Estimation Error Bound of Battery Electrode Parameters With Limited Data Window

The accuracy of radio-based positioning systems will be limited by multipath interference in realistic application scenarios. This paper derives closed-form expressions for the Cramér–Rao lower bound (CRLB) on the achievable time-of-arrival (ToA) and angle-of-arrival (AoA) estimation-error variances, considering the presence of multipath radio channels, and extends these results to position estimation. The derivations are based on channel models comprising deterministic, specular multipath components as well as stochastic, diffuse/dense multipath. The derived CRLBs thus allow an evaluation of the influence of channel parameters, the geometric configuration of the environment, and system parameters such as signal bandwidth and array geometry. Our results quantify how the ToA and AoA accuracies decrease when the signal bandwidth is reduced, because more multipath will then interfere with the useful LoS component. Antenna arrays can (partly) compensate this performance loss, exploiting diversity among the multipath interference. For example, the AoA accuracy with a 16-element linear array at 1 MHz bandwidth is similar to a two-element array at 1 GHz , in the magnitude order of one degree. The ToA accuracy, on the other hand, still scales by a factor of 100 from the cm-regime to the m-regime because of the dominating influence of the signal bandwidth. The position error bound shows the relationship between the range and angle information under realistic indoor channel conditions and their different scaling behaviors as a function of the anchor–agent placement. Specular multipath components have a maximum detrimental influence near the walls. It is shown for an L-shaped room that a fairly even distribution of the position error bound can be achieved throughout the environment, using two anchors equipped with 2 × 2 -array antennas. The accuracy limit due to multipath increases from the 1–10-cm-range at 1 GHz bandwidth to the 0.5–1-m-range at 100 MHz .

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Information Geometrical Characterization of Quantum Statistical Models in Quantum Estimation Theory

Entropy ◽

10.3390/e21070703 ◽

2019 ◽

Vol 21 (7) ◽

pp. 703 ◽

Cited By ~ 14

Author(s):

Jun Suzuki

Keyword(s):

Statistical Model ◽

Error Bound ◽

Statistical Models ◽

Estimation Error ◽

Estimation Theory ◽

Geometrical Characterization ◽

Classical Models ◽

Quantum Statistical ◽

Equivalent Conditions

In this paper, we classify quantum statistical models based on their information geometric properties and the estimation error bound, known as the Holevo bound, into four different classes: classical, quasi-classical, D-invariant, and asymptotically classical models. We then characterize each model by several equivalent conditions and discuss their properties. This result enables us to explore the relationships among these four models as well as reveals the geometrical understanding of quantum statistical models. In particular, we show that each class of model can be identified by comparing quantum Fisher metrics and the properties of the tangent spaces of the quantum statistical model.

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Bridging the Gap between Few-Shot and Many-Shot Learning via Distribution Calibration

10.36227/techrxiv.14380697 ◽

2021 ◽

Author(s):

Shuo Yang ◽

Songhua Wu ◽

Tongliang Liu ◽

Min Xu

Keyword(s):

Error Bound ◽

Estimation Error ◽

Data Distribution ◽

Approximation Error ◽

Ground Truth ◽

Generalization Error ◽

Learning To Learn ◽

Ground Truth Data ◽

Generalization Error Bound ◽

Training Examples

A major gap between few-shot and many-shot learning is the data distribution empirically observed by the model during training. In few-shot learning, the learned model can easily become over-fitted based on the biased distribution formed by only a few training examples, while the ground-truth data distribution is more accurately uncovered in many-shot learning to learn a well-generalized model. In this paper, we propose to calibrate the distribution of these few-sample classes to be more unbiased to alleviate such an over-fitting problem. The distribution calibration is achieved by transferring statistics from the classes with sufficient examples to those few-sample classes. After calibration, an adequate number of examples can be sampled from the calibrated distribution to expand the inputs to the classifier. Extensive experiments on three datasets, miniImageNet, tieredImageNet, and CUB, show that a simple linear classifier trained using the features sampled from our calibrated distribution can outperform the state-of-the-art accuracy by a large margin. We also establish a generalization error bound for the proposed distribution-calibration-based few-shot learning, which consists of the distribution assumption error, the distribution approximation error, and the estimation error. This generalization error bound theoretically justifies the effectiveness of the proposed method.

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Minimization of the estimation error of the Kalman filter with an H/sub ∞/ error bound by Secant method

Proceedings of 1995 34th IEEE Conference on Decision and Control ◽

10.1109/cdc.1995.480356 ◽

2002 ◽

Author(s):

Bing-Fei Wu ◽

Hung-Hseng Hsu

Keyword(s):

Kalman Filter ◽

Error Bound ◽

Estimation Error ◽

Secant Method

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Multi-Target Joint Detection and Estimation Error Bound for the Sensor with Clutter and Missed Detection

Sensors ◽

10.3390/s16020169 ◽

2016 ◽

Vol 16 (2) ◽

pp. 169 ◽

Cited By ~ 1

Author(s):

Feng Lian ◽

Guang-Hua Zhang ◽

Zhan-Sheng Duan ◽

Chong-Zhao Han

Keyword(s):

Error Bound ◽

Estimation Error ◽

Joint Detection ◽

Detection And Estimation

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Learning from Imprecise Observations: An Estimation Error Bound based on Fuzzy Random Variables

2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) ◽

10.1109/fuzz45933.2021.9494497 ◽

2021 ◽

Author(s):

Guangzhi Ma ◽

Feng Liu ◽

Guangquan Zhang ◽

Jie Lu

Keyword(s):

Error Bound ◽

Estimation Error ◽

Random Variables ◽

Fuzzy Random Variables ◽

Imprecise Observations ◽

Fuzzy Random

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Bridging the Gap between Few-Shot and Many-Shot Learning via Distribution Calibration

10.36227/techrxiv.14380697.v1 ◽

2021 ◽

Author(s):

Shuo Yang ◽

Songhua Wu ◽

Tongliang Liu ◽

Min Xu

Keyword(s):

Error Bound ◽

Estimation Error ◽

Data Distribution ◽

Approximation Error ◽

Ground Truth ◽

Generalization Error ◽

Learning To Learn ◽

Ground Truth Data ◽

Generalization Error Bound ◽

Training Examples

A major gap between few-shot and many-shot learning is the data distribution empirically observed by the model during training. In few-shot learning, the learned model can easily become over-fitted based on the biased distribution formed by only a few training examples, while the ground-truth data distribution is more accurately uncovered in many-shot learning to learn a well-generalized model. In this paper, we propose to calibrate the distribution of these few-sample classes to be more unbiased to alleviate such an over-fitting problem. The distribution calibration is achieved by transferring statistics from the classes with sufficient examples to those few-sample classes. After calibration, an adequate number of examples can be sampled from the calibrated distribution to expand the inputs to the classifier. Extensive experiments on three datasets, miniImageNet, tieredImageNet, and CUB, show that a simple linear classifier trained using the features sampled from our calibrated distribution can outperform the state-of-the-art accuracy by a large margin. We also establish a generalization error bound for the proposed distribution-calibration-based few-shot learning, which consists of the distribution assumption error, the distribution approximation error, and the estimation error. This generalization error bound theoretically justifies the effectiveness of the proposed method.

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