Fig. 1. PMSLM mover position measuring system

Fig. 2. Three target images

Fig. 3. Error comparison of different types of graphs

Fig. 4. Schematic of traditional incremental sensors for long travel displacement measurement

Fig. 5. Schematic of the proposed cumulative error reduction method. (a) Schematic diagram; (b) flow chart

Fig. 6. Comparison of measurement range. (a) Traditional gradient algorithm; (b) proposed method

Fig. 7. Comparison between the proposed variable benchmark method and the traditional method. (a) Displacement tracking comparison; (b) cumulative error comparison; (c) error analysis

Fig. 8. Cumulative error at different thresholds

Fig. 9. Experiment platform

Fig. 10. Measurement accuracy verification. (a) Verification of the measurement range of adjacent frames; (b) cumulative error reduction

Fig. 11. Comparison of different algorithms. (a) Comparison of displacement measurement errors of adjacent frames; (b) cumulative error comparison; (c) cumulative error analysis

Fig. 12. Robustness comparison. (a) Comparison of measurement error under different illuminations; (b) error comparison of different algorithms under low illumination; (c) error analysis