Data assimilation into a Princeton Ocean Model of the Mediterranean Sea using advanced Kalman filters

This study investigates the effectiveness of the Singular Evolutive Extended Kalman filter (SEEK) and its variants (SEIK and SFEK filters) for data assimilation into a Princeton Ocean Model (POM) of the Mediterranean Sea. The SEEK filters are sub-optimal Kalman filters based on the approximation of the filter's error covariance matrices by singular low-rank matrices, reducing in this way extensive computational burden. At the initialization, the filters error covariance matrix is parameterized by a set of multivariate empirical orthogonal functions (EOFs) which describe the dominant modes of the system's variability. The Mediterranean model is implemented on a 1/4° × 1/4° horizontal grid with 25 sigma levels and is forced with 6-hour ECMWF re-analysis atmospheric data. Several twin experiments, in which pseudo-observations of altimetric data and/or data profiles were assimilated, were first performed to evaluate the filters performances and to study their sensitivities to different parameters and setups. The results of these experiments were very encouraging and helped in setting up an effective configuration for the assimilation of real data in near-real time situation. In the hindcast experiments, Topex/Poseidon and ERS weekly sea level anomaly data were first assimilated during 1993 and the filters solution was evaluated against independent Reynolds sea surface temperature (SST) analysis. The assimilation system was able to significantly enhance the consistency between the model and the assimilated data, although the improvement with respect to independent SST data was significantly less pronounced. The model SST was only improved after including SST data in the assimilation system.     

Application of an Ensemble Kalman filter to a 1-D coupled hydrodynamic-ecosystem model of the Ligurian Sea

The Ensemble Kalman filter (EnKF) has been applied to a 1-D complex ecosystem model coupled with a hydrodynamic model of the Ligurian Sea. In order to improve the performance of the EnKF, an ensemble subsampling strategy has been used to better represent the covariance matrices and a pre-analysis step for correcting the non-normality of the members distribution has been implemented. Twin experiments have been realized to assess the performance of the developed tool and a real data assimilation experiment has been conducted to hindcast the ecosystem at the Dyfamed site during the year 2000. Finally the performance of the EnKF has been compared with a Singular Evolutive Extended Kalman (SEEK) filter with a fixed basis. We conclude that, on one hand, there is a benefit in using the subsampling strategy and the lognormal transformation with the EnKF, and on the other hand, this filter presents better performance than the fixed basis version of the SEEK filter. However, it also incurs a large computational cost.     

Improving assimilation of SeaWiFS data by the application of bias correction with a local SEIK filter

Ocean-biogeochemical models show typically significant errors in the representation of chlorophyll concentrations. The model state can be improved by the assimilation of satellite chlorophyll data with algorithms based on the Kalman filter. However, these algorithms do usually not account for the possibility that the model prediction contains systematic errors in the form of model bias. Accounting explicitly for model biases can improve the assimilation performance. To study the effect of bias estimation on the estimation of surface chlorophyll concentrations, chlorophyll data from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) are assimilated on a daily basis into the NASA Ocean Biogeochemical Model (NOBM). The assimilation is performed by the ensemble-based SEIK filter combined with an online bias correction scheme. The SEIK filter is simplified here by the use of a static error covariance matrix. The performance of the filter algorithm is assessed by comparison with independent in situ data over the 7-year period 1998–2004. The bias correction results in significant improvements of the surface chlorophyll concentrations compared to the assimilation without bias estimation. With bias estimation, the daily surface chlorophyll estimates from the assimilation show about 3.3% lower error than SeaWiFS data. In contrast, the error in the global surface chlorophyll estimate without bias estimation is 10.9% larger than the error of SeaWiFS data.     

Application of a SEEK filter to a 1D biogeochemical model of the Ligurian Sea: Twin experiments and real in-situ data assimilation

The Singular Evolutive Extended Kalman (SEEK) filter has been implemented to assimilate in-situ data in a 1D coupled physical-ecosystem model of the Ligurian Sea. The biogeochemical model describes the partly decoupled nitrogen and carbon cycles of the pelagic food web. The GHER hydrodynamic model (1D version) is used to represent the physical forcings. The data assimilation scheme (SEEK filter) parameterizes the error statistics by means of a set of empirical orthogonal functions (EOFs). Twin experiments are first performed with the aim to choose the suitable experimental protocol (observation and estimation vectors, number of EOFs, frequency of the assimilation,…) and to assess the SEEK filter performances. This protocol is then applied to perform real data assimilation experiments using the DYFAMED data base. By assimilating phytoplankton observations, the method has allowed to improve not only the representation of the phytoplankton community, but also of other variables such as zooplankton and bacteria that evolve with model dynamics and that are not corrected by the data assimilation scheme. The validation of the assimilation method and the improvement of model results are studied by means of suitable error measurements.     

