Autonomous navigation vehicle algorithms - Revision history

Mol: /* Filtering (Bayesian) */

2025-08-06T15:59:44Z

Filtering (Bayesian)

← Older revision		Revision as of 18:59, 6 August 2025
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	bel(x_t) &= P(x_t\| o_{1:t-1}, u_{1:t}) \\		bel(x_t) &= P(x_t\| o_{1:t-1}, u_{1:t}) \\
	&= \int P(x_t \| x_{t-1}, o_{1:t-1}, u_{1:t} bel(x_{t-1} ) d(x_{t-1})		&= \int P(x_t \| x_{t-1}, o_{1:t-1}, u_{1:t} bel(x_{t-1} ) d(x_{t-1})
			\end{align}
			</math>

			Step 2. Correction with the observation (Bayes)
			\begin{align}
			bel_{posterior}(x_t) = \dots
	\end{align}		\end{align}
	</math>		</math>

2025-08-06T15:58:36Z

Filtering (Bayesian)

2025-08-06T15:58:16Z

Filtering (Bayesian)

← Older revision		Revision as of 18:58, 6 August 2025
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	''3 Recursive Bayes filter''. Hidden Markov Model. Action model <math>p(x_t\| u_t, x_{t-1})</math>, sensor model <math>p(o_t\| x_t) </math>.		''3 Recursive Bayes filter''. Hidden Markov Model. Action model <math>p(x_t\| u_t, x_{t-1})</math>, sensor model <math>p(o_t\| x_t) </math>.

			Step 1. Prediction with the control input (like in dead reckoning)

			<math>
			\begin{align}
			bel(x_t) &= P(x_t\| o_{1:t-1}, u_{1:t}) \\
			&= \int P(x_t \| x_{t-1}, o_{1:t-1}, u_{1:t} bel(x_{t-1} ) d(x_{t-1})
			\end{align*}
			</math>

	=== Localization: Particle Filter ===		=== Localization: Particle Filter ===

2025-08-06T15:54:06Z

Filtering (Bayesian)

← Older revision		Revision as of 18:54, 6 August 2025
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	Conditional probability <math>P(B\|A)</math> the chance of B when A has already happened.		Conditional probability <math>P(B\|A)</math> the chance of B when A has already happened.
	<math>P(B\|A) = \frac{P(A\|B) P(B)}{P(A)}</math>.		<math>P(B\|A) = \frac{P(A\|B) P(B)}{P(A)}</math>.


			''3 Recursive Bayes filter''. Hidden Markov Model. Action model <math>p(x_t\| u_t, x_{t-1})</math>, sensor model <math>p(o_t\| x_t) </math>.

	=== Localization: Particle Filter ===		=== Localization: Particle Filter ===

2025-08-06T15:46:25Z

Filtering (Bayesian)

← Older revision		Revision as of 18:46, 6 August 2025
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	Dead reckoning: the current state using previous state and estimates of varibales (speed, heading, time etc). Noise; the approximate distribution of the position.		Dead reckoning: the current state using previous state and estimates of varibales (speed, heading, time etc). Noise; the approximate distribution of the position.

			Observation: correction.

			''2 Probability and Bayes rule''.
			Conditional probability <math>P(B\|A)</math> the chance of B when A has already happened.
			<math>P(B\|A) = \frac{P(A\|B) P(B)}{P(A)}</math>.

	=== Localization: Particle Filter ===		=== Localization: Particle Filter ===

2025-08-06T15:43:16Z

Filtering (Bayesian)

← Older revision		Revision as of 18:43, 6 August 2025
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	</math>		</math>

	Dead reckoning: the current state using previous state and estimates of varibales (speed, heading, time etc).		Dead reckoning: the current state using previous state and estimates of varibales (speed, heading, time etc). Noise; the approximate distribution of the position.

	=== Localization: Particle Filter ===		=== Localization: Particle Filter ===

2025-08-06T15:40:37Z

Filtering (Bayesian)

← Older revision		Revision as of 18:40, 6 August 2025
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	\end{align}		\end{align}
	</math>		</math>

			Dead reckoning: the current state using previous state and estimates of varibales (speed, heading, time etc).

	=== Localization: Particle Filter ===		=== Localization: Particle Filter ===

2025-08-06T15:39:22Z

Filtering (Bayesian)

← Older revision		Revision as of 18:39, 6 August 2025
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	# Tuning particles		# Tuning particles

	''State estimation''.		''1 State estimation''.
	Motor u, output y. System matrix A, Output matrix C, input matrix B.		Motor u, output y. System matrix A, Output matrix C, input matrix B.

2025-08-06T15:38:55Z

Filtering (Bayesian)

← Older revision		Revision as of 18:38, 6 August 2025
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	# Tuning particles		# Tuning particles

	''State estimation''		''State estimation''.
	Motor u, output y.		Motor u, output y. System matrix A, Output matrix C, input matrix B.

	<math>		<math>

2025-08-06T15:37:47Z

Filtering (Bayesian)