392 IEEE SENSORS JOURNAL, VOL. 7, NO. 3, MARCH 2007 Optimal Estimation of the Acceleration of a Car Under Performance Tests Wilmar Hernandez, Member, IEEE Abstract—In this paper, a recursive least-squares lattice (RLSL) adaptive filter was used to carry out the optimal estimation of the relevant signal coming from an accelerometer placed in car under performance tests. Here, the signal of interest is buried in a broad- band noise background where we have little knowledge of the noise characteristics. In addition, due to the fact that the noise and the relevant information sometimes share the same or a very similar frequency spectrum, it is very difficult to cancel the noise that cor- rupts the relevant information without causing that information to deteriorate. The results of the experiment are satisfactory and, in order to compare classical filtering with optimal adaptive fil- tering, the signal coming from the accelerometer was also filtered by using a third-order lowpass digital Butterworth filter. The re- sults of comparing the aforementioned filters show that the optimal adaptive filter is superior to the classical filter. Here, a significant improvement of 22.4 dB in the signal-to-noise ratio (SNR) at the RLSL adaptive filter output was achieved. However, the improve- ment in the SNR at the Butterworth filter output was 6.1 dB, which shows very clear that the optimal adaptive filter performs much better than the classical one. Index Terms—Accelerometer, adaptive noise canceller, recursive least-squares lattice (RLSL) adaptive filter, third-order lowpass digital Butterworth filter. I. INTRODUCTION T ODAY’S automotive industry has a growing interest in ap- plying the most advanced scientific and technological ad- vances in electronic instrumentation, signal processing, and au- tomatic control to improve the performance of the sensors that our cars use. Due to the fact that the automobile is one of our main means of transportation and we make extensive use of it throughout our lives, car manufacturers from all around the world are working on the fabrication of cars able to make intelligent driving deci- sions. What is more, the continuously growing need for better comfort and safety makes it almost impossible to imagine a fu- ture without intelligent systems looking after us. In fact, the last two decades have experienced a continuous positive change from classical techniques of designing sensors to the most advanced ones, which are focused on designing Manuscript received September 8, 2006; revised November 6, 2006; accepted November 20, 2006. This work was supported by the Universidad Politecnica de Madrid, Spain. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Denise Wilson. The author is with the Department of Circuits and Systems, EUIT de Teleco- municacion, Universidad Politecnica de Madrid, Madrid 28031, Spain (e-mail: whernan@ics.upm.es). Digital Object Identifier 10.1109/JSEN.2007.891928 intelligent devices consisting of not only sensors, but also ad- vanced materials and microprocessors that incorporate a certain amount of intelligence into the sensors themselves. Among the first international references on intelligent or smart sensors, [1] and [2] stand out as two of the most important. In [1], both the integration of the sensor and the microcontroller unit on one chip, and the benefits of silicon as a sensor material were discussed. Also, academic and industrial results in the field of smart sensors were presented. In addition, in [2], the continually growing need for building simpler systems by using smart sensors was discussed. Furthermore, in that paper, the importance of improving the performance of sensors and the importance of smart sensors when performing very difficult and/or expensive functions were made clear. Since the publication of the above excellent references, many researchers from all around the world have published their sci- entific results on smart sensors. An excellent reference of this century on understanding smart sensors, what is possible today, and what can be expected in the future can be found in [3]. How- ever, in spite of the fact that a significant step forward is taking place in sensing technology, the application of optimal signal processing algorithms to improve the performance of smart sen- sors should be exploited more significantly. The reality is that sensor manufacturers are working hard to adapt processes used to manufacture advanced semiconductor technologies and are manufacturing sensors that take advantage of the performance enhancements that integrated circuit tech- nology can provide [3]. Nevertheless, most of the algorithms that today’s smart sensors used to carry out the filtering of un- wanted signals are based on classical filtering techniques. For instance, according to Monk et al. [4], the practical accelerom- eter analog interface circuit design of airbags usually has a low- pass filter that is a 2- or 4-pole Bessel function, which is unable to cancel satisfactorily the signal that corrupts the relevant infor- mation coming from the accelerometer. Therefore, in practical accelerometer architectures, in order to avoid that the output be a false representation of the original signal, the signal gain is re- distributed. But this redistribution of gain requires knowledge of the worst-case signals to be applied and an acceptance of noise in the output signal [4]. Optimal signal processing techniques are being gradually in- troduced in smart sensors to carry out the optimal estimation of mechanical variables in today’s cars. In [5], the standard re- cursive least-squares (RLS) adaptive algorithm was used to im- prove the performance of an accelerometer placed in a bus under performance tests. In [6], the response of several accelerometers placed in a car under performance tests was improved by using a Kalman filter. 1530-437X/$25.00 © 2007 IEEE