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glossaries.tex
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glossaries.tex
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% Definition of glossary items
% This package raises warnings 'overriding \printglossary'. 'overriding 'theglossary' environment
%\usepackage{glossaries}
\usepackage[toc,acronym]{glossaries}
% The command \makeglossaries must be written before the first glossary entry.
\makeglossaries
% The command \printglossaries is the one that will actually render the list of words and definitions
% According to this, these warnings can be ignored:
% https://tex.stackexchange.com/questions/163479/glossaries-conflict-with-memoir
% Define acronyms
\newacronym{SAG}{SAG}{semi-autogenous grinding}
\newacronym{AG}{AG}{autogenous grinding}
\newacronym{MPC}{MPC}{model predictive control}
\newacronym{PI}{PI}{proportional-integral}
\newacronym{PID}{PID}{proportional-integral-derivative}
\newacronym{HNMPC}{HNMPC}{hybrid non-linear model predictive control}
\newacronym{SISO}{SISO}{single-input, single-output}
\newacronym{MIMO}{MIMO}{multiple-input, multiple-output}
\newacronym{MJLS}{MJLS}{Markov jump linear system}
\newacronym{EKF}{EKF}{extended Kalman filter}
\newacronym{RODD}{RODD}{randomly-occurring deterministic disturbance}
\newacronym{ARIMA}{ARIMA}{autoregressive integrated moving average}
\newacronym{kWh}{kWh}{kilowatt-hours}
\newacronym{MLE}{MLE}{maximum likelihood estimation}
\newacronym{EM}{EM}{expectation maximization}
\newacronym{DOB}{DOB}{disturbance observer based}
\newacronym{LQG}{LQG}{linear quadratic Gaussian}
\newacronym{GMM}{GMM}{Gaussian mixture model}
\newacronym{BRW}{BRW}{bounded random walk}
\newacronym{HMM}{HMM}{hidden Markov model}
\newacronym{RMSE}{RMSE}{root-mean-squared error}
\newacronym{KF}{KF}{Kalman filter}
\newacronym{MKF}{MKF}{multiple-model Kalman filter}
\newacronym{SKF}{SKF}{scheduled Kalman filter (with pre-scheduled mode switching)}
\newacronym{GPB}{GPB}{generalised pseudo-Bayesian}
\newacronym{GPB1}{GPB1}{first-order generalised pseudo-Bayesian estimator}
\newacronym{GPB2}{GPB2}{second order generalised pseudo-Bayesian estimator}
\newacronym{AFMM}{AFMM}{adaptive forgetting through multiple models}
\newacronym{RMSD}{RMSD}{root-mean-squared differences}
\newacronym{PSD}{PSD}{particle size distribution}
\newacronym{P80}{P80}{80\% passing size, a measure of a particle size distribution}
\newacronym{PRNG}{PRNG}{pseudo-random number generator}
\newacronym{SMC}{SMC}{sequential Monte Carlo}
\newacronym{PRBS}{PRBS}{pseudo-random binary sequence}
\newacronym{SNR}{SNR}{signal-to-noise ratio}
% NOTE: Don't add periods at end of description. Don't use capitals at beginning of description.