Assimilation of altimetric data in the mid-latitude oceans using the Singular Evolutive Extended Kalman filter with an eddy-resolving, primitive equation model

A new data assimilation scheme has been elaborated for ocean circulation models based on the concept of an evolutive, reduced-order Kalman filter. The dimension of the assimilation problem is reduced by expressing the initial error covariance matrix as a truncated series of orthogonal perturbations. This error sub-space evolves during the assimilation so as to capture the growing modes of the estimation error. The algorithm has been formulated in quite a general fashion to make it tractable with a large variety of ocean models and measurement types. In the present paper, we have examined three possible strategies to compute the evolution of the error subspace in the so-called Singular Evolutive Extended Kalman (SEEK) filter: the steady filter considers a time-independent error sub-space, the apprentice filter progressively enriches the error sub-space with the information learned from the innovation vector after each analysis step, and the dynamical filter updates the error sub-space according to the model dynamics. The SEEK filter has been implemented to assimilate synthetic observations of the surface topography in a non-linear, primitive equation model that uses density as vertical coordinate. A simplified box configuration has been adopted to simulate a Gulf Stream-like current and its associated eddies and gyres with a resolution of 20 km in the horizontal, and 4 levels in the vertical. The concept of twin experiments is used to demonstrate that the conventional SEEK filter must be complemented by a learning mechanism in order to model the misrepresented tail of the error covariance matrix. An approach based on the vertical physics of the isopycnal model, is shown particularly robust to control the velocity field in deep layers with surface observations only. The cost of the method makes it a suitable candidate for large-size assimilation problems and operational applications.     

Wave data assimilation with the Kalman filter

A new data assimilation method for ocean waves is presented, based on an efficient low-rank approximation to the Kalman filter. Both the extended Kalman filter and a truncated second-order filter are implemented. In order to explicitly estimate past wind corrections based on current wave measurements, the filter is extended to a fixed-lag Kalman smoother for the wind fields. The filter is tested in a number of synthetic experiments with simple geometries. Propagation experiments with errors in the boundary condition showed that the KF was able to accurately propagate forecast errors, resulting in spatially varying error correlations, which would be impossible to model with time-independent assimilation methods like OI. An explicit comparison with an OI assimilation scheme showed that the KF also is superior in estimating the sea state at some distance from the observations. In experiments with errors in the driving wind, the modeled error estimates were also in agreement with the actual forecast errors. The bias in the state estimate, which is introduced through the nonlinear dependence of the waves on the driving wind field, was largely removed by the second-order filter, even without actually assimilating data. Assimilation of wave observations resulted in an improved wave analysis and in correction of past wind fields. The accuracy of this wind correction depends strongly on the actual place and time of wave generation, which is correctly modeled by the error estimate supplied by the Kalman filter. In summary, the KF approach is shown to be a reliable assimilation scheme in these simple experiments, and has the advantage over other assimilation methods that it supplies explicit dynamical error estimates.     

基于采样的非线性滤波算法比较

在处理目标跟踪等动态系统实时估计问题中,通常采用EKF作为状态估计方法提高估计精度。由于EKF进行非线性估计存在一些缺陷,将系统进行线性化近似存在估计误差,从而影响目标跟踪的精度。为了获得更高的估计精度,介绍了几种非线性滤波算法,包括unscented卡尔曼滤波算法、简单粒子滤波算法以及无味粒子滤波算法（UPF）。分析了这几种算法的原理和实现,对各种算法的适应性进行了比较。通过目标跟踪仿真实验,表明UKF、PF较EKF估计精度和收敛速度有所提高。     

Bayesian statistical data assimilation for ecosystem models using Markov Chain Monte Carlo

This study considers advanced statistical approaches for sequential data assimilation. These are explored in the context of nowcasting and forecasting using nonlinear differential equation based marine ecosystem models assimilating sparse and noisy non-Gaussian multivariate observations. The statistical framework uses a state space model with the goal of estimating the time evolving probability distribution of the ecosystem state. Assimilation of observations relies on stochastic dynamic prediction and Bayesian principles. In this study, a new sequential data assimilation approach is introduced based on Markov Chain Monte Carlo (MCMC). The ecosystem state is represented by an ensemble, or sample, from which distributional properties, or summary statistical measures, can be derived. The Metropolis-Hastings based MCMC approach is compared and contrasted with two other sequential data assimilation approaches: sequential importance resampling, and the (approximate) ensemble Kalman filter (including computational comparisons). A simple illustrative application is provided based on a 0-D nonlinear plankton ecosystem model with multivariate non-Gaussian observations of the ecosystem state from a coastal ocean observatory. The MCMC approach is shown to be straightforward to implement and to effectively characterize the non-Gaussian ecosystem state in both nowcast and forecast experiments. Results are reported which illustrate how non-Gaussian information originates, and how it can be used to characterize ecosystem properties.     

