The Vector Delay-Locked Loop (VDLL) uses an extended Kalman filter to estimate user position and velocity. These estimates are used to compute estimated pseudorange or its rate for feedback to number-controlled oscillators (NCOs). The NCOs and Kalman filter both act as integrators in the feedback control loop, giving a double-pole at the origin. There are also one or more stable real poles for loop filtering. This system cannot be stabilized using a simple gain, but requires at least dynamic compensation. It becomes a challenge to ensure that the estimated position and velocity track the true values.
Has anyone else encountered these issues?
Dear Mr. Blankinship,
"It becomes a challenge to ensure that the estimated position and velocity track the true values." perhaps refers to stability of the EKF. Is that what you're looking for? If so, you could look at:
ieeexplore.ieee.org/iel4/9/16302/00754809.pdf
Also, more details on the model would be desirable. It seems that you enquire about both stability of estimation and stability of the system.
Dear Mr. Blankinship,
The problem, that you have mentioned in your inquiry, is common problem for any researcher involved in the Kalman filtering for sensor fusion. Any feedback stabilization of VDLL will not produce positive result, because in this case you will obtained biased estimations. That is why the basic method of this problem solving is the increasing of the accuracy of the Kalman filtering and the sensor errors compensation via this filter. From my point of view, one of the most promising method for enhancing of the Kalman filtering is so called Unscented Kalman Filtering (UKF). In Attachment you will find invited paper devoted to the UKF, where further references are quoted.
I'd like to make just a short remark.
Actually, a KF is an unbiased estimator. A UKF can only improve accuracy of tracking in terms of, say, RMSE, but the stability analysis is pretty much the same.
www.sciencedirect.com/science/article/pii/S0005109805003705
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