. (C) 2019 Elsevier B.V. All rights reserved.
机译：本文提出了许多新的状态估计算法，这些算法统一了精确连续离散离散和无味卡尔曼滤波器在处理具有离散测量的非线性连续时间随机系统中的最佳功能。特别是，我们的混合类型算法可以成功地估计具有非线性和/或不可微测量的连续离散随机系统。这些方法的主要缺点是需要对预测的协方差矩阵进行Cholesky分解。这种分解对数值积分和舍入误差非常敏感，这可能导致失去协方差的正性，从而使Cholesky分解失败。后者的问题通常以平方根滤波实现的形式解决，该实现不传播协方差矩阵，而仅传播其平方根（Cholesky因子）。不幸的是，在将我们的混合类型方法应用于高维随机系统时产生的负权重无法设计常规的平方根滤波器。我们通过一阶Cholesky因子更新或用于产生J正交平方根滤波器的双曲QR变换来解决上述问题。这些新颖的算法在解决七维雷达跟踪问题的严酷条件下（其中飞机在存在高斯或闪烁噪声的情况下执行协调的转弯）在严峻条件下在理论上进行了论证并与非平方根算法进行了数值比较。 （C）2019 Elsevier B.V.保留所有权利。

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