Marit, my personal experience is that it is easier to completely abandon the Kalman framework in favor of a more simple, though less general state observer, in which all the tunable parameters have clear physical meaning (see an example in the attached paper). I believe that such observers could exist for many systems, but I don't know any general design strategy. In the most trivial case, the Kalman filter is replaced by a set of scalar RC filters, whose time constants are directly related with the required convergence times.

Article A Simple Observer for Gyro and Accelerometer Biases in Land ...

Thank you for your suggestion. I'll take a look at your paper.

Although, I am interested in using the Kalman Filter architecture because I DO know the sensor characteristics, and can easily calculate the measurement noise covariance, R, from test data.

Marit, certainly, everyone knows R, but nobody knows Q, since the process noise is a fiction and there is no physical device that produces it. It only reflects how much you trust your mathematical model. Generally it is less intuitive to tune Q than to find suitable constant gains for a filter. 

Have a look at this oldie.  Perhaps it'll help.

http://arc.aiaa.org/doi/10.2514/6.2000-4558

You can work with Q in two ways:

1. based on your modeling process to estimate the process noise level and decide its eleements quantatively;

2. You can estimate their residuals (their assumed values are ZERO), calculate their redundant indexes, and then perform the posteriori variance component estimation.

Should you need any furtehr help, please do not hesitate to contact me! 

Please see the reports arXiv:1503.04313v1.pdf, arXiv:1505.07201v1.pdf and arXiv:1505.07208v1.pdf.and the two papers in SADHANA December 2016 issue.

Please see the reports arXiv:1503.04313v1.pdf, arXiv:1505.07201v1.pdf and arXiv:1505.07208v1.pdf.and the two papers in SADHANA December 2016 issue.

We can use machine learning methods to tune the process noise. as it is difficult to model a cost function(for example: Residual Prediction error) as a function of Q, It is easier to go for black box optimization techniques. An example being Bayesian Optimization.

I have used the biogeography based optimization to tune the Kalman gains such as P, and Q in my paper:

State estimation of an advanced rowing machine using optimized Kalman filtering

Hanieh Mohammadi

Yes I read your paper, it looks like you manually tuned the 4x4 diagonal Q matrix, however for my problem I wanted to include both the on-axis and a few off-axis Q terms (error in the model or nonlinearities which are unknown). In total it was ~14 elements to tune so do you think your same technique would handle that additional about of terms well (without issues of correlation between parameters)?

You can use adaptive fuzzy-based method to tune Matrix Q and R in Kalman filter. For more information, you can see the following articles:

1- S. Soltani, M. Kordestani, P. Karimaghaee, “New estimation methodologies for well logging problems via a combination of fuzzy Kalman filter and different smoothers” Journal of Petroleum Science and Engineering, June 2016.

2- S Soltani , M Kordestani, P Karim Aghaee, M Saif, “Improved Estimation for Well-Logging Problems Based on Fusion of Four Types of Kalman Filters,” IEEE Transactions on Geoscience and Remote Sensing, 2017.