Increasing Measurement Agreement Between Different Instruments in Sports Environments: A Jump Height Estimation Case Study

View full-text article in PMC

. 2025 Aug 29;25(17):5354. doi: 10.3390/s25175354

Algorithm 1 Iterative algorithm based on linear regression

1:
Input: Jump Measurement from Instr1-Instr2
2:
%Training phase
3:
Length of TS = subset of measures is considered for the training phase (TS1 and TS2)
4:
5:
$T m e a n$ = Mean of TS1 and TS2
6:
Define Peak To Peak Initial Distance (PPID)
7:
${P P I D}_{T S 1}$ = $M A X (T S 1) - M I N (T S 1)$
8:
${P P I D}_{T S 2}$ = $M A X (T S 2) - M I N (T S 2)$
9:
$i t e r a t i o n = 1$ ;
10:
11:
repeat
12:
13:
$i = i t e r a t i o n$
14:
$[m_{1 i}, q_{1 i}] = p o l y f i t (T S 1, T m e a n, 1)$
15:
$[m_{2 i}, q_{2 i}] = p o l y f i t (T S 2, T m e a n, 1)$
16:
17:
$T S 1_{n} = m_{1 i} * T S 1 + q_{1 i}$
18:
$T S 2_{n} = m_{2 i} * T S 2 + q_{2 i}$
19:
20:
$T m e a n = m e a n (T S 2_{n}, T S 1_{n})$
21:
${M G}_{V a l u e} = D i s t a n c e (T S 2 n, T S 1 n)$
22:
${C o h e n K}_{V a l u e} = C o h e n K (T S 2 n, T S 1 n)$
23:
24:
${N P P D}_{T S 1 n}$ = $\frac{M A X (T S 1 n) - M I N (T S 1 n)}{{P P I D}_{T S 1}}$
25:
26:
${N P P D}_{T S 2 n}$ = $\frac{M A X (T S 2 n) - M I N (T S 2 n)}{{P P I D}_{T S 2}}$
27:
28:
$c o n d i t i o n_1$ = ${M G}_{V a l u e} (i) < {M G}_{V a l u e} (i - 1)$ ;
29:
30:
$c o n d i t i o n_2$ = ${C o h e n K}_{V a l u e} (i) > {C o h e n K}_{V a l u e} (1)$
31:
32:
$c o n d i t i o n_3$ = $({N P P D}_{T S 1 n} > 0.60) &$ $({N P P D}_{T S 2 n} > 0.60)$
33:
34:
$i t e r a t i o n = i t e r a t i o n + 1$ ;
35:
36:
until $c o n d i t i o n_1$ & $c o n d i t i o n_2$ & $c o n d i t i o n_3$
37:
38:
%Test phase
39:
Length of TS = subset of measures is considered for the test phase (TS1 and TS2)
40:
41:
$T S 1_{n}$ = $T S 1$ ∗ $\prod_{i = 1}^{x - 1} m_{1 i}$ + $\sum_{i = 1}^{x - 1} q_{1 i}$ ∗ $\prod_{j = i + 1}^{x - 1} m_{1 j}$
42:
43:
$T S 2_{n}$ = $T S 2$ ∗ $\prod_{i = 1}^{x - 1} m_{2 i}$ + $\sum_{i = 1}^{x - 1} q_{2 i}$ ∗ $\prod_{j = i + 1}^{x - 1} m_{2 j}$
44:
$w i t h$ $x = 1 - n u m b e r$ $o f$ $i t e r a t i o n$
45:
Output: $T S 1_{n}$ , $T S 2_{n}$