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B.P. Salmon 1,2* , W. Kleynhans 1,2 , F. van den Bergh 2 , J.C. Olivier 1 ,

Meta-optimization of the Extended Kalman filter’s parameters for improved feature extraction on hyper-temporal images. B.P. Salmon 1,2* , W. Kleynhans 1,2 , F. van den Bergh 2 , J.C. Olivier 1 , W.J. Marais 3 and K.J. Wessels 2

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B.P. Salmon 1,2* , W. Kleynhans 1,2 , F. van den Bergh 2 , J.C. Olivier 1 ,

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  1. Meta-optimization of the Extended Kalman filter’s parameters for improved feature extraction on hyper-temporal images. B.P. Salmon1,2* , W. Kleynhans1,2, F. van den Bergh2, J.C. Olivier1, W.J. Marais3 and K.J. Wessels2 1. Department of Electrical Engineering, University of Pretoria, South Africa 2. Remote Sensing Research Unit, Meraka, CSIR, South Africa 3. Space Science and Engineering Center, University of Wisconsin-Madison, Wisconsin, USA * Presenting author

  2. Overview • Problem statement – Reliable surveying of land cover and transformation • Discuss the importance of time series analysis • Study area: Gauteng province, South Africa • Using the EKF as feature extractor from time series data • Meta-optimization of EKF’s parameters • Results: Land cover classification • Conclusions

  3. Problem Statement Reliable surveying of land cover and transformation

  4. Band 2 Separation Band 1 Separation Band 2 Separation Band 1 Separation Band 2 Vegetation Band 1 Vegetation Band 2 Settlement Band 1 Settlement Time Series Analysis MODIS Band 2 MODIS Band 1

  5. Objective Time series can be modulated with a triply modulated cosine function [1]. [1] W. Kleynhans et. al, 'Improving land cover class separation using an extended Kalman filter on MODIS NDVI time-series data', IEEE Geoscience and Remote Sensing Letters, vol. 6, no. 4. April 2010

  6. Objective Parameters of a triply modulated cosine can be used to distinguish between several different land cover classes. Parameters derived using a EKF framework has been proven as a feasible solution. Introduce a meta-optimization approach for setting the parameters of a Extended Kalman filter to rapidly estimate better features for a triply modulated cosine function.

  7. Triply modulated time series • Time series modelled as a triply modulated cosine function • Where • = Mean • = Amplitude • = Angular frequency • = Spectral band • = Time index • = Seasonal cycle (8/365) • = Phase • = Noise • = Pixel index

  8. Extended Kalman Filter Framework Mean Phase Amplitude • State vector • Process model • Observation model

  9. Modelling the time series Unstable parameter Mean Unstable parameter Unstable parameter Amplitude Phase

  10. Tuneable parameters • Process model • Observation model Initial estimates of state vector Process covariance matrix Observation noise covariance matrix

  11. Tuneable parameters Initial estimates of state vector Process covariance matrix Observation noise covariance matrix Tunable parameters Where j denotes the epoch number

  12. What do we want? Tunable parameters Absolute Error Mean Amplitude Phase

  13. Creating extreme conditions Tunable parameters Absolute Error Set Capture a probability density function (PDF) for each time increment k using all the pixels and if ideal will be denoted by

  14. Creating extreme conditions Tunable parameters Mean Set Capture a probability density function (PDF) for each time Increment k using all the pixels and if ideal will be denoted by

  15. Creating extreme conditions Tunable parameters Amplitude Set Capture a probability density function (PDF) for each time Increment k using all the pixels and if ideal will be denoted by

  16. Creating extreme conditions Tunable parameters Phase Set Capture a probability density function (PDF) for each time Increment k using all the pixels and if ideal will be denoted by

  17. Creating a metric • Set an initial (candidate) state as • Calculated the f-divergent distance as • Absolute error • Mean • Amplitude • Phase

  18. Define a comparison metric • Create a vector containing all the f-divergent distances as • Define a metric for an unbiased Extended Kalman filter • Optimize the vector using comparison metric

  19. Iterative updates

  20. Results: Standard deviation for MODIS spectral band 1 Mean Amplitude Absolute Error 1142 MODIS pixels = 285.5km2

  21. Results: Standard deviation for MODIS spectral band 2 Mean Amplitude Absolute Error 1142 MODIS pixels = 285.5km2

  22. Results: Standard deviation for MODIS bands 1142 MODIS pixels = 285.5km2

  23. Results: Classification on labelled data K-means (Band 1, Band 2) Vegetation Accuracy Settlement accuracy 1142 MODIS pixels = 285.5km2

  24. Results: Accuracy for MODIS bands 1142 MODIS pixels = 285.5km2

  25. Results: Gauteng province settlements 23.16% Settlement 78704 MODIS pixels = 19676km2

  26. Conclusions • Temporal property is of high importance in remote sensing • A meta-optimization for the EKF using a spatio-temporal window was proposed. • Proper feature analysis can greatly enhance analysis of data. • Presentation of features to any machine learning algorithm

  27. Questions? Mining Informal settlements Expansion of irrigation Commercial forestry Alien tree removal

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