My conclusion:

Simple DO NOT use Mendeley.
Zotero can do everything Mendeley could, even more elegantly.

Sadly the development of Docear stopped.

The problem of Mendeley is that it locks you in, in almost every aspect:

  • the database is encrypted and you cannot port out your the data completely to another software.
  • the annotation is not embedded in PDF files, meaning you have to rely on Mendeley to read, search, edit your annotations.
    • no batch operations to export annotations.
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USNavalResearchLaboratory/TrackerComponentLibrary at GitHub

The Tracker Component Library is a collection of Matlab routines for simulating and tracking targets in various scenarios. Due to the complexity of the target tracking problem, a great many routines can find use in other areas including combinatorics, astronomy, and statistics.

Recently, I ran into a very comprehensive MATLAB repository, which is very rare to my knowledge. Usually people find comprehensive packages in other languages, like Orekit in Java, GMAT in C++, many others in Python, and even one in Julia.
So, I decide to have a look at it and take nots here.

Although modern radar signal processing can provide both range and range-rate measurements, this measurement type is not always available in SSA. [1]


Most papers can be obtained for academic purpose via https://sci-hub.tw, see Several ways that shouldn't be used to download learning materials.

  1. Hyun Chul Ko, and Daniel J. Scheeres, “Maneuver Detection with Event Representation Using Thrust Fourier Coefficients”, Journal of Guidance, Control, and Dynamics, vol. 39, 2016, pp. 1080–1091. [Link].


In the centimeter range, the dominant source is fragments followed by slag particles from solid rocket motors.

[1]: Horstmann, A., Kebschull, C., Müller, S., Gamper, E., Hesselbach, S., Soggeberg, K., Ben Larbi, M. K., Becker, M., Lorenz, J., Wiedemann, C., and Stoll, E., “Survey of the Current Activities in the Field of Modeling the Space Debris Environment at TU Braunschweig,” Aerospace, vol. 5, Apr. 2018, p. 37.

The third largest contribution is sodium-potassium droplets (NaK droplets) that have been released from orbital nuclear reactors and are highlighted here as an example. These droplets are found today mainly in orbits near 900km altitude and are treated as a historical source due to their early generation but relatively late discovery.

An estimated 250 g have been released per event [23]; however, since these droplets were observed during radar measurements [25], they are considered in the model for the sake of completeness. In total, there are now about 20,000 droplets in space, mostly in orbits near 900km altitude [26].

The contribution of droplets in the entire centimeter population at 800km altitude today is about 10% [23].


[1]: Horstmann, A., Kebschull, C., Müller, S., Gamper, E., Hesselbach, S., Soggeberg, K., Ben Larbi, M. K., Becker, M., Lorenz, J., Wiedemann, C., and Stoll, E., “Survey of the Current Activities in the Field of Modeling the Space Debris Environment at TU Braunschweig,” Aerospace, vol. 5, Apr. 2018, p. 37.

Two Line Elements that are provided by the Joint Space Operations Center (JSpoC) have a low precision due to the analytic SGP4-propagation theory, which can amount to several hundred meters [41,42], whereas precise orbit data is not accessible to publicity.


See Orekit implementation here.

It is described in the paper:

The DTM-2000 empirical thermosphere model with new data assimilation and constraints at lower boundary: accuracy and properties S. Bruinsma, G. Thuillier and F. Barlier
Journal of Atmospheric and Solar-Terrestrial Physics 65 (2003) 1053–1070

This model provides dense output for altitudes beyond 120 km.

The model needs geographical and time information to compute general values, but also needs space weather data : mean and instantaneous solar flux and geomagnetic indices.

Mean solar flux is (for the moment) represented by the F10.7 indices. Instantaneous flux can be set to the mean value if the data is not available. Geomagnetic activity is represented by the Kp indice, which goes from 1 (very low activity) to 9 (high activity).

All these data can be found on the NOAA (National Oceanic and Atmospheric Administration) website.

Rasmussen, Carl Edward, and Christopher K. I. Williams. 2006. Gaussian Processes for Machine Learning. Adaptive Computation and Machine Learning. Cambridge, Mass: MIT Press. http://www.gaussianprocess.org/gpml/chapters/.


Sec 2讲了做regression的几乎所有基础理论。

Sec 3讲做classification,没有看。

Sec 4讲不同covairance的性质,未看,待看。

在Sec 5讲模型的训练理论。 这本书里把通常的机器学习中的训练的概念称为model selection,所以作为一个外行花了很长时间才弄明白这部分是讲如何训练的。

Bayesian inference

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Michalis K. Titsias, Magnus Rattray, and Neil D. Lawrence, “Markov chain Monte Carlo algorithms for Gaussian processes,” Bayesian Time Series Models, David Barber, A. Taylan Cemgil, and Silvia Chiappa, eds., Cambridge: Cambridge University Press, 2011, pp. 295–316. [Link].