扩张状态观测器在惯导系统初始对准中的应用研究

根据平台式惯导系统初始对准的误差模型,首先介绍了初始对准的卡尔曼滤波方法,而后研究了把扩张状态观测器与卡尔曼滤波器相结合用于惯导系统的初始对准方法,最后对系统在受干扰和未受干扰2种情况下,分别进行了仿真研究.仿真结果表明,该方法与卡尔曼滤波方法相比,在保证对准精度的条件下,系统姿态角对准时间大大缩短;在系统受到干扰时,该方法仍具有很强的适应性和稳定性.     

Gaussian anamorphosis extension of the DEnKF for combined state parameter estimation: Application to a 1D ocean ecosystem model

We consider the problem of combined state-parameter estimations in biased nonlinear models with non-Gaussian extensions of the Deterministic Ensemble Kalman Filter (DEnKF). We focus on the particular framework of ocean ecosystem models. Such models present important obstacles to the use of data assimilation methods based on Kalman filtering due to the non-linearity of the models, the constraints of positiveness that apply to the variables and parameters, and the non-Gaussian distribution of the variables in which they result.We present extensions of the DEnKF dealing with these difficulties by introducing a nonlinear change of variables (anamorphosis function) in order to execute the analysis step with Gaussian transformed variables and parameters. Several strategies to build the anamorphosis functions are investigated and compared within the framework of twin experiments realized in a simple 1D ocean ecosystem model. A solution to the problem of the specification of the observation error for transformed observations is suggested. The study highlights the inability of the plain DEnKF with a simple post-processing of the negative values to properly estimate parameters when constraints of positiveness apply to the variables. It goes on to show that the introduction of the Gaussian anamorphosis can remedy these assimilation biases.     

基于模型预测扩展卡尔曼滤波的动力定位状态估计

针对传统扩展卡尔曼滤波由于动力定位系统过程噪声不能自适应更新,导致滤波精度下降的问题,提出了一种模型预测扩展卡尔曼滤波算法。该算法通过比较一段时间内的量测值和预测值,估计系统噪声参数,从而实时修正系统过程噪声方差。仿真结果表明,当系统的过程噪声未知的情况下,模型预测扩展卡尔曼滤波的滤波性能明显优于传统扩展卡尔曼滤波。     

改进UKF算法在双基阵纯方位目标跟踪中的应用

传统算法在解决纯方位目标跟踪时存在有偏、收敛速度慢或发散等不足,无迹卡尔曼滤波（UKF）虽然改善了系统线性化误差,但并没有明显改善卡尔曼滤波器容易发散的问题。文章在扩展卡尔曼滤波和UKF算法的基础上,提出一种衰减记忆UKF算法（MAUKF）,引进衰减因子加强对当前测量数据的利用,减小历史数据对滤波的影响。理论分析和仿真结果表明,MAUKF算法在纯方位目标跟踪中的滤波精度、稳定性和收敛时间都优于EKF、UKF算法。     

基于一种改进粒子滤波算法的目标跟踪研究

为了解决非线性、非高斯系统目标跟踪问题,研究了一种新的滤波方法——高斯粒子滤波算法。通过基于重要性采样和蒙特卡罗模拟方法得到一高斯分布来近似未知状态变量的后验分布。并讨论了此算法在机动目标非线性转弯运动中的跟踪应用,与粒子滤波算法相比,其优点是不需要重采样步骤。在闪烁噪声下比较了高斯粒子滤波器、粒子滤波器和扩展卡尔曼滤波器在滤波精度、运算时间等方面的差异,仿真结果表明该算法性能优于其他算法。     

基于Unscented卡尔曼滤波器的地磁辅助组合导航

将船位推算与地磁测量相结合构成组合导航方法.首先建立了推算模型,然后利用Unscented卡尔曼滤波方法,直接将地磁测量的结果用于校正推算结果,进行导航定位.此方法不采用匹配方法进行定位,可进行实时定位,能适用于非线性和离散的地磁模型.仿真表明,此方法能减小定位误差,适用于基于船位推算和地磁定位的实时组合导航.     

