To properly process data, we need to take into account both the measurement errors and the fact that some of the observations may be outliers. This is especially important in radar-based localization problems, where some signals may reflect not from the analyzed object, but from some nearby object. There are known methods for dealing with both measurement errors and outliers in situations in which we have full information about the corresponding probability distributions. There are also known statistics-based methods for dealing with measurement errors in situations when we only have partial information about the corresponding probabilities. In this paper, we show how these methods can be extended to situations in which we also have partial inf0ormation about the outliers (and even to situations when we have no information about the outliers). In some situations in which efficient semi-heuristic methods are known, our methodology leads to a justification of these efficient heuristics -- which makes us confident that our new methods will be efficient in other situations as well.