% General notation
%\newglossaryentry{Ndist2}{name={$\mathcal{N}(\mathbf{y}, \mathbf{\mu}, \Sigma)$},
% description={multivariate normal probability density of $\mathbf{y}$ with mean $\mathbf{\mu}$ and covariance $\Sigma$}}
%\newglossaryentry{Ndist}{name={$\mathcal{N}(0,\sigma_{w_p}^2)$},
% description={normal distribution with mean zero and variance $\sigma_{w_p}^2$}}
%\newglossaryentry{pagb}{name={$p(a \mid b)$}, description={probability density of $a$ given $b$}}
%\newglossaryentry{PrAgB}{name={$\Pr(A \mid B)$}, description={probability of $A$ given $B$}}
%\newglossaryentry{nabla}{name=\ensuremath{\nabla}, description={defined as $1-q^{-1}$}}
%\newglossaryentry{gammak}{name=\ensuremath{\gamma(k)}, description={random shock indicator at time $k$}}
% Signals
%\newglossaryentry{Ts}{name=\ensuremath{T_s}, description={sampling interval in units of time}}
%\newglossaryentry{N}{name=\ensuremath{N}, description={length of simulation in number of sampling intervals}}
%\newglossaryentry{uk}{name=\ensuremath{\mathbf{u}(k)}, description={system inputs at time $k$}}
%\newglossaryentry{xk}{name=\ensuremath{\mathbf{x}(k)}, description={system states at time $k$}}
%\newglossaryentry{yk}{name=\ensuremath{\mathbf{y}(k)}, description={system outputs at time $k$}}
%\newglossaryentry{wk}{name=\ensuremath{\mathbf{w}(k)}, description={process disturbances at time $k$}}
%\newglossaryentry{vk}{name=\ensuremath{\mathbf{v}(k)}, description={measurement noises at time $k$}}
%\newglossaryentry{A}{name=\ensuremath{\mathbf{A}}, description={transition matrix of the system model}}
%\newglossaryentry{B}{name=\ensuremath{\mathbf{B}}, description={input matrix of the system model}}
%\newglossaryentry{C}{name=\ensuremath{\mathbf{C}}, description={output matrix of the system model}}
%\newglossaryentry{yMk}{name=\ensuremath{\mathbf{y}_M(k)}, description={system output measurements at time $k$}}
%\newglossaryentry{pk}{name=\ensuremath{p(k)}, description={disturbance signal at time $k$}}
%\newglossaryentry{wpk}{name=\ensuremath{w_p(k)}, description={random shock signal at time $k$}}
%\newglossaryentry{rk}{name=\ensuremath{\mathbf{r}(k)},
% description={mode indicator of a switching system at time $k$ (vector)}}
%\newglossaryentry{porek}{name=\ensuremath{p_\text{ore}(k)}, description={simulated ore disturbance signal at time $k$}}
%\newglossaryentry{np}{name=\ensuremath{n_p}, description={number of independent random shocks}}
% Disturbance models
%\newglossaryentry{epsilon}{name=\ensuremath{\varepsilon}, description={probability of a random shock}}
%\newglossaryentry{sigmawp}{name=\ensuremath{\sigma_{w_p}},
% description={standard deviation of the persistent noise component of the random shock variable}}
%\newglossaryentry{sigmawp2}{name=\ensuremath{\sigma_{w_p}^2},
% description={variance of the persistent noise component of the random shock variable}}
%\newglossaryentry{b}{name=\ensuremath{b},
% description={ratio of the variance of the shocks and the persistent noise components of the random shock process}}
%\newglossaryentry{Piwp}{name={$\Pi_{w_{p}}$}, description={transition probability matrix of the disturbance process $w_p$}}
%\newglossaryentry{sigmaM}{name=\ensuremath{\sigma_M}, description={standard deviation of the measurement noise}}
% State estimation
%\newglossaryentry{xkp1_pred}{name={$\hat{\mathbf{x}}(k+1 \mid k)$},
% description={predictions of system states at time $k+1$ made with information available at time $k$}}
%\newglossaryentry{xk_pred}{name={$\hat{\mathbf{x}}(k \mid k-1)$},
% description={predictions of system states at time $k$ made with information available at time $k-1$}}
%\newglossaryentry{xk_hat}{name={$\hat{\mathbf{x}}(k \mid k)$}, description={estimates of system states at time $k$ made with information available at time $k$}}
%\newglossaryentry{yk_hat}{name={$\hat{\mathbf{y}}(k \mid k)$}, description={estimates of system outputs at time $k$ made with information available at time $k$}}
