rank_update.h File Reference

Symmetric rank-k update: P' = F·P·Fᵀ + Q. More...

#include "config.h"
#include "fused/fused_matrix.h"

Include dependency graph for rank_update.h:

Go to the source code of this file.

Namespaces
namespace	matrix_algorithms

Functions
template<typename T , my_size_t N>
FusedMatrix< T, N, N >	matrix_algorithms::symmetric_rank_k_update (const FusedMatrix< T, N, N > &F, const FusedMatrix< T, N, N > &P, const FusedMatrix< T, N, N > &Q)
	Compute the symmetric rank-k update P' = F·P·Fᵀ + Q.
template<typename T , my_size_t N>
FusedMatrix< T, N, N >	matrix_algorithms::symmetric_rank_k_update (const FusedMatrix< T, N, N > &F, const FusedMatrix< T, N, N > &P)
	Compute the symmetric rank-k update P' = F·P·Fᵀ (no noise term).

Detailed Description

Symmetric rank-k update: P' = F·P·Fᵀ + Q.

Core building block for Kalman filter prediction step. Propagates a covariance matrix P through a state transition F with process noise Q.

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ALGORITHM

P' = F · P · Fᵀ + Q

Computed as two matrix multiplications and one addition:

1. tmp = F · P (N×N · N×N → N×N)
2. P' = tmp · Fᵀ + Q (N×N · N×N + N×N → N×N)

Complexity: O(2N³) for the two multiplications, O(N²) for the addition.

Note

For Kalman filters where F is sparse or structured (e.g. identity plus small perturbation), specialized implementations can exploit that structure. This generic version assumes dense F.

The result is guaranteed symmetric if P and Q are symmetric, since F·P·Fᵀ preserves symmetry and Q is symmetric by definition (covariance).

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