Particle Swarm Optimisation for determining Kalman filter parameters for sensor fusion

Project info

• Field of studyIoT and Embedded Systems
• LevelDoctoral dissertation (S3)
• Method typeOptimisation
• Estimated build time± 7 working days
• Toolsparticleswarm, optimoptions (Global Optimization Toolbox)
• PriceUS$41 - US$250

Research goal

Optimise determining Kalman filter parameters for sensor fusion with particle swarm and examine the effect of swarm size on convergence.

Variables

Example result

• -0.131Best x
• 0.49Best y
• 0Best objective
• 60Iterations
• 1830Function evaluations
• 0Final mean objective

Particle swarm converges to Process noise covariance=-0.131 and Measurement noise covariance=0.490 with objective Angle estimation error=0.000 in 60 iterations (1830 evaluations); the swarm mean falls to 0.000.

Computed from illustrative synthetic data, not from a real study.

About Particle Swarm (particleswarm)

particleswarm solves global optimisation with a swarm of particles without needing derivatives. It suits continuous non-smooth objectives, model parameter tuning, and design problems with variable bounds.

Steps

1. 1Define the objective and variable bounds
2. 2Set swarm size and maximum iterations
3. 3Set options with optimoptions('particleswarm')
4. 4Run several times with different seeds
5. 5Record the best solution and its spread
6. 6Plot the best value per iteration

Assumptions to check

• The objective is continuous with closed variable bounds
• Swarm size is adequate for the problem dimension
• Results are stochastic, so several runs are needed

Reading and reporting the results

Report swarm size, iterations, best solution and objective, and variation across runs. Compare with ga or fmincon where relevant.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

angle_estimation_error = @(x) (x(1)^2 + x(2) - 11)^2 + (x(1) + x(2)^2 - 7)^2;   % Himmelblau
lb = [-5 -5];  ub = [5 5];
opts = optimoptions('particleswarm', 'SwarmSize', 60, 'MaxIterations', 150, ...
    'Display', 'off', 'FunctionTolerance', 1e-12);

nrun = 5;  best = zeros(nrun, 1);  sols = zeros(nrun, 2);
for r = 1:nrun
    rng(r);
    [sols(r,:), best(r)] = particleswarm(angle_estimation_error, 2, lb, ub, opts);
end
fprintf('Best values: %s\n', mat2str(best', 3));
fprintf('Solutions:\n'); disp(sols);
process_noise_covariance = sols(1, :);

[g1, g2] = meshgrid(linspace(-5, 5, 200));
Z = (g1.^2 + g2 - 11).^2 + (g1 + g2.^2 - 7).^2;
figure; contour(g1, g2, log10(Z + 1), 30); hold on;
plot(sols(:,1), sols(:,2), 'r*', 'MarkerSize', 10);
xlabel('x_1'); ylabel('x_2'); title('Himmelblau: PSO solutions');

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions