## 1 Introduction
However, despite its precision, the lengthy data acquisition process limits the applicability of this approach in industrial settings, where the conditions are not fully controllable [3; 13]. To overcome these challenges, rapid measurement techniques have been proposed. [PERSON] et al. [21] developed a spindle-heating test using a single interferometer within a two-dimensional plane, and this test was later refined by [PERSON] et al. [22] to include additional displacement measurements for systems lacking rotary tables. [PERSON] et al. [23] demonstrated that single-axis interferometry could effectively capture 2D positioning errors, mitigating thermal influences by reducing the measurement duration. Additionally, [PERSON] et al. [24] introduced a cost-effective absolute multilateration system, replacing conventional TIs with a single ADM and four measuring heads, significantly lowering the implementation costs of simultaneous multilateration systems. [PERSON] et al. [25] further explored simultaneous laser multilateration using a telescopic instrument, eliminating the need for multiple TIs. Among these methodologies, absolute interferometry has gained traction as a robust measurement approach. [PERSON] et al. [26; 27] pioneered the Multiline(tm) system, which employs multiple measurement lines anchored to key MT components to quantify thermal distortions. [PERSON] et al. [28] later introduced an integrated laser-based technique that utilises a pentaprism, a laser source, and position sensitive devices (PSDs) to measure thermal-induced displacements within small and medium-sized MTs. The ISO Standard 230-3:2020 [29] serves as the primary framework for evaluating environmental thermal influences on machine tools, enabling the characterisation of five degrees of freedom at a single measurement point. However, as noted by [PERSON] et al. [2], its applicability to medium and large MTs remains limited due to its restricted coverage of geometric error parameters. This underscores the necessity for alternative methodologies that are capable of minimising measurement uncertainty while addressing the complexities of temperature-induced distortions within an expanded working volume. In light of these limitations, the present study extends previous research [30; 31; 32; 33] by further developing a methodology to assess the ambient thermal effects on large machine tools within their operational workspace. The approach builds upon the machine tool integrated inverse multilateration (MIIM) method, which was initially introduced by [PERSON] et al. [34]. While the initial results from single-machine experiments were promising, extending the methodology to other machine architectures is crucial for assessing its broader applicability. This study was conducted in two distinct industrial workshop environments, analysing two large-scale MTs under standard operational conditions without imposing artificial environmental constraints. Testing the methodology across varied working environments ensures its robustness, scalability, and general validity, revealing any architecture-dependent limitations. By incorporating an absolute distance measurement system into the MT spindle, the MIM method enables a fully integrated multilateration-based assessment, mitigating the challenges associated with traditional techniques such as the use of climatic chambers, high-cost TIs, and artefact-based calibration, which are often impractical for large MTs. Section 2 elaborates on the MIM methodology, which employs a LEICA AT960(tm) (Hexagon, Stockholm, Sweden) laser tracker and four wide-angle retro-reflectors to facilitate automated, long-duration thermal assessments. This study evaluates two distinct MT architectures, the THERA(tm) (gantry type) and ZERO(tm) (bed type) architectures, expanding on prior investigations involving the ARION G(tm) (bridge type) architecture, all three of which are manufactured by Zayer MT builder (Vitoria, Spain).