Nonlinear Filtering for Hybrid GPS/GSM Mobile Terminal Tracking

Table 2

Computational complexity of the EKF, RBUKF, and MCKF. The dimension of the state vector is given by 𝑛_𝑥 and the dimension of the measurement vector is given by 𝑛_𝑦. 𝒳(𝑘∣𝑘−1) denotes the matrix composed of sigma/cubature point vectors.

Quantity	Complexity
	EKF	RBUKF
𝐱(𝑘∣𝑘−1)	2𝑛^2𝑥−𝑛𝑥	2𝑛^2𝑥−𝑛𝑥	2𝑛^2𝑥−𝑛𝑥
𝐏(𝑘∣𝑘−1)	8𝑛^3𝑥−15𝑛^2𝑥+10𝑛𝑥	8𝑛^3𝑥−15𝑛^2𝑥+10𝑛𝑥	8𝑛^3𝑥−15𝑛^2𝑥+10𝑛𝑥
𝓧(𝑘∣𝑘−1)	—	13𝑛^3𝑥/3+2𝑛^2𝑥	13𝑛^3𝑥/3+2𝑛^2𝑥
𝐲(𝑘∣𝑘−1)	—	2𝑛𝑥𝑛𝑦+2𝑛𝑦	2𝑛𝑥𝑛𝑦
𝐏𝐲𝐲(𝑘∣𝑘−1)	2𝑛^2𝑦𝑛𝑥+2𝑛^2𝑥𝑛𝑦−𝑛𝑥𝑛𝑦	4𝑛^2𝑦𝑛𝑥+2𝑛𝑥𝑛𝑦+4𝑛^2𝑦+𝑛𝑦	4𝑛^2𝑦𝑛𝑥+3𝑛^2𝑦
𝐏𝐱𝐲(𝑘∣𝑘−1)	2𝑛^2𝑥𝑛𝑦−𝑛𝑥𝑛𝑦	4𝑛^2𝑥𝑛𝑦+3𝑛𝑥𝑛𝑦+2𝑛^2𝑥+𝑛𝑥	4𝑛^2𝑥𝑛𝑦+2𝑛𝑥𝑛𝑦
𝐊(𝑘)	𝑛^3𝑦+2𝑛^2𝑦𝑛𝑥−𝑛𝑥𝑛𝑦	𝑛^3𝑦+2𝑛^2𝑦𝑛𝑥−𝑛𝑥𝑛𝑦	𝑛^3𝑦+2𝑛^2𝑦𝑛𝑥−𝑛𝑥𝑛𝑦
𝐱(𝑘∣𝑘)	2𝑛𝑥𝑛𝑦+2𝑛𝑦	2𝑛𝑥𝑛𝑦+2𝑛𝑦	2𝑛𝑥𝑛𝑦+2𝑛𝑦
𝐏(𝑘∣𝑘)	2𝑛^2𝑦𝑛𝑥+2𝑛^2𝑥𝑛𝑦−𝑛𝑥𝑛𝑦	2𝑛^2𝑦𝑛𝑥+2𝑛^2𝑥𝑛𝑦−𝑛𝑥𝑛𝑦	2𝑛^2𝑦𝑛𝑥+2𝑛^2𝑥𝑛𝑦−𝑛𝑥𝑛𝑦