Estimate latent function



yi=fi+ϵiy_i = f_i + \epsilon_i

Joint distribution is

p(y,f)=p(yf)p(f)p(\bm{y},\bm{f}) = p(\bm{y}|\bm{f}) p(\bm{f})

Applying Bayes’ rule and posterior over f\bm{f} is

p(fy)=p(yf)p(f)p(yf)p(f)dfp(\bm{f}|\bm{y}) = \frac{p(\bm{y}|\bm{f})p(\bm{f})}{\int p(\bm{y}|\bm{f})p(\bm{f})\,{\rm d}\bm{f}}

Predict the function value f\bm{f}_* at an unseen inputs X\bm{X}_*

p(fy)=p(ff)p(fy)df\textcolor{blue}{p(\bm{f}_*|\bm{y})} = \int p(\bm{f}_*|\bm{f}) p(\bm{f}|\bm{y})\,{\rm d}\bm{f}

where p(ff)p(\bm{f}_*|\bm{f}) is the conditional GP prior given by,

p(ff)=N(f,)p(\bm{f}_*|\bm{f}) = \mathcal{N}(\bm{f}_*|\circ,\circ)

Predict y\bm{y}_* corresponding to f\bm{f}_* is

p(yy)=p(yf)p(fy)df\textcolor{red}{p(\bm{y}_*|\bm{y})} = \int p(\bm{y}_*|\bm{f}_*) \textcolor{blue}{p(\bm{f}_*|\bm{y})} \,{\rm d}\bm{f}_*

In a mainstream machine learning application involving large datasets and where fast inference is required, deterministic methods are usually preferred simply because they are faster.
In contrast, in applications related to scientific questions that need to be carefully addressed by carrying out a statistical data analysis, MCMC is preferred.

Jonathan Ko, “Gaussian Process for Dynamic Systems”, PhD Thesis, University of Washington, 2011.

Bayes filter equation in Eq. 4.1 (p.34) has a typo (should be \propto, not ==)

p(xtz1:t,u1:t1)p(ztxt)p(xtxt1,ut1)p(xt1z1:t1,u1:t2)dxt1p(x_t|z_{1:t},u_{1:t-1}) \propto p(z_t|x_t) \int \textcolor{red}{p(x_t|x_{t-1},u_{t-1})} \textcolor{green}{p(x_{t-1}|z_{1:t-1},u_{1:t-2})} dx_{t-1}

  • Red\textcolor{red}{Red} part is dynamics model, describing how the state xx evolves in time based on the control input uu (p.34)
  • Green\textcolor{green}{Green} part is observation model, describing the likelihood of making an observation zz given the state xx
  • GP-BayesFilter improves these two parts.

The dynamics model maps the state and control (xt,ut)(x_t,u_t) to the state transition Δxt=xt+1xt\Delta x_t = x_{t+1} - x_t. So, the training data is

Dp=<(X,U),X>D_p = <(X,U),X'>

The observation model maps from the state xtx_t to the observation ztz_t. So, the training data is

Do=<X,Z>D_o = <X,Z>

The resulting GP dynamics and observation models are (p.44)

p(xtxt1,ut1)N(GPμ([xt1,ut1],Dp),GPΣ([xt1,ut1],Dp))p(x_t|x_{t-1},u_{t-1}) \approx \mathcal{N}(\text{GP}_\mu([x_{t-1},u_{t-1}],D_p), \text{GP}_\Sigma([x_{t-1},u_{t-1}],D_p))


p(ztxt)N(GPμ(xt,Do),GPΣ(xt,Do))p(z_t|x_t) \approx \mathcal{N}(\text{GP}_\mu(x_t,D_o), \text{GP}_\Sigma(x_t,D_o))

Mark E Pittelkau, “Survey of Calibration Algorithms for Spacecraft Attitude Sensors and Gyros”, Advances in the Astronautical Sciences, vol. 129, 2007, pp. 1–55.

1. Introduction

The purpose of this paper is to present an overview of the various calibration algorithms, to examine their merits, and to show where and how they have been applied.

This survey extends back to 1969, although there were some relatively minor developments before that time.

This survey focuses mainly on methods rather than applications.

A critical review of the literature is provided, including strengths and weaknesses of algorithms and an assessment of results and conclusions in the literature.

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