微机械陀螺随机误差补偿研究

为了提高微机械陀螺使用精度,研究了随机漂移误差补偿方法。对静态陀螺输出数据进行预处理,提取出随机漂移数据,采用时序分析方法对其建立AR模型。基于模型设计Kalman滤波器,进行静态和动态仿真。结果表明：静态条件下滤波效果显著;动态条件下,滤波效果变差。针对此问题设计了标量因子时变的自适应Kalman滤波器,试验表明,此算法能够有效降低微机械陀螺的随机漂移。     

伪距GPS/INS组合导航系统的多模型自适应卡尔曼滤波器设计

对多模型自适应估计滤波进行了仿真研究.仿真结果表明,多模型自适应估计滤波可以克服单一模型卡尔曼滤波器在对真实系统状态参数发生变化时的滤波误差过大甚至发散的问题,对于环境的变化具有较强的适应性,整体上可提高组合导航系统的导航精度.     

重力图匹配导航方法研究

提出一种利用重力异常信息校正惯导系统的方法按照一定方法将重力实测数据和数字重力图进行相关分析和匹配以得到最优路径,再用位置误差对惯性器件误差进行扩展Kalman滤波估计,最后对惯导系统的导航状态进行修正,得到最优导航状态。     

船舶MEMS微惯导网络精度技术研究

为了减少误差积累,提高导航精度,通过船舶上的CAN总线网络,利用高精度主惯导系统对低精度的MEMS微惯导系统进行在线修正。根据微惯导网络系统姿态角的误差模型,将惯导系统的角速率输出值作为量测信息设计卡尔曼滤波器,对姿态角修正算法进行了仿真运算,估计出了MEMS微惯导系统姿态角误差。     

Validation of a hybrid optimal interpolation and Kalman filter scheme for sea surface temperature assimilation

A hybrid data assimilation scheme designed for operational assimilation of satellite sea surface temperatures (SST) into an ocean model has been developed and validated against in-situ observations. The scheme consists of an optimal interpolation (OI) part and a greatly simplified Kalman filter (KF) part.The OI is performed only in the longitudinal and latitudinal directions. A climatological field is used as a background field for the interpolation. It is constructed by fitting daily averages of satellite SST to the annual mean, annual, and semiannual harmonics in a 20 km by 20 km grid. The background error covariance is approximated by a spatially varying two-dimensional exponential covariance model. The parameters of the covariance model are fitted to the deviations of the satellite data from the background field using data from a full year.The simplified KF uses ocean model forecasts as a background field. It is based on the assumption that it is possible to neglect horizontal SST covariances in the filter and that the typical time scale for vertical mixing in the mixed layer is much shorter than the average time between observations. We therefore assume that the error variance in a column of water is evenly spread out throughout the mixed layer. The result of these simplifications is a computationally very efficient KF.A one year validation of the scheme is performed for year 2001 using an operational eddy resolving ocean model covering the North Sea and the Baltic Sea. It is found that assimilation of sea surface temperature data reduces the model root mean square error from 1.13 °C to 0.70 °C. The hybrid scheme is found to reduce the root mean square error slightly more than the simplified KF without OI to 0.66 °C. The inclusion of spatially varying satellite error variances does not improve the performance of the scheme significantly.     

基于渐消记忆自适应滤波的船舶动力定位算法仿真

由于船舶在海上运动的复杂性和非线性,精确的船舶动力定位系统数学模型难以建立.为了实现有效的动力定位控制,需要应用一定的状态估计滤波算法得到所需的船舶运动低频信号.采用常规的Kalman滤波,状态变量的新测量值对预测值的修正作用下降,旧测量值的影响随着计算步数的累积而相对提高,这是引起滤波发散的主要原因之一.文章针对船舶动力定位系统中使用常规的Kalman滤波而存在的模型不精确、 不能准确表达系统噪声和测量噪声等问题,采用渐消记忆自适应滤波估算低频运动信息,在状态估计算法中引入渐消记忆因子,减小旧测量值对状态估计值的影响权重,从而增大新测量值的作用;并根据滤波发散判断准则,选择适当的渐消记忆因子值来抑制滤波器的发散,使控制器输出较为平稳,从而降低推力系统不必要的能耗.仿真实验表明,所设计的自适应滤波器的收敛性、跟踪性优于常规的Kalman滤波,有效地提高了系统的定位精度和稳定性.