I've read several articles about using chaos theory in GPS. One of them about using Duffing oscillator to detecting periodic signal. As you know GPS carrier is a periodic cosine signal.
First realization was with ode45() in the Matlab. But matlab has non-constant step with Runge-Kutta algorithm and when I added AWGN into incoming signal ode45() hold. So we need our custom Runge-Kutta solver with constant step. Refer to [2] I made solution. When you find k and gamma constants, you can devide gamma into 2 parts - local periodic motion power and incoming carrier. Sample of the algo here.
But also I face to several problems. Need to implement Lyapunov exponent, bcoz it's conventional approach to detect periodic signal with Duffing oscillator. Found way to determine the gamma and k constant.
Some pictures)))
Signal presented
Chaos (incoming frequency higher than internal periodic driven power frequency)
[1] The Study of Weak GPS Signal Acquirtion Based on Duffing Chaotic Oscillator. Hongguang Chen
Xudong Zhang
[2] http://www.amazon.com/Mathematical-Handbook-Scientists-Engineers-Definitions/dp/0486411478/ref=sr_1_2?ie=UTF8&qid=1336339560&sr=8-2
First realization was with ode45() in the Matlab. But matlab has non-constant step with Runge-Kutta algorithm and when I added AWGN into incoming signal ode45() hold. So we need our custom Runge-Kutta solver with constant step. Refer to [2] I made solution. When you find k and gamma constants, you can devide gamma into 2 parts - local periodic motion power and incoming carrier. Sample of the algo here.
But also I face to several problems. Need to implement Lyapunov exponent, bcoz it's conventional approach to detect periodic signal with Duffing oscillator. Found way to determine the gamma and k constant.
Some pictures)))
Signal presented
Chaos (incoming frequency higher than internal periodic driven power frequency)
[1] The Study of Weak GPS Signal Acquirtion Based on Duffing Chaotic Oscillator. Hongguang Chen
Xudong Zhang
[2] http://www.amazon.com/Mathematical-Handbook-Scientists-Engineers-Definitions/dp/0486411478/ref=sr_1_2?ie=UTF8&qid=1336339560&sr=8-2
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