Method and system for multiple dataset gaussian process modeling

• US 8,825,456 B2
• Filed: 09/15/2010
• Issued: 09/02/2014
• Est. Priority Date: 09/15/2009
• Status: Expired due to Fees

• Current Assignee: Sydney The University of Business Liaison Office
• Original Assignee: University of Sydney
• Inventors: Vasudevan, Shrihari, Ramos, Fabio Tozeto, Nettleton, Eric, Durrant-Whyte, Hugh
• Primary Examiner(s): Thangavelu, Kandasamy
• Application Number:
  US13/496,480
• Publication Number:
  US 20120179635A1
• Time in Patent Office: 1,448 Days
• Field of Search: 703/2, 704/250, 706/12, 706/20, 706/21, 367/43, 707/748, 381/94.1, 702/81, 382/154, 382/224
• US Class Current: 703/2
• CPC Class Codes: G01S 17/89 for mapping or imaging
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: G06T 2207/10028 Range image; Depth image; 3D point clouds
• CPC Class Codes: G06T 7/521 from laser ranging, e.g. using interferometry; from the projection of structured light

Abstract

A method of computerized data analysis and synthesis is described. First and second datasets of a quantity of interest are stored. A Gaussian process model is generated using the first and second datasets to compute optimized kernel and noise hyperparameters. The Gaussian process model is applied using the stored first and second datasets and hyperparameters to perform Gaussian process regression to compute estimates of unknown values of the quantity of interest. The resulting computed estimates of the quantity of interest result from a non-parametric Gaussian process fusion of the first and second measurement datasets. The first and second datasets may be derived from the same or different measurement sensors. Different sensors may have different noise and/or other characteristics.

Claims

1. A method of computerised data analysis and synthesis comprising:

receiving first and second datasets relating to a quantity of interest within a domain, each dataset comprising a plurality of datapoints;

storing, in a data storage, the first and second datasets;

generating, using a training processor, a Gaussian process model by using the first and second datasets to compute optimized kernel and noise hyperparameters;

storing, in the data storage, the optimized kernel and noise hyperparameters; and

using an evaluation processor, applying the Gaussian process model by using the stored first and second datasets and hyperparameters to perform Gaussian process regression to compute estimates of unknown values of the quantity of interest within the domain;

wherein generating the Gaussian process model includes, in the training processor;

using the first dataset to learn optimized kernel hyperparameters and a first noise hyperparameter, and

using the learnt kernel hyperparameters and second dataset to learn an optimized second noise hyperparameter; and

wherein Gaussian process regression is performed using the first and second datasets, first and second noise hyperparameters and kernel hyperparameters.

2. The method of claim 1 wherein the first and second datasets are formed using different measurement sensors.

3. The method of claim 1 wherein the first and second datasets are formed using the same measurement sensor at different times or locations.

4. The method of claim 1 wherein the quantity of interest is geographical elevation.

5. The method of claim 4 wherein the domain is a mining region.

6. The method of claim 1 wherein the quantity of interest is a geological characteristic within a body of earth.

7. The method of claim 1 including a plurality of datasets wherein a separate noise hyperparameter is computed for each using the same optimized kernel hyperparameters.

8. The method of claim 1 wherein the first and second datasets are stored in a kd-tree data structure.

9. The method of claim 1 wherein generating a Gaussian process mode includes using the first dataset to learn first kernel and noise hyperparameters, using the second dataset to learn second kernel and noise hyperparameters, and using the first and second kernel and noise hyperparameters to compute both auto-covariances and cross-covariances;

and

wherein Gaussian process regression is performed using the first and second datasets, first and second kernel and noise hyperparameters and computed auto-covariances and cross-covariances.

10. The method of claim 9 wherein different Gaussian process kernels are used with respect to the first and second datasets.

11. The method of claim 9 wherein the same Gaussian process kernel is used with respect to the first and second datasets.

12. The method of claim 9, wherein the first and second datasets describe different quantities and the quantity of interest is the quantity described by the first dataset and wherein computation of the auto-covariance and cross-covariance includes computing a measure of task similarity with the computation of the hyperparameters.

13. The method of claim 9, wherein the first and second datasets describe the same quantity of interest and computation of the auto-covariance and cross-covariance includes computing a measure of dataset similarity with the computation of the hyperparameters.

14. The method of claim 1, wherein the first dataset comprises color data.

15. The method of claim 14, wherein the second dataset comprises data other than color data.

16. A system for analysing and synthesising data to estimate a quantity of interest, comprising:

a training processor adapted to

obtain and store first and second datasets, each comprising a plurality of datapoints, representing separate sets of measurements or indicators of the quantity of interest within a domain,

generate a Gaussian process model by using,

the first dataset to learn optimized kernel hyperparameters and a first noise hyperparameter, and the

learnt kernel hyperparameters and the second dataset to learn a second noise hyperparameter;

data storage in communication with the training processor, wherein the training processor is adapted to store in the data storage the first and second datasets and computed hyperparameters, and

an evaluation processor in communication with the data storage, the evaluation processor adapted to apply the Gaussian process model by performing Gaussian process regression using both the first and second datasets, respective first and second noise hyperparameters, and kernel hyperparameters to compute estimates of unknown values of the quantity of interest within the domain.

17. The system of claim 16 including at least one sensor for generating sets of measurements comprising the datapoints of the first and second datasets.

18. The system of claim 17 wherein the first and second datasets are derived from the same sensor.

19. The system of claim 16 including a plurality of sensors for generating sets of measurements, wherein the first and second datasets are derived from different sensors.

20. The system of claim 16, wherein the quantity of interest is geographical elevation.

21. The system of claim 20 wherein the domain is a mine pit.

22. The system of claim 16 wherein the quantity of interest is a geological characteristic within a body of earth.

23. The system of claim 16 wherein the data storage includes a kd-tree data structure for storage and access to the first and second datasets.

24. The system of claim 16:

wherein the training processor is adapted;

to use the first dataset to compute first kernel and noise hyperparameters, and

to use the second dataset to compute second kernel and noise hyperparameters and,

to use the first and second kernel and noise hyperparameters to compute both auto-covariances and cross-covariances; and

wherein the evaluation processor is adapted to use the first and second datasets, first and second kernel and noise hyperparameters and computed auto-covariances and cross-covariances for Gaussian process regression.

25. The system of claim 24 wherein the evaluation processor is adapted to use different Gaussian process kernels with respect to the first and second datasets.

26. The system of claim 24 wherein the evaluation processor is adapted to use the same Gaussian process kernel with respect to the first and second datasets.

27. The system of claim 24, wherein the first and second datasets describe different quantities and the quantity of interest is the quantity described by the first dataset and wherein the training processor is adapted to compute the auto-covariance and cross-covariance by computing a measure of task similarity with the computation of the hyperparameters.

28. The system of claim 24, wherein the first and second datasets describe the same quantity of interest and the training processor is adapted to compute the auto-covariance and cross-covariance by computing a measure of dataset similarity with the computation of the hyperparameters.

29. The system of claim 16, wherein the first dataset comprises color data.

30. The system of claim 29, wherein the second dataset comprises data other than color data.