This appendix collects the symbols and terms used throughout the book in one place. The notation table fixes the meaning of each symbol so that a formula pulled from Chapter 4 reads the same way as one from Chapter 18. The glossary gives short, working definitions of the vocabulary that recurs across parts. Neither section is a substitute for the chapter that introduces a concept in full; both are meant for quick reference while you read or build.
J.1 Notation
The book keeps a single convention: a physical scene has a hidden state \(s\), a sensor turns that state into an observation \(y\) or a signal \(x\), and an estimator recovers an estimate \(\hat{s}\) of the state. The measurement model that ties them together is written
$$ x = h(s) + \eta, $$where \(h\) is the (possibly nonlinear) sensor response and \(\eta\) is measurement noise. When we reason under uncertainty we track a belief \(p(s \mid x)\), the posterior over the state given what the sensor reported. The table below lists the symbols in the order you will most often meet them.
| Symbol | Meaning |
|---|---|
| \(x(t)\) | Continuous-time signal, for example a raw voltage or pressure trace |
| \(x[n]\) | Discrete-time (sampled) signal, index \(n = 0, 1, 2, \dots\) |
| \(t\) | Time (seconds); \(n\) is its discrete sample index |
| \(f_s\) | Sampling rate in samples per second (hertz) |
| \(s\) | Hidden state of the world we want to know (position, class, health) |
| \(y\) | Observation or label produced from the sensor stream |
| \(h(\cdot)\) | Measurement or observation model mapping state to signal |
| \(\eta\) | Measurement noise, often modeled as zero-mean Gaussian |
| \(\hat{s}\) | Estimate of the state produced by an estimator or network |
| \(p(s \mid x)\) | Belief: posterior probability of state \(s\) given signal \(x\) |
| \(p(x \mid s)\) | Likelihood of the signal under a state hypothesis |
| \(\theta\) | Learnable model parameters (weights and biases) |
| \(f_\theta(\cdot)\) | A model (network) with parameters \(\theta\) |
| \(\mathcal{L}\) | Loss (objective) minimized during training |
| \(\mathcal{D}\) | Dataset of examples \(\{(x_i, y_i)\}_{i=1}^{N}\) |
| \(N\) | Number of examples, or number of samples in a window |
| \(\mathbb{E}[\cdot]\) | Expectation over the indicated distribution |
| \(\sigma\) | Standard deviation, or a nonlinearity when written \(\sigma(\cdot)\) |
| \(\mathbf{K}\) | Kalman gain in a recursive state estimator |
| \(\|\cdot\|\) | Norm, defaulting to the Euclidean (\(\ell_2\)) norm |
| \(\nabla_\theta\) | Gradient with respect to the parameters \(\theta\) |
A few habits keep the notation unambiguous. Bracketed indices such as \(x[n]\) always mean a sampled signal; parenthesized arguments such as \(x(t)\) always mean a continuous one. A hat marks an estimate, so \(\hat{s}\) is never the true state \(s\). Bold symbols such as \(\mathbf{K}\) denote vectors or matrices, while plain italics denote scalars. Where a chapter needs an extra symbol it defines it locally, but it never reassigns one from this table.
J.2 Glossary
Definitions below are deliberately short. Each term has a home chapter where it is developed with examples; use this list to jog your memory, not to learn a concept for the first time.
- Aliasing
- The false low-frequency content that appears when a signal is sampled below twice its highest frequency (the Nyquist rate). Once present it cannot be removed, so it is prevented with an anti-aliasing filter before sampling.
- Bias
- A systematic offset between what a sensor or estimator reports and the truth. Distinct from noise, which averages out; bias does not.
- Calibration
- Adjusting a sensor or model so its outputs match a trusted reference. For probabilistic models it also means making predicted confidences match observed accuracy.
- Conformal prediction
- A distribution-free method that turns any point predictor into prediction sets or intervals with a guaranteed coverage rate, using a held-out calibration split.
