Kalman time series prediction

RTSNET: DEEP LEARNING AIDED KALMAN SMOOTHING Xiaobai reading notes - You know

Kalman Filter encounter Deep Learning : Kalman filter and deep learning related papers _Phoenixtree_DongZhao The blog of -CSDN Blog _ Kalman filtering Deep learning

 

Understanding of the relationship between Kalman filtering and Kalman smoothing _foreseerwang The blog of -CSDN Blog _ Kalman smoothing filter // Must see , The comment area is also very exciting

 

  Kalman smoothing has a graph 、 Formula derivation _GHelpU The blog of -CSDN Blog _ Kalman smoothing // Theoretical formula derivation has , Very important

For several previous blog posts related to Kalman filtering , The algorithms described are The state of the system at the current time is estimated based on the past and current sensor observations , This is the filtering algorithm . In some application scenarios , Users The real-time requirement for system state estimation is low , They prefer to obtain more accurate system state estimation results , At this time, all sensor observations obtained over a long period of time can be used to estimate the system state at each time during the period , This is the smoothing algorithm .

Kalman smoothing algorithm is one of the commonly used methods , Also known as RTS smooth ——Rauch–Tung–Striebel smoother （RTSS, Rauch et al., 1965）, This blog post will introduce the algorithm in detail .
 

 

Kalman smoothing algorithm is actually an enhanced version of Kalman filtering algorithm , It includes Forward recurrence and backward recursion Two steps , The forward recursive process is consistent with the Kalman filter algorithm , Backward recurrence can further reduce the fluctuation of the estimation results . The derivation of the algorithm mainly depends on lemma 1 And lemmas 2 The repeated use of , Bayesian probability theory is used to realize a posteriori estimation of system state , With the Bowen Kalman filter series —— The derivation process of standard Kalman filter is somewhat different , But the result is uniform .

According to the experimental results , For the same observations , The processing results of the two algorithms with the same parameters are different , among Kalman smoothing algorithm is not as real-time as Kalman filtering algorithm , But the estimated signal waveform is smoother . And if you look carefully, you can see , The Kalman filtering algorithm has a small phase lag relative to the true value of the signal , The estimation result of Kalman smoothing algorithm keeps good phase consistency , This has important value in practical application . By calculating the mean square error between the processing results of the two algorithms and the true value of the signal , For example, in the above experiment , Kalman filter algorithm MSE by 0.0078, The Kalman smoothing algorithm MSE false 0.0025, so , The smoothing algorithm has higher estimation accuracy , better .

in application , If the signal length is large , The signal can be divided into several overlapping periods according to time , Then the smoothing algorithm is used for each segment , This can get better results , At the same time, it also reduces the measurement time of the sensor to a certain extent , Reduce algorithm processing time , Improve real-time .

 

Reference material

Feature Engineering ： Processing time series with Kalman filter （ Quick start +python Realization ）_ WeChat official account [ Machine learning alchemy ] The blog of -CSDN Blog _ Kalman filtering Time series smoothing

Use Kalman filter to smooth time series , Improve the accuracy of time series prediction _deephub The blog of -CSDN Blog _ Kalman filter time series prediction

Time series prediction | Python Realize Kalman filter model time series prediction _ Data analysis and algorithm practice blog -CSDN Blog _ Kalman filter time series prediction

GitHub - cerlymarco/tsmoothie: A python library for time-series smoothing and outlier detection in a vectorized way.

Python pykalman package _ Program modules - PyPI - Python Chinese net