Principles

This chapter considers a range of non-linear estimation techniques. In reality, the majority of real-world estimation problemswould be expected to be non-linear, with linear problems as a minor special case. This book's emphasis on linear problems reflects current practice – most progress has been made on these more tractable problems. This reflects the simplicity of the linear problems and their suitability for illustrating principles of indirect estimation. Most of the cases for which there are results with explicit mathematical expressions are linear problems.

Non-linear problems are defined by what they lack, rather than by any common type of behaviour. Furthermore, there have been relatively few applications of non-linear techniques in tracer studies. Consequently, this chapter is rather more exploratory than most of the rest of this book. Simple cases are used to illustrate the techniques so that analytical solutions can illustrate the key features. Analysing the corresponding cases with real-world complexity will almost always require numerical techniques.

Taking the case of linear estimation as a starting point, there are a number of approaches of varying degrees of generality.

1. ▪ Cases in which linear estimation is used because it is optimal. The requisite conditions are described below.

2. ▪ Cases in which linear estimation is used for convenience, even though it is not optimal.

3. […]