- Domain shift
- A change between the data a model was trained on and the data it meets in deployment, for example a new sensor, season, or site. It is the usual cause of silent accuracy loss.
- Drift
- A slow change over time in a sensor's response or in the data distribution, such as a gas sensor whose baseline creeps as it ages. Corrected by recalibration or adaptation.
- Foundation model
- A large model pretrained on broad data that serves as a reusable starting point, fine-tuned or prompted for many downstream sensing tasks rather than trained from scratch.
- Inertial measurement unit (IMU)
- A package of accelerometers and gyroscopes (often a magnetometer) that reports motion. Central to dead reckoning, gesture sensing, and fusion with cameras or GPS.
- Kalman filter
- A recursive estimator that fuses a motion model with noisy measurements to track a state, updating the estimate \(\hat{s}\) and its uncertainty through a predict step and a correct step weighted by the Kalman gain.
- Leakage
- When information from the test set or the future sneaks into training, inflating reported accuracy. Common in sensor data through overlapping windows or per-subject splits done wrong.
- Micro-Doppler
- The small frequency shifts a radar sees from the moving parts of a target, such as swinging arms or spinning rotor blades, used to classify what is moving, not just that something moves.
- Nyquist rate
- Twice the highest frequency present in a signal; the minimum sampling rate that captures it without aliasing.
- Occupancy
- A representation of which regions of space are filled, free, or unknown. Occupancy grids and occupancy networks let a robot reason about where it can move.
- Odometry
- Estimating change in position over time from onboard sensors (wheels, an IMU, or a camera). Accurate over short spans but subject to accumulating drift.
- Point cloud
- A set of 3D points, typically from lidar or depth cameras, describing surfaces in a scene without an imposed grid.
- Remaining useful life (RUL)
- The predicted time or cycles a machine or component has left before failure, a core target of predictive maintenance from vibration, temperature, and current signals.
- Sensor fusion
- Combining measurements from several sensors so the joint estimate is better than any one alone, exploiting complementary strengths (radar range plus camera semantics, for instance).
- Self-supervised learning
- Learning useful representations from unlabeled data by solving a pretext task the data supplies its own answer to, such as predicting a masked segment of a signal. Well suited to sensing, where raw data is plentiful and labels are scarce.
- Signal-to-noise ratio (SNR)
- The ratio of signal power to noise power, usually in decibels. It sets a ceiling on how well any downstream model can perform.
- SLAM (simultaneous localization and mapping)
- Building a map of an unknown environment while at the same time tracking the sensor's own pose within it, a chicken-and-egg problem solved by joint estimation.
- Spectrogram
- A time-frequency image showing how a signal's frequency content changes over time, produced by a short-time Fourier transform and widely used as a network input.
- Test-time adaptation
- Adjusting a deployed model to the current data stream without labels, for example by updating normalization statistics, to counter domain shift on the fly.
- TinyML
- Machine learning that runs on microcontrollers and other severely constrained devices, with kilobytes of memory and milliwatts of power, so inference happens at the sensor.
- Time of flight (ToF)
- Measuring distance by the time a pulse of light or sound takes to travel to a target and back. The principle behind lidar, sonar, and many depth cameras.
- Uncertainty (aleatoric and epistemic)
- Aleatoric uncertainty is irreducible noise in the data; epistemic uncertainty reflects what the model does not know and shrinks with more data. Separating them guides where to collect more or trust less.
- Window
- A fixed-length slice of a streaming signal, the basic unit fed to a model. Choices of length and overlap trade latency against context.
- World model
- A learned internal model that predicts how a scene evolves, letting an agent imagine the consequences of actions before taking them. Increasingly used to give perception a predictive, physics-aware backbone.
If a symbol or term you meet in the text is missing here, check the index and the chapter that introduces it; the definitions in the running text are always the authoritative ones, and this appendix simply gathers them for convenience.