Shida Jiang

Shida Jiang, Junzhe Shi, Scott Moura

The Kalman filter (KF) is an optimal linear state estimator for linear systems, and numerous extensions, including the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF), have been developed for nonlinear systems. Although these nonlinear KFs differ in how they approximate nonlinear transformations, they all retain the same update framework as the linear KF. In this paper, we show that, under nonlinear measurements, this conventional framework inherently tends to underestimate the true posterior covariance, leading to overconfident covariance estimates. To the best of our knowledge, this is the first work to provide a mathematical proof of this systematic covariance underestimation in a general nonlinear KF framework. Motivated by this analysis, we propose a covariance-recalibrated framework that re-approximates the measurement model after the state update to better capture the actual effect of the Kalman gain on the posterior covariance; when recalibration indicates that an update is harmful, the update can be withdrawn. The proposed framework can be combined with essentially any existing nonlinear KF, and simulations across four nonlinear KFs and five applications show that it substantially improves both state and covariance estimation accuracy, often reducing errors by several orders of magnitude. The code and supplementary material are available at https://github.com/Shida-Jiang/A-new-framework-for-nonlinear-Kalman-filters.

Shida Jiang, Shengyu Tao, Zihe Liu et al.

The ensemble Kalman filter (EnKF) is widely used for nonlinear and high-dimensional state estimation because it replaces complex covariance propagation with simple ensemble statistics. However, conventional EnKF implementations can become overconfident in the presence of measurement nonlinearity. The commonly used covariance inflation technique only partially alleviates this issue. This paper proposes a covariance-adaptive and recalibrated ensemble Kalman filter (CAR-EnKF) framework for nonlinear state estimation. The framework introduces two improvements that are only active for nonlinear measurements and reduce to the conventional EnKF framework without covariance inflation in the linear case: (i) a recalibration mechanism that reassesses the effect of the chosen Kalman gain after updating the ensemble mean, and (ii) a positive semidefinite covariance compensation term that accounts for measurement nonlinearity. An adaptive update law based on the normalized innovation squared further tunes the compensation magnitude online. The framework is algorithmically general and is specialized here to the stochastic EnKF and the ensemble transform Kalman filter (ETKF). Experiments on feature-based SLAM and the Lorenz--96 system show that CAR-EnKF consistently reduces RMSE relative to conventional EnKF baselines, with especially large improvements at low measurement-noise levels. The related codes are available at \href{https://github.com/Shida-Jiang/CAR-EnKF-A-Covariance-Adaptive-and-Recalibrated-Ensemble-Kalman-Filter-Framework}

Shida Jiang, Jaewoong Lee, Shengyu Tao et al.

Nonlinear extensions of the Kalman filter (KF), such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are indispensable for state estimation in complex dynamical systems, yet the conditions for a nonlinear KF to provide robust and accurate estimations remain poorly understood. This work proposes a theoretical framework that identifies the causes of failure and success in certain nonlinear KFs and establishes guidelines for their improvement. Central to our framework is the concept of covariance compensation: the deviation between the covariance predicted by a nonlinear KF and that of the EKF. With this definition and detailed theoretical analysis, we derive three design guidelines for nonlinear KFs: (i) invariance under orthogonal transformations, (ii) sufficient covariance compensation beyond the EKF baseline, and (iii) selection of compensation magnitude that favors underconfidence. Both theoretical analysis and empirical validation confirm that adherence to these principles significantly improves estimation accuracy, whereas fixed parameter choices commonly adopted in the literature are often suboptimal. The codes and the proofs for all the theorems in this paper are available at https://github.com/Shida-Jiang/Guidelines-for-Nonlinear-Kalman-Filters.

Shida Jiang, Shengyu Tao, Vincent Molina et al.

A conventional electric vehicle (EV) powertrain relies on a centralized high-voltage DC-AC inverter, thereby limiting cell-level control and potentially reducing overall driving range and battery lifetime. This paper studies an H-bridge-based cell-level inverter topology that performs power conversion at the cell level, enabling independent control of individual cells and expanding the design space for battery management. Leveraging these additional degrees of freedom, we propose a model-agnostic energy-throughput control strategy that extends EV range while improving battery-pack lifetime. Because usable energy (and thus driving range) and lifetime are governed by the cells with the lowest state-of-charge (SOC) and state-of-health (SOH), respectively, the proposed controller preferentially routes energy throughput to healthier cells. Specifically, during charging, it permits cell SOCs to diverge to promote SOH equalization; during discharging, it rebalances SOC to maximize usable capacity under per-cell constraints. The proposed SOC-SOH-aware control strategy is evaluated on two aging models representing lithium manganese oxide and lithium iron phosphate chemistries, using a Tesla Model 3 charge-discharge profile across 14 different parameter settings. Simulations show a 7-38% improvement in lifetime relative to a conventional SOC-only balancing baseline. More broadly, the results suggest a software-defined pathway to extend EV pack life through routine charging, with minimal reliance on specific degradation models or discharge profiles.