This code contains a portable demo of our CCMLE algorithm [1] for obtaining maximum likelihood estimates of signals with a priori known bounds on the relative change in the value at consecutive sampling times. The algorithm is based on a bounded variable least squares (BVLS) problem.
We run CCMLE with a relative change bound of 0.01 on a signal of 5000 samples constructed by the sum of two sinusoids, subject to zero-mean Gaussian noise with a standard deviation of 3. The results can be seen in the figure below.
For the noisy signal, the computed standard deviation was 3.05, whereas after CCMLE, the resulting signal had a computed standard deviation of 0.38.
This code should run both in Python 2 and 3, although only Python 3 has been verified to run successfully. In addition, the following dependencies are required:
numpycvxpymatplotlib(only for plotting)
The same results can be obtained in a more efficient manner by using Dykstra's set projection algorithm. This code will be posted as a C++ package at a later date.
[1] El-Kebir, H., & Ornik, M. (2020). In-flight Air Density Estimation and Prediction for Hypersonic Flight Vehicles. In 23rd AIAA International Space Planes and Hypersonic Systems and Technologies Conference. https://doi.org/10.2514/6.2020-2412 (open access).