%\newglossaryentry{Kpk}{name={$\mathbf{K}_p(k)$}, description={correction gain of the Kalman filter (prediction form)}}
%\newglossaryentry{Kk}{name={$\mathbf{K}(k)$}, description={correction gain of the Kalman filter (filtering form)}}
%\newglossaryentry{Kfk}{name={$\mathbf{K}_f(k)$},
% description={correction gain of the Kalman filter (filtering form), or correction gain of Kalman filter $f$ (filtering form)}}
%\newglossaryentry{Sk}{name=\ensuremath{\mathbf{S}(k)}, description={covariance of the output prediction errors at time $k$}}
%\newglossaryentry{Pk}{name={$\mathbf{P}(k \mid k)$},
% description={state estimation error covariance at time $k$ made with information available at time $k$}}
%\newglossaryentry{Pkp1_pred}{name={$\mathbf{P}(k+1 \mid k)$},
% description={predictions of the state estimation error covariance at time $k+1$ made with information available at time $k$}}
%\newglossaryentry{Pk_pred}{name={$\mathbf{P}(k \mid k-1)$},
% description={predictions of the state estimation error covariance at time $k$ made with information available at time $k-1$}}
%\newglossaryentry{Qset}{name=\ensuremath{\mathcal{Q}},
% description={set of process noise covariance matrices of a switching system model}}
%\newglossaryentry{Qk}{name=\ensuremath{\mathbf{Q}(k)},
% description={covariance of the process disturbances in the observer model at time $k$}}
%\newglossaryentry{R}{name=\ensuremath{\mathbf{R}},
% description={covariance of the measurement noises in the observer model}}
%\newglossaryentry{E}{name={$\mathbb{E}\{\cdot\}$}, description={expectation operator}}
%\newglossaryentry{wpkv}{name={$\mathbf{w}_p(k)$}, description={disturbance model noise inputs at time $k$}}
% I don't think these need to be in glossary
%\newglossaryentry{xak}{name={$\mathbf{x}_a(k)$}, description={augmented system states at time $k$}}
%\newglossaryentry{Aa}{name={$\mathbf{A}_a$}, description={transition matrix of the augmented system model}}
%\newglossaryentry{Ba}{name={$\mathbf{B}_a$}, description={input matrix of the augmented system model}}
%\newglossaryentry{Ca}{name={$\mathbf{C}_a$}, description={output matrix of the augmented system model}}
% Multiple model approaches
%\newglossaryentry{nj}{name=\ensuremath{n_j}, description={number of modes or models of a switching system}}
%\newglossaryentry{nh}{name=\ensuremath{n_h}, description={number of hypotheses}}
%\newglossaryentry{gamma_fk}{name=\ensuremath{\gamma_f(k)},
% description={random shock indicator of hypothesis $f$ at time $k$}}
%\newglossaryentry{Gammafk}{name=\ensuremath{\Gamma_f(k)},
% description={shock indicator hypotheses sequence $f$ from time $0$ to $k$}}
%\newglossaryentry{Gammafkmnk}{name=\ensuremath{\Gamma_m(k-N_f+1,k)},
% description={shock indicator hypotheses sequence $f$ over the fusion horizon}}
%\newglossaryentry{nm}{name=\ensuremath{n_m}, description={number of merged hypotheses}}
%\newglossaryentry{Zmk}{name=\ensuremath{Z_m(k)},
% description={normalization variable at time $k$ used in merged probability calculations}}
%\newglossaryentry{Hbranch}{name=\ensuremath{\mathcal{H}_{\text{branch}}},
% description={hypothesis index used in branching operations}}
%\newglossaryentry{Hmerge}{name=\ensuremath{\mathcal{H}_{\text{merge}}},
% description={hypothesis index used in merging operations}}
%\newglossaryentry{rmk}{name=\ensuremath{\mathbf{r}_m(k)},
% description={indicator of the system modes of the merged hypotheses at time $k$ used in branching and merging operations}}
%\newglossaryentry{rb1k}{name=\ensuremath{\mathbf{r}_{b,1}(k)},
% description={indicators of the system modes of the branched hypotheses at time $k$ before merging}}
%\newglossaryentry{rb2k}{name=\ensuremath{\mathbf{r}_{b,2}(k)},
% description={indicators of the system modes of the branched hypotheses at time $k$ after branching}}
%\newglossaryentry{nf}{name=\ensuremath{N_f},
% description={sequence fusion parameter: length of fusion horizon in number of sampling intervals}}
%\newglossaryentry{m}{name=\ensuremath{n_\text{max}},
% description={sequence fusion parameter: maximum number of shock occurrences within the fusion horizon}}
%\newglossaryentry{d}{name=\ensuremath{N_d},
% description={sequence fusion parameter: shock spacing parameter or length of detection interval, in number of sampling intervals}}
%\newglossaryentry{nmin}{name=\ensuremath{N_\text{min}},
% description={sequence pruning parameter: minimum life of a branched hypothesis}}
%\newglossaryentry{epsilond}{name=\ensuremath{\varepsilon_d},
% description={sequence fusion parameter: probability of at least one shock within the detection interval}}
%\newglossaryentry{beta}{name=\ensuremath{\beta},
% description={sequence fusion parameter: total probability of the modelled shock hypothesis sequences}}
%\newglossaryentry{xfk_hat}{name={$\mathbf{\hat{x}}_f(k \mid k)$},
% description={estimates of the system states at time $k$ for hypothesis $f$}}
%\newglossaryentry{yfk_hat}{name={$\mathbf{\hat{y}}_f(k \mid k)$},
% description={estimates of the system outputs at time $k$ for hypothesis $f$}}
%\newglossaryentry{Pfk}{name={$\mathbf{P}_f(k \mid k)$},
% description={state estimation error covariance at time $k$ for hypothesis $f$}}
%\newglossaryentry{Sfk}{name=\ensuremath{\mathbf{S}_f(k)},
% description={covariance of the output prediction errors of Kalman filter $f$ at time $k$}}
%\newglossaryentry{Pfkp1_pred}{name={$\mathbf{P}_f(k+1 \mid k)$},
% description={predictions of the state estimation error covariance of hypothesis $f$ at time $k+1$}}
%\newglossaryentry{Pfk_pred}{name={$\mathbf{P}_f(k \mid k-1)$},
% description={predictions of the state estimation error covariance of filter $f$ at time $k$}}
%\newglossaryentry{xmk_hat}{name={$\mathbf{\hat{x}}_m(k \mid k)$},
% description={merged estimates of the system states at time $k$ for merged hypothesis $m$}}
%\newglossaryentry{ymk_hat}{name={$\mathbf{\hat{y}}_m(k \mid k)$},
% description={merged estimates of the system outputs at time $k$ for merged hypothesis $m$}}
%\newglossaryentry{Pmk}{name={$\mathbf{P}_m(k \mid k)$},
% description={merged state estimation error covariance at time $k$ for merged hypothesis $m$}}
% Simulations
%\newglossaryentry{RMSEY}{name=\ensuremath{\mathrm{RMSE}(\hat{Y},Y)},
% description={root-mean-squared error of the output estimates compared to the true system outputs}}
%\newglossaryentry{RMSEYM}{name=\ensuremath{\mathrm{RMSE}(\hat{Y},Y_M)},
% description={root-mean-squared error of the output estimates compared to the system output meaurements}}
%\newglossaryentry{tset95}{name=\ensuremath{t_{\pm5\%}}, description={settling time of the process to within $\pm5\%$ of steady-state}}
%\newglossaryentry{Nset95}{name=\ensuremath{N_{\pm5\%}}, description={settling time of the process to within $\pm5\%$ of steady-state, measured in number of sampling intervals}}
%\newglossaryentry{Tp1}{name=\ensuremath{T_{p,1}}, description={time constant of the process model used in sensitivity analysis}}
%\newglossaryentry{Kp}{name=\ensuremath{K_p}, description={gain of the process model used in sensitivity analysis}}
%\newglossaryentry{tstep}{name=\ensuremath{t_\text{step}}, description={time when a step change in the ore feed occurred in the grinding process simulations}}
%\newglossaryentry{Ys}{name=\ensuremath{Y(s)}, description={Laplace transform of the process output signal}}
%\newglossaryentry{Us}{name=\ensuremath{U(s)}, description={Laplace transform of the process input signal}}
% Control - No longer used in this work
%\newglossaryentry{Hp}{name={$H_p$}, description={MPC parameter : prediction horizon in number of sampling intervals}}
%\newglossaryentry{Hc}{name={$H_c$}, description={MPC parameter : control horizon in number of sampling intervals}}
%\newglossaryentry{Deltau}{name={$\Delta \mathbf{u}(k)$},
% description={change in the manipulatable variable between time $k-1$ and $k$}}