Hi Elder,

It seems you are interested in a hybrid observation model. A lot of researchers have explored hybrid observation model by having varying observation matrix and observation noise.

In one of my previous works I did work on a hybrid observation model which you can read here.

Thanks,

Sumeet

Conference Paper Integrating On-board Diagnostics Speed Data with Sparse GPS ...

Thank you very much Kumar, I will read this paper!

I assume these are discrete physical sensors and the 'weight' you want to change is a linear function?

Can you apply the weight deviation function when you zero calibrate the min/max/spread signal function for the sensor of interest.

Dear Eider Carlos Paulino Silva,

Look the link. May be useful.

http://www.mtc.edu.eg/asat13/pdf/sp01.pdf

Regards,Shafagat

It is normal in a Kalman Filter to define and provide the error characteristics of each sensor. If you have reason to believe that the sensor errors vary with time or with some other, perhaps geometrical, property of the scenario, you should model that sensor behaviour. This is perfectly standard thing to do. If your model of the sensor behaviour is accurate, the standard KF will provide optimal results. 

Kalman Filter has been designed for a single target (no clutter) and single sensor. 

Sensor Fusion requires associating data from multiple frames and sensors. Kalman Filter does not do this. It requires a separate association algorithm. 

A much more powerful algorithm for tracking and fusion jointly with association is described in various papers (and a book) by Perlovsky and Deming.

Best

Leonid

I compare some simple approaches in ...

https://www.researchgate.net/publication/251692923_Fusion_of_possibly_biased_location_estimates_using_Gaussian_mixture_models

Article Fusion of possibly biased location estimates using Gaussian ...

One solution to this problem is to decrease the value of the covariance matrix associated with the sensor which you want to give more weight (reliability) or to increase the value of the covariance matrix you have less reliability on.

I did some research and I'm finding that the Extended Kalman Filter is the solution, but like the others papers and articles on the web there is no clear sample about this, I started reading some papers and now I am with some questions, mainly about the jacobians. Does anyone here understand about this implementation?

In fact, the Extended Kalman Filter allows to work with Quaternions, which is the orientation data provided by the two sensors I'm using. So, by now, my worry is about deal properly with Quaternions, and I know that EKF is appropriate! I Just can't understand the math formulas and equations described in most artigos and tutorials....

 Try to write a set of dynamical state space equations for your problem and then you will start seeing how to convert that in a Kalman filter framework.

I will be happy to review.

Best.

Kalman filter was design to track a single target without clutter (unrelated signal), with noise (target-related extraneous signals), and sensor errors. At that time radars were fast but computers were slow, so the problem was how to get read of most data, still keeping some useful information.

Sensor fusion with Kalman filter requires a separate algorithm for data association. Data association is the most difficult part of sensor fusion. There are several algorithms doing this by combining various data association algorithms with Kalman filter. All of this combinations are far from optimal (in difficult cases they are much worse than Cramer Rao Bounds).

Remember, Kalman filter is more than 50-year old technology, which is kind off optimal for a very narrow problem. There is no reason to use Kalman filter today except tradition.

Optimal performance is achieved by joint tracking and association using maximum likelihood estimation:

Open publications:

Perlovsky, L.I. & Deming, R. W. (2010). Maximum Likelihood Joint Tracking and Association in a Strong Clutter without Combinatorial Complexity; arXiv:1010.4236; http://arxiv.org/abs/1010.4236

Perlovsky, L.I. & Deming, R. W. (2013). Maximum likelihood joint tracking and association in a strong clutter without combinatorial complexity. International Journal of Advanced Robotic Systems, 9, 1-9.

a book with great details for many algorithms:

Perlovsky, L.I., Deming R.W., & Ilin, R. (2011). Emotional Cognitive Neural Algorithms with Engineering Applications. Dynamic Logic: from vague to crisp. Springer, Heidelberg, Germany.

other publications:

Perlovsky, L.I. (1987). Multiple sensor fusion and neural networks. DARPA Neural Network Study, 1987.

Perlovsky, L.I. & McManus, M.M. (1991). Maximum Likelihood Neural Networks for Sensor Fusion and Adaptive Classification. Neural Networks 4 (1), 89-102.

Perlovsky, L.I. (2009). Maximum likelihood joint association, tracking, and fusion in strong clutter. Invited Lecture at the Engineering Seminar, University of Connecticut, Storrs, CT.

Deming, R.W. and Perlovsky, L.I. (2007). Concurrent multi-target localization, data association, and navigation for a swarm of flying sensors, Information Fusion, 8, pp.316-330.

Perlovsky, L.I. (2007a). Cognitive high level information fusion, Information Sciences, 177, pp. 2099-2118.

Perlovsky, L.I., Webb, V.H., Bradley, S.R. & Hansen, C.A. (1998). Improved ROTHR Detection and Tracking Using MLANS . AGU Radio Science, 33(4), pp.1034-44.

Perlovsky, L.I., Webb, V.H., Bradley, S.R. & Hansen, C.A. (1998). Improved ROTHR Detection and Tracking Using MLANS . AGU Radio Science, 33(4), pp.1034-44.

 Deming R., Schindler J., Perlovsky L. (2009). Multitarget/Multisensor Tracking using only Range and Doppler Measurements, IEEE Transactions on Aerospace and Electronic Systems, 45 (2), pp. 593-611.

Perlovsky, L.I. & Deming, R. W. (2010). Maximum Likelihood Joint Tracking and Association in a Strong Clutter without Combinatorial Complexity; arXiv:1010.4236; http://arxiv.org/abs/1010.4236

Perlovsky, L.I. (1997). Cramer-Rao Bound for Tracking in Clutter and Tracking Multiple Objects. Pattern Recognition Letters, 18(3), pp.283-288.

Kovalerchuk, B. & Perlovsky, L.I.. (2011). Integration of Geometric and Topological Uncertainties for Geospatial Data Fusion and Mining. Applied Imagery Pattern Recognition Workshop (AIPR), IEEE, doi: 10.1109/AIPR. 2011.6176346

These algorithms achieve the best possible performance (CRB) for joint associatiion, tracking, and fusion:

Perlovsky, L.I. (1997). Cramer-Rao Bound for Tracking in Clutter and Tracking Multiple Objects. Pattern Recognition Letters, 18(3), pp.283-288.

This theory of joint association, tracking, and fusion received McLucas Award - the highest AF award for basic research, and a number of high level endorsements for real world applications.

Thank you very much guys! I will keep researching and studying! Any discover I will write here!