Control and Estimation Theory in Ranging Applications

For the last 50 years, oscillator modeling in ranging systems has received considerable

attention. Many components in a navigation system, such as the master oscillator

driving the receiver system, as well the master oscillator in the transmitting system

contribute significantly to timing errors. Algorithms in the navigation processor must

be able to predict and compensate such errors to achieve a specified accuracy. While

much work has been done on the fundamentals of these problems, the thinking on said

problems has not progressed. On the hardware end, the designers of local oscillators

focus on synthesized frequency and loop noise bandwidth. This does nothing to

mitigate, or reduce frequency stability degradation in band. Similarly, there are not

systematic methods to accommodate phase and frequency anomalies such as clock

jumps. Phase locked loops are fundamentally control systems, and while control

theory has had significant advancement over the last 30 years, the design of timekeeping

sources has not advanced beyond classical control. On the software end,

single or two state oscillator models are typically embedded in a Kalman Filter to

alleviate time errors between the transmitter and receiver clock. Such models are

appropriate for short term time accuracy, but insufficient for long term time accuracy.

Additionally, flicker frequency noise may be present in oscillators, and it presents

mathematical modeling complications. This work proposes novel H∞ control methods

to address the shortcomings in the standard design of time-keeping phase locked loops.

Such methods allow the designer to address frequency stability degradation as well

as high phase/frequency dynamics. Additionally, finite-dimensional approximants of

flicker frequency noise that are more representative of the truth system than the

tradition Gauss Markov approach are derived. Last, to maintain timing accuracy in

a wide variety of operating environments, novel Banks of Adaptive Extended Kalman

Filters are used to address both stochastic and dynamic uncertainty.