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 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 YearEstimated PopulationChange 20008,038,200- 20018,243,7192.56% 20028,499,9003.11% 20038,775,2003.23% 20048,851,4550.87% 20059,002,5341.71% 20069,193,8002.12% 20079,665,8415.13% 200810,450,0008.11% 200910,531,3000.77%

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

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

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

9. Modelling the time series Unstable parameter Mean Amplitude Phase

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

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

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

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

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

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 1142 MODIS pixels = 285.5km 2 Mean Amplitude Absolute Error

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

22. Results: Standard deviation for MODIS bands 1142 MODIS pixels = 285.5km 2

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

24. Results: Accuracy for MODIS bands 1142 MODIS pixels = 285.5km 2

25. Results: Gauteng province settlements 78704 MODIS pixels = 19676km 2 23.16% Settlement

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? Expansion of irrigation Commercial forestry MiningInformal settlements Alien tree removal