"INTRODUCTION Identification@ in the context of the response of a system@ is the study of the correlation between the actual behaviour or performance of a real system and the predicted behaviour from a mathematical model which is assumed to characterise that system. When the mathematical model is expressed in terms of a known set of differential equations with constant coefficients?@ in which a number of these coefficients are unknown@ the parameter estimation process aims at determining the best values of these unknown coefficients from the measured input and output of the system. Output measurements differ from the predicted model outputs for various reasons: firstly@ as a result of an imperfect model representation of the real system and@ secondly@ as the result of noise@ of which there are two kinds@ process noise and measurement noise. Process noise affects the actual output of a system and can be an input (or external noise)@ such as the turbulence affecting the motion of an aircraft in flight@ or an internal system quantity@ such as the noise introduced by a sensor that forms part of a feedback loop of a system. Measurement noise arises from noise in the instrumentation used to measure the input and output. Process noise affects the actual output@ whereas measurement noise does not. The remaining discrepancy between measured quantities and those deduced from the mathematical model may be termed observation error. This Item restricts attention to systems that are assumed free from process noise and whose models are assumed linear. This Data Item presents a number of digital optimisation techniques for parameter estimation that are based on the least-squares principle@ a technique known mainly from its use in curve fitting or regression analysis. These digital computer based methods have superseded@ to a large extent@ older techniques such as steady-state tests@ the time vector method and response matching using an analogue computer@ since these earlier methods were dependent on the operator's skill and judgement in the application of these methods and on the restrictive nature of the form and magnitude of the inputs that could be accommodated. The essence of techniques described here is the minimisation of a chosen Objective Function (often referred to as a Cost Function) that is formed from the square of the difference between the measured output of a particular variable and the model output of this same variable@ where the model output is calculated in terms of the unknown coefficients for the same input. Broadly the techniques divide into the following two classes: (i) the system equation(s) are solved in terms of all the measurements@ both input and output@ (ii) the system equation(s) are solved in terms of the input measurements only. Within each of the above two classes the methods vary according to the availability of the measured outputs of the system. Sketch 1.1@ where it is assumed that only measurement noise is present in the system@ shows a general flow chart of the parameter estimation process. Section 3 of this Item presents the general form of the mathematical model of a linear system in which only measurement noise is assumed present within the model of the system. Section 4 introduces various parameter estimation techniques that consider a system model described by a single first-order equation involving a single unknown parameter. Two of these techniques are usually referred to in the literature as the Equation Error method and the Output Error method. An example illustrates the application of each of these techniques. Section 5 considers the generalised form of the equations representing a multiparameter system of many degrees-of-freedom. Another class of method that may be used for parameter estimation is the Maximum Likelihood method. It is an advanced method capable of dealing with both linear and nonlinear systems containing measurement noise and is covered in other Items in this series. For systems with process noise@ the Filter Error method is used (see Reference 3). ? In the literature ""parameter"" is a commonly used term for those coefficients in the analysis that are assumed unknown."