For Beginners With Matlab Examples Download Fix Top — Kalman Filter

Widely used in everything from spacecraft navigation to financial modeling and autonomous robotics, the Kalman Filter is an algorithm that estimates the "true state" of a system over time, even when that system is obscured by noise and uncertainty.

: Process noise covariance (uncaught environmental variations, like wind pushing a drone). Phase 2: Update (Measurement Update) Once a new sensor reading ( Widely used in everything from spacecraft navigation to

%% 4. Plotting Results figure('Name', 'Kalman Filter Demo', 'Color', 'w'); hold on; Kalman Filter Loop for k = 1:duration %

%% 1D Kalman Filter Simulation: Noisy Voltage Estimation clear; clc; close all; % 1. Simulation Parameters duration = 100; % Total time steps true_voltage = 1.2; % The actual, constant physical voltage sensor_noise_std = 0.2; % Standard deviation of the voltmeter noise % Generate fake experimental data (True value + Gaussian Noise) rng(42); % Seed the random number generator for reproducibility measurements = true_voltage + sensor_noise_std * randn(1, duration); % 2. Kalman Filter Initialization estimated_voltage = zeros(1, duration); P = zeros(1, duration); % Error covariance array % Initial guesses x_hat = 0.0; % We guess the voltage starts at 0V P_current = 1.0; % High initial uncertainty % Tuning parameters Q = 1e-5; % Process noise (very low because voltage is constant) R = sensor_noise_std^2; % Measurement noise variance (0.2^2 = 0.04) A = 1; % State transition matrix (x_k = x_k-1) H = 1; % Measurement matrix (we measure the voltage directly) % 3. Kalman Filter Loop for k = 1:duration % --- PREDICT PHASE --- x_hat_minus = A * x_hat; P_minus = A * P_current * A + Q; % --- UPDATE PHASE --- % Compute Kalman Gain K = (P_minus * H) / (H * P_minus * H + R); % Update estimate with measurement x_hat = x_hat_minus + K * (measurements(k) - H * x_hat_minus); % Update error covariance P_current = (1 - K * H) * P_minus; % Save results for plotting estimated_voltage(k) = x_hat; P(k) = P_current; end % 4. Plotting Results figure('Color', [1 1 1]); plot(1:duration, measurements, 'r.', 'MarkerSize', 8); hold on; plot(1:duration, estimated_voltage, 'b-', 'LineWidth', 2); yline(true_voltage, 'g--', 'LineWidth', 2); grid on; title('1D Kalman Filter: Voltage Estimation'); xlabel('Time Step'); ylabel('Voltage (V)'); legend('Noisy Measurements', 'Kalman Filter Estimate', 'True Voltage Value', 'Location', 'best'); fprintf('Final Estimated Voltage: %.4f V (True Value: %.1f V)\n', estimated_voltage(end), true_voltage); Use code with caution. 4. Advanced: 2D Tracking (Position & Velocity) Advanced: 2D Tracking (Position & Velocity)