状态估计的新框架？！

50 年代末到60 年代初, 航天技术的发展涉及到大量的多输入多输出系统的最优控制问题, 用经典

1. 经典状态空间法：

State Space Model 状态空间模型包括两个模型：

• Approximate Gaussian Conjugacy: Parametric Recursive Filtering under Nonlinearity, Multimodality, Uncertainty, and Constraint, and Beyond, Frontiers of Information Technology & Electronic Engineering, 2017, 18(12):1913-1939,   ＬＩＮＫ

Ho, Y., Lee, R., 1964. A Bayesian approach to problems in stochastic estimation and control. IEEE Trans. Autom. Contr., 9(4):333-339.

2. 抛弃HMM： 对于传感器数据越来越多，传感器精度越来越高的情况，是否可以有新的解决方案（HMM弃之不用）呐？见 ： 如果我有成百上千个传感器，是否还需要动态模型？  以及  轻松多传感器多目标探测与跟踪！这类方案主要应对完全未知系统背景，但数据量很大的情况

Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.

--  Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces, p. 74

3.  数据驱动的新框架：

• Joint Smoothing, Tracking, and Forecasting Based on Continuous-Time Target Trajectory Fitting, IEEE Trans. Automation Science and Engineering, Oct. 2018. DOI:10.1109/TASE.2018.2882641. @ IEEE Xplore Pre-print @ arXiv:1708.02196 [stat.AP]

Joint Smoothing and Tracking Based on Continuous-Time Target Trajectory Function Fitting

Abstract:

This paper presents a joint trajectory smoothing and tracking framework for a specific class of targets with smooth motion. We model the target trajectory by a continuous function of time (FoT), which leads to a curve fitting approach that finds a trajectory FoT fitting the sensor data in a sliding time-window. A simulation study is conducted to demonstrate the effectiveness of our approach in tracking a maneuvering target, in comparison with the conventional filters and smoothers.

xk = f(t) ,

F(t;Ck )f(t),

1. 对于线性观测系统，那么只需要线性拟合，并一般定义量测误差为范数2的马氏距离，曲线拟合退化为加权最小二乘直接给出，计算效率胜过线性卡尔曼滤波。

2. 对于非线性观测系统进行线性拟合如多项式拟合，拟合需要往往需要迭代近似。对于非线性观测系统下的曲线拟合计算效率至关重要的是 参数的初始化，

Ck =Ck-1 + ρk

4.  约束下的SSM和轨迹曲线拟合：

Abstract:

We consider the single-road-constrained estimation problem for positioning a target that moves on a single, deterministic and exactly known trajectory. Based on the geometry of the trajectory curve, we cast the constrained estimation problem as an unconstrained problem with reduced state dimension. Two approaches are devised based on a Markov transition model for unscented Kalman filtering and a continuous function of time for (weighted) least square fitting, respectively. A popular simulation model has been used for demonstrating the performance of the proposed approaches in comparison to existing approaches.

https://blog.sciencenet.cn/blog-388372-1151526.html

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