The article in this link from skybrary.aero, describes a Canadian Transportation Safety Board report on a Boeing 737 CFIT (controlloed flight into terrain) accident about 3 years ago. The airplane was on an ILS approach in instrument conditions. They started the approach high and fast, passing through 10,000' MSL at 310 KIAS; Canada, like the USA, has a 250 KIAS speed limit below 10,000'. This is already a sign of trouble.
For various reasons you can read about the 737 flew through the localizer. The First Officer noticed, but the Captain insisted that the current heading would allow them to reintercept the localizer. They were discussing the discrepancy between the GPS track and the localizer as they descended through 1,000' AGL.
They were lost. They knew they were lost. And they continued to descend.
Folks, if you are below 1,000' in the clouds and not sure whether you are on course, then you are not on course. This crew had full localizer deflection but continued to follow the glide slope, with fatal results.
Swallow your pride and go around.