A Scaled Spherical Simplex Filter (S3F) with a decreased n + 2 sigma points set size and equivalent 2n + 1 Unscented Kalman Filter (UKF) accuracy

The computational efficiency of a sampling based nonlinear Kalman filtering process is mainly conditional on the number sigma/sample points required by filter at each time step to effectively quantify statistical properties related states and parameters. Efficaciously minimizing needed would therefore have important implications, especially for large n-dimensional systems. A set minimum n + 1 sigma necessary in application order provide mean nonsingular covariance estimates. Incorporating additional than this improves accuracy estimates can take advantage richer information content that possibly exist, but same increases demand. To end, adding one more point set, assigning general, well defined weights scaling factors, new Scaled Spherical Simplex Filter (S3F) with 2 size presented work, it theoretically proven practically achieve all cases numerical stability as typical 2n Unscented (UKF), almost 50% less requirements. comprehensive study suggested presented, including detailed derivations, theoretical examples results, demonstrating efficiency, robustness